Notice of Pre-AIA or AIA Status
The present application, filed on or after March 16, 2013, is being examined under the first inventor to file provisions of the AIA .
DETAILED ACTION
Claim Objections
Claim 1 is objected to because of the following informalities:
Claim recites “comprising” is missing colon (:) after comprising. It should be “comprising:”. Appropriate correction is required.
Claim Rejections - 35 USC § 112
The following is a quotation of 35 U.S.C. 112(b):
(b) CONCLUSION.—The specification shall conclude with one or more claims particularly pointing out and distinctly claiming the subject matter which the inventor or a joint inventor regards as the invention.
The following is a quotation of 35 U.S.C. 112 (pre-AIA ), second paragraph:
The specification shall conclude with one or more claims particularly pointing out and distinctly claiming the subject matter which the applicant regards as his invention.
Claims 1-4,6-17 are rejected under 35 U.S.C. 112(b) or 35 U.S.C. 112 (pre-AIA ), second paragraph, as being indefinite for failing to particularly point out and distinctly claim the subject matter which the inventor or a joint inventor (or for applications subject to pre-AIA 35 U.S.C. 112, the applicant), regards as the invention.
Claim 1 recites the limitation "the identified group" in line 9 and 11. There is insufficient antecedent basis for this limitation in the claim.
Claim 4 recites the limitation "the shortest" in line. There is insufficient antecedent basis for this limitation in the claim.
Claim 13 recites the limitation "the selection" in line 2. There is insufficient antecedent basis for this limitation in the claim.
Claims 2-4, 6-17 are rejected based on the rejection of independent claim 1.
Claim Rejections - 35 USC § 103
In the event the determination of the status of the application as subject to AIA 35 U.S.C. 102 and 103 (or as subject to pre-AIA 35 U.S.C. 102 and 103) is incorrect, any correction of the statutory basis (i.e., changing from AIA to pre-AIA ) for the rejection will not be considered a new ground of rejection if the prior art relied upon, and the rationale supporting the rejection, would be the same under either status.
The following is a quotation of 35 U.S.C. 103 which forms the basis for all obviousness rejections set forth in this Office action:
A patent for a claimed invention may not be obtained, notwithstanding that the claimed invention is not identically disclosed as set forth in section 102, if the differences between the claimed invention and the prior art are such that the claimed invention as a whole would have been obvious before the effective filing date of the claimed invention to a person having ordinary skill in the art to which the claimed invention pertains. Patentability shall not be negated by the manner in which the invention was made.
The factual inquiries for establishing a background for determining obviousness under 35 U.S.C. 103 are summarized as follows:
1. Determining the scope and contents of the prior art.
2. Ascertaining the differences between the prior art and the claims at issue.
3. Resolving the level of ordinary skill in the pertinent art.
4. Considering objective evidence present in the application indicating obviousness or nonobviousness.
1. Claims 1-4, 6-13, 16-17 are rejected under 35 U.S.C. 103 as being unpatentable over Storti et al., IDS, U.S Patent Application Publication No.20009/0244065 (“Storti”) in view of Mecca et al. U.S Patent Application Publication No.2021/0044788 (“Mecca”) further in view of Van Lierde et al., U.S Patent Application Publication No.2015/0248538 (“Van Lierde”)
Regarding independent claim 1, Storti teaches a computer implemented method for digitally designing appliance comprising receiving digital 3D data in a digital 3D volumetric space, wherein the digital 3D volumetric space includes a plurality of subgrids and wherein the digital 3D data includes a first surface and a second surface ( see at least abstract “The geometry of an object is inferred from values of the signed distance sampled on a uniform grid to efficiently model objects based on data derived from imaging technology that is now ubiquitous in medical diagnostics. Techniques for automated segmentation convert imaging intensity to a signed distance function (SDF), and a voxel structure imposes a uniform sampling grid. Essential properties of the SDF are used to construct upper and lower bounds on the allowed variation in signed distance in 1, 2, and 3 (or more) dimensions. The bounds are combined to produce interval-valued extensions of the SDF, including a tight global extension and more computationally efficient local bounds that provide useful criteria for root exclusion/isolation, enabling modeling of the objects and other applications”; [0010] Accordingly, an exemplary method is described for creating a model of an object from volumetric scan data produced by using a scanner to scan a region in which at least a portion of the object is disposed. The volumetric scan data is processed with a computing device to create a signed distance grid of points, where each point in the signed distance grid corresponds to a vertex of a volumetric cell in the volumetric scan data and is associated with a signed distance value specifying a distance from the point to a surface of the object. A sign (i.e., "+" or "-") of the signed distance value for each point indicates whether the point is interior or exterior to the object. A unit magnitude gradient is then applied to the signed distance values, to determine an interval signed distance function that models the object. [0011] The method can further include the step of identifying a minimum sample value and a maximum sample value in the signed distance data at vertices of each volumetric cell, to determine local extensions that define local interval bounds for the signed distance function that models the object.”);
computing at least two signed distances for each subgrid of the plurality of subgrids in relation to the received digital 3D data, wherein the at least two signed distances includes a first signed distance and a second signed distance, and the first signed distance is determined between a first point of a subgrid of the identified group of subgrids and the first surface, and the second signed distance is determined between a second point of a subgrid of the identified group of subgrids and the second surface( [0141] Exemplary logical steps 170 illustrated in FIG. 14 can be employed for evaluating signed distance value data for signed distance grid 140 so that a region in which the object of interest is located can be divided into successively smaller cubes using the octree decomposition approach. A step 172 provides for identifying corner vertices of a cube (initially, a large cube that encompasses the region occupied by the object of interest), to produce vertex SDF values 174. Next, a step 176 applies local SDF bounds to the SDF values at the vertices of the cube to determine an interval SDF bound over the cube, D.sub.min.ltoreq.SDF.ltoreq.D.sub.max, as noted in a block 178. A decision step 180 then provides for examining the bounds to determine whether the cube being evaluated is empty of any portion of the object of interest, or may include a portion of the surface of the object, or may be fully occupied by a portion of the object. If the examination of the cube determines that D.sub.min>0, the result indicated in a block 182 is that the cube is empty, and the resulting data are stored in block 184. If the value of D.sub.max<0, then the result indicated in a block 194 is that the cube is fully occupied, and that result is stored as data in block 184. Finally, if D.sub.min.ltoreq.0.ltoreq.D.sub.max, the cube may contain part of the surface of the cube (and be partially occupied), as indicated in a block 186. A decision step then determines if the length of the edge of the cube is greater than the spacing between points for the signed distance grid. If so, a step 190 subdivides the cube in eight smaller cubes to refine the classification of the cubes as noted above. The logic then loops back to step 172, to identify the vertices of the corners for the next cube being evaluated. If the result of decision step 188 is negative, the current cube being examined is classified as an ON cube in a step 192--i.e., to provide an indication that part of the surface may be included in the cube. That result is also stored in data, in block 184. After storing a result in the data, while not shown, it will be understood that the process reiteratively continues with the next cube to be examined until all cubes that can be further subdivided have (in step 190), and all of the cubes that have been produced by subdividing larger cubes and are neither empty nor full have been examined.”);
identifying, based on the at least two computed signed distances, a group of subgrids from the plurality of subgrids such that the identified group of subgrids collectively correspond to the received digital 3D data (see at least [0135] -[0141] A flowchart 130 shown in FIG. 13 illustrates exemplary steps for implementing different aspects of the novel approach discussed above. This approach is implemented using volumetric scan data that have been collected for an N-dimensional object, as indicated in a block 132. In some of the examples that are discussed herein, a 3-D object such as part of a patient's body is the object; however, it should be understood that the object is not limited to part of a body, but can be almost any type of object. Furthermore, the object can have more or fewer than three dimensions. A step 134 provides for carrying out an N-dimensional scan of the object, for example, using a CT, MR, PET, or other type of volumetric scanner. The result of this scan is an image stack 136, in which the object is delineated from surrounding material based on a characteristic, such as intensity. While the term "object" is used in the singular form, it will be understood that a plurality of objects of interest may be scanned so that a model can be produced for each object or group of objects using the present novel approach. For example, if an CT scanner is employed, the image stack may represent generally parallel contiguous "slices" through one or more objects (such as one or more bones) and any surrounding material (such as tissue), wherein the object is visually apparent in the images because it has a substantially different intensity or gray-scale value than the surrounding material. However, it must be stressed that segmentation of the raw image data, which is carried out in the following step, is not simply a matter of applying a threshold test. Indeed, a step 138 provides for converting the intensities (or other characteristic, such as color) of the voxels comprising the image stack data using segmentation (which may optionally use a level sets algorithm, such as the exemplary approach discussed above) to produce signed distance values on a signed distance grid 140. Based on the characteristic of the image stack data, this step determines the distance from the center of the voxels comprising the image stack data to the nearest point on the surface of the object. Voxels that have a positive signed distance value are thus outside the object, while those with a negative value are inside the object…[0141] Exemplary logical steps 170 illustrated in FIG. 14 can be employed for evaluating signed distance value data for signed distance grid 140 so that a region in which the object of interest is located can be divided into successively smaller cubes using the octree decomposition approach. A step 172 provides for identifying corner vertices of a cube (initially, a large cube that encompasses the region occupied by the object of interest), to produce vertex SDF values 174. Next, a step 176 applies local SDF bounds to the SDF values at the vertices of the cube to determine an interval SDF bound over the cube, D.sub.min.ltoreq.SDF.ltoreq.D.sub.max, as noted in a block 178. A decision step 180 then provides for examining the bounds to determine whether the cube being evaluated is empty of any portion of the object of interest, or may include a portion of the surface of the object, or may be fully occupied by a portion of the object. If the examination of the cube determines that D.sub.min>0, the result indicated in a block 182 is that the cube is empty, and the resulting data are stored in block 184. If the value of D.sub.max<0, then the result indicated in a block 194 is that the cube is fully occupied, and that result is stored as data in block 184. Finally, if D.sub.min.ltoreq.0.ltoreq.D.sub.max, the cube may contain part of the surface of the cube (and be partially occupied), as indicated in a block 186. A decision step then determines if the length of the edge of the cube is greater than the spacing between points for the signed distance grid. If so, a step 190 subdivides the cube in eight smaller cubes to refine the classification of the cubes as noted above. The logic then loops back to step 172, to identify the vertices of the corners for the next cube being evaluated. If the result of decision step 188 is negative, the current cube being examined is classified as an ON cube in a step 192--i.e., to provide an indication that part of the surface may be included in the cube. That result is also stored in data, in block 184. After storing a result in the data, while not shown, it will be understood that the process reiteratively continues with the next cube to be examined until all cubes that can be further subdivided have (in step 190), and all of the cubes that have been produced by subdividing larger cubes and are neither empty nor full have been examined.”) and digitally designing the appliance based on the identified group of subgrids (see at least [0014] The step of processing the volumetric scan data with a computing device can include the step of segmenting the volumetric scan data to produce the signed distance grid of points and to determine the signed distance values specifying the distances from the points to the surface of the object.” Fig. 9, 10A-10D) Storti is understood to be silent on the remaining limitations of claim 1.
In the same field of endeavor, Mecca teaches wherein the first signed distance is a minimum distance between the first point and the digital 3D data, and where the second signed distance is a minimum distance between the second point and the digital 3D data (see at least [0035] As mentioned above, in an embodiment, the photometric stereo approach determines the position of the surface of the object by using a signed distance function where the signed distance function determines the distance from a point to a surface, wherein the signed distance function is related to the surface normal: n(x)=∇d(x). (1) [0036] where n(x) is the surface normal at 3D point x, d(x) is the signed distance function at 3D point x and ∇ is the gradient operator, the signed distance function being substituted for the surface normal when modelling irradiance. [0037] By using the above, the surface is indicated when the signed distance function is at a minimum.”; [0094] In an embodiment, to provide suitable mathematical characterisation of a collection of solid objects, the implicit surface parameterisation is considered in terms of the signed distance function SDF …[0095] A signed distance function, when given the coordinates of a point x return the shortest distance between x and a defined surface. This parameterisation is suitable for this embodiment due to its practical way of describing the outgoing normal vector to a surface.”)
Therefore, it would have been obvious to one of ordinary skill in the art before the effective filling date of claimed invention to modify the method of creating a model of an objection based on volumetric scan data including a signed distance grid of point to a surface of the object of Storti with using a shortest distance between a point in space and a surface as signed distance as seen in Mecca because this modification would achieve the expected benefits of providing not only how far a point is from a surface, but also which side of the surface the point is on. Both Storti and Mecca are understood to be silent on the remaining limitations of claim 1.
In the same field of endeavor, Van Lierde teaches receiving digital 3D dental data in a digital 3D volumetric space, wherein the digital 3D volumetric space includes a plurality of subgrids and wherein the digital 3D dental data includes a first surface and a second surface ([0033] In a particular a method 100 of carrying out the first aspect of the invention is described with reference to FIG. 6 whereby a scanning of the body provides different scanned points (4). All scanned data is loaded into a computer in step 101--such as computer 54 of FIG. 5. Computer 54 is adapted to carry out any of the methods of the present invention. A determined space (2) is divided into elementary spaces (3) in step 102 as illustrated in FIGS. 1-a, 1-b and 1-c. As the model of the body (1) that will be obtained by the method is using these elementary spaces (3), only the part of the body within this determined space will be modelled. For clarity, the FIGS. 1-a, 1-b and 1-c use a two dimensional representation, but the invention is not limited thereto. Each of these elementary spaces (3) has a signed distance parameter and a weight parameter assigned to it in step 103. The signed distance parameter is indicative of the distance between the elementary space (3) it is assigned to and the body (1) that is to be modelled from the scanning of the body. The weight parameter is indicative of the importance of this distance parameter. For example, when the model would be used later on to create a digital surface representation of the body, such as a triangle mesh, the weight value indicates how much importance can be given to its accompanying signed distance value. From the scanning of the body different scanned points (4) are obtained. Said scanned point uniquely defines a point within the determined space, for example by being given the coordinates within a global reference system. The assignment of variables to a scanned point can also comprise implicitly or explicitly information to determine whether the point is inside, outside or on the surface of the body. This type of information is typically provided by the scanning device. The ways in which these scanned points are acquired by the scanning are not limiting on the present invention. In step 104, for each scanned point that is then obtained by the scanning of the body, the signed distance and weight parameter of each elementary space is optionally modified taking into account the newly scanned point as this point comprises information on the distance from the elementary spaces to the body. In order to increase the detail of the model of the body in step 105, selected elementary spaces (5) are modified by subdividing these selected elementary spaces into smaller elementary spaces (6) that have also a signed distance and weight parameter assigned. The selected elementary spaces (5) are considered to be lower level elementary spaces relative to the smaller elementary spaces (6) that are considered higher level elementary spaces. The detail of the model is hence improved in the location where the elementary spaces (5) are divided into smaller elementary spaces (6) resulting in a locally improved detail of the model. This process of increasing the detail of the model can be performed at any time during the modelling of the body. The smaller elementary spaces are then also elementary spaces that can possibly be modified when new points are provided by scanning. The dividing of an elementary space (5) does not mean that this elementary space ceases to exist. In this case, the smaller elementary spaces (6) can thus be seen as higher level elementary spaces relative to the elementary space (5) they originated from, the lower level elementary space. Again, when a new point is added to the model, the signed distance and weight parameter of both this original elementary space and smaller elementary spaces can possibly be modified. As with the increasing of the details of the model, one can also decrease the details of the model of the body in step 106 by replacing selected elementary spaces (6) with less elementary spaces (5) defined based on the signed distance and weight parameters of the selected elementary spaces (6). Again, the replacing does not imply that the original elementary spaces cease to exist, but that a hierarchically lower level elementary space was introduced in the model. [0057] In a preferred embodiment of the second aspect of the present invention the method from the first aspect of the present invention is used in a method 300 for obtaining a 3D digital surface representation of a dental arch. Initial measurement data and thus scanned points are then acquired via an intra-oral scanner. All scanned data is loaded into a computer in step 302--such as computer 54 of FIG. 5. An initial surface representation is constructed with a predefined resolution in step 302 of FIG. 8. The predefined resolution is specified by the subdivision criterion in the disclosed method. These initial scanned points are then converted into an initial model of the dental arch by applying the method of the first aspect of the invention in step 303. The initial model is then converted on its turn into a surface representation in step 304. The surface is converted into an image and displayed to the user, i.e. the dentist. The user then indicates on this display where more detail is required in step 305. This user input is then translated into a starting point for the scanner for the acquisition of a new set of data and the pre-set criterion in this location of the model is updated to a higher resolution in step 306. The pre-set criterion could also stay unchanged, if it is for example specified so that the detail is increased based on the number of scanned points in this location. The new scanned points are then added to the model and the model is converted into an updated surface representation comprising enhanced details in the selected areas in step 307.”);
computing at least two signed distances for each subgrid of the plurality of subgrids in relation to the received digital 3D dental data, wherein the at least two signed distances includes a first signed distance and a second signed distance, and the first signed distance is determined between a first point of a subgrid of the identified group of subgrids and the first surface, and the second signed distance is determined between a second point of a subgrid of the identified group of subgrids and the second surface ([0036] A preferred way of calculating the new signed distance values is based on the scanned point and its normal (i.e. the direction perpendicular to the surface of the body in said point, which is typically estimated). First, a plane is fitted through the scanned point and perpendicular to the normal of that point. For each corner point, the distance is then measured between the corner point and this normal plane as illustrated in FIG. 3. The sign of the distance value is determined by whether the scanned point is inside (a minus sign) or outside (a plus sign) of the body. The information on the location inside or outside the body can be derived from the scanned points, but can also be specified by the scanner device as extra information within the scanned point. [0037] A preferred way of calculating the new weight value of a corner point is assigning it a `1` when the scanned point will result in a modification of the signed distance value for this corner point and assigning it a `0` otherwise. In other words, the weight value of a corner point represents the number of scanned points that resulted in a signed distance value for this corner point.”)
Therefore, it would have been obvious to one of ordinary skill in the art before the effective filling date of claimed invention to modify the method of creating a model of an objection based on volumetric scan data including a signed distance grid of point to a surface of the object of Storti and Mecca with apply signed distances and grid structure to model 3D volumetric dental data as seen in Van Lierde because this modification would achieve expected benefits of 3D body modelling, especially for use in dentistry ([0001] of Van Lierde)
Thus the combination of Storti, Mecca and Van Lierde teaches a computer implemented method for digitally designing a dental appliance comprising receiving digital 3D dental data in a digital 3D volumetric space, wherein the digital 3D volumetric space includes a plurality of subgrids and wherein the digital 3D dental data includes a first surface and a second surface; computing at least two signed distances for each subgrid of the plurality of subgrids in relation to the received digital 3D dental data, wherein the at least two signed distances includes a first signed distance and a second signed distance, and the first signed distance is determined between a first point of a subgrid of the identified group of subgrids and the first surface, and the second signed distance is determined between a second point of a subgrid of the identified group of subgrids and the second surface wherein the first signed distance is a minimum distance between the first point and the digital 3D dental data, and where the second signed distance is a minimum distance between the second point and the digital 3D dental data; identifying, based on the at least two computed signed distances, a group of subgrids from the plurality of subgrids such that the identified group of subgrids collectively correspond to the received digital 3D dental data; and digitally designing the dental appliance based on the identified group of subgrids.
Regarding claim 2, Storti, Mecca and Van Lierde teach the computer implemented method according to claim 1, further comprising defining the plurality of subgrids in the digital 3D volumetric space, wherein the plurality of subgrids is dimensioned equally (see at least [0130]; [0141] of Storti “ A second important approach to gain significant efficiency is based on local bounds. The efficiency gain occurs in two ways: (1) an interval bound applies over an input interval that spans a gap between sample points (rather than at just a single point); and, (2) the local bound depends only on a subset of the sample values within the cube, e.g., the sample values at the vertices of the input interval. Again using a uniformly sampled 3-D grid for discussion, consider a cube whose eight vertices are sample points at which the SDF value is known. This approach employs bounds that are valid across the entire cube, but depend only on the vertex values of the cube. (It will be apparent that the dimensions or sides of this cube need not correspond to the sample spacing intervals. When applied to larger cubes, local bounds support multi-resolution classification.) If the cube edge length is .delta., then the cube's long diagonal has a length equal to .delta. {square root over (3)}. Since the signed distance value between two points cannot differ by more than the distance between the points (and the distance between any two points within the cube cannot exceed the long diagonal extending between vertices of the cube), the SDF at any two points in the cube cannot differ by more than .delta. {square root over (3)}. If the eight SDF values at the vertices are designated as: f={f.sub.1, . . . , f.sub.8}, let f.sub.min=Min[ f] and f.sub.max=Max[ f], then a valid bounding interval across the cube is: f({right arrow over (r)}).di-elect cons.F.sub.1=[f.sub.max-.delta. {square root over (3)}, f.sub.min+.delta. {square root over (3)}]. In other words, the SDF value at any point in the cube must not be less than the maximum vertex value minus the long diagonal, or greater than the minimum vertex value plus the long diagonal. [0034] of Van Lierde “In a further particular way 200 of carrying out the method of the first aspect of the present invention is shown in FIG. 7, all scanned data having been loaded into a computer in step 201--such as computer 54 of FIG. 5. The determined space is subdivided by a grid (7) in step 202, as illustrated in FIGS. 1-a and d and 1-c and f for a two-dimensional case. The grid (7) divides the determined space in sampling units, e.g. regular sampling units, which define the elementary spaces. Preferably the grid coincides with the elementary spaces. Regular sampling units are equally sized sampling units. These equally sized sampling units are not necessarily cube shaped for example, because they could also be rectangular.”; 0041] In order to increase the level of detail of the model, a selection of elementary spaces (e.g. sampling units such as regular sampling units) with a related selection of corner points is subdivided into new and smaller elementary spaces (sampling units) in step 205. Regular sampling units are equally sized sampling units. These equally sized sampling units are not necessarily cube shaped for example, because they could also be rectangular. When subdividing an existing elementary space or lower-level elementary space into new elementary spaces or higher-level elementary spaces, corner points are generated at all the corners of the sampling unit itself and within that sampling unit. As these higher-level corner points are also corner points, they also need a signed distance and weight parameter to be assigned to. After creation of the higher-level corner point, its signed distance and weight parameters need to be initialized by assigning them an initial value. One preferred way to calculate the initial values is by giving them a default value, for example zero.”; [0128] of Mecca “ In FIG. 8, a node simply contains the information of a 3D cube (position, size), a SDF value (coded with the grayscale here; light grey is positive, dark grey is negative) as well as pointers to next level nodes corresponding to subdividing the box in all 3 dimensions (this 2D figure only shows 4 children nodes but in reality they are 8). [0129] The initial voxel size is set in S401. In 403, the SDF is estimated. For the first time the algorithm is run, the SDF is estimated from the initial surface estimate from the MVS data. The process of estimating an SDF for a voxel is an iterative process. Using this SDF estimate, ray tracing is performed in step S405. [0140] FIGS. 10(a) and 10(b) are an illustration of increase of surface quality after each voxel subdivision step. The figure shows the different level of details that are encoded at each tree level. For this example, the octree was initialised with depth 7 and after 3 subdivision steps reached depth 10, reducing the voxel size by a factor of 8 and increasing the voxel count from around 96K to around 4.2M. The resulting final surface consists of 1.1M vertices and 2.2M triangles.”) In addition, the same motivation is used as the rejection for claim 1.
Regarding claim 3, Storti, Mecca and Van Lierde teach the computer implemented method according to claim 2, wherein the equally dimensioned plurality of subgrids includes same shape and same size (see at least [0013] of Storti “Another step of the method can provide for creating an interval octree representation by initially employing a coarse octree cube level of resolution for the region, and then successively subdividing coarser octree cubes into finer resolution octree cubes. The step of employing the coarse octree cube can include the step of employing an initial octree cube sized to encompass an entire region that was scanned to produce the volumetric scan data. Further, each octree cube can be classified, and a complete categorization of the octree cubes defines the octree cubes as full (inside the object), empty (outside the object), as well as octree cubes whose vertex values include opposite signs so the surface of the object definitely passes through the octree cube so that the octree cube is partially occupied (on), octree cubes with all positive vertex values but which may still include some portion of the solid, and octree cubes with all negative vertex values but which may still include a portion of the exterior volume that is outside the object. Subdivision to full resolution may not eradicate these last two categories. The interval signed distance function can be employed to determine bounds for each octree cube, to determine if more detail for the surface of the object can be determined by further subdividing the octree cube. Any octree cube not yet classified as full or empty and having an edge length that is equal to the sample spacing between points on the signed distance grid can be treated as possibly containing one or more portions of the surface of the object, and as being not sub-dividable into higher resolution octree cubes, since classification of the resulting smaller octree cubes based solely on the volumetric scanner data would produce unreliable results.”; [0041] of Van Lierde “In order to increase the level of detail of the model, a selection of elementary spaces (e.g. sampling units such as regular sampling units) with a related selection of corner points is subdivided into new and smaller elementary spaces (sampling units) in step 205. Regular sampling units are equally sized sampling units. These equally sized sampling units are not necessarily cube shaped for example, because they could also be rectangular. When subdividing an existing elementary space or lower-level elementary space into new elementary spaces or higher-level elementary spaces, corner points are generated at all the corners of the sampling unit itself and within that sampling unit. As these higher-level corner points are also corner points, they also need a signed distance and weight parameter to be assigned to. After creation of the higher-level corner point, its signed distance and weight parameters need to be initialized by assigning them an initial value. One preferred way to calculate the initial values is by giving them a default value, for example zero.”; [0140] of Mecca “FIGS. 10(a) and 10(b) are an illustration of increase of surface quality after each voxel subdivision step. The figure shows the different level of details that are encoded at each tree level. For this example, the octree was initialised with depth 7 and after 3 subdivision steps reached depth 10, reducing the voxel size by a factor of 8 and increasing the voxel count from around 96K to around 4.2M. The resulting final surface consists of 1.1M vertices and 2.2M triangles. [0141] In practice, for the examples of FIG. 10(a) the tree reached level 10 hence N=210=1024 thus the speedup compared to the other parameterisations is around×100 and ×10.sup.5 respectively. In practice, raytracing visibilities as well as cast shadows to all the views took only a few minutes on these datasets.”) In addition, the same motivation is used as the rejection for claim 1.
Regarding claim 4, Storti, Mecca and Van Lierde teach the computing implemented method according to claim 1, wherein the shortest signed distance of the first signed distance and the second signed distance determines whether the identified subgrid is assigned to the first surface or the second surface of the digital 3D digital dental data (see at least [0141] of Storti “Exemplary logical steps 170 illustrated in FIG. 14 can be employed for evaluating signed distance value data for signed distance grid 140 so that a region in which the object of interest is located can be divided into successively smaller cubes using the octree decomposition approach. A step 172 provides for identifying corner vertices of a cube (initially, a large cube that encompasses the region occupied by the object of interest), to produce vertex SDF values 174. Next, a step 176 applies local SDF bounds to the SDF values at the vertices of the cube to determine an interval SDF bound over the cube, D.sub.min.ltoreq.SDF.ltoreq.D.sub.max, as noted in a block 178. A decision step 180 then provides for examining the bounds to determine whether the cube being evaluated is empty of any portion of the object of interest, or may include a portion of the surface of the object, or may be fully occupied by a portion of the object. If the examination of the cube determines that D.sub.min>0, the result indicated in a block 182 is that the cube is empty, and the resulting data are stored in block 184. If the value of D.sub.max<0, then the result indicated in a block 194 is that the cube is fully occupied, and that result is stored as data in block 184. Finally, if D.sub.min.ltoreq.0.ltoreq.D.sub.max, the cube may contain part of the surface of the cube (and be partially occupied), as indicated in a block 186. A decision step then determines if the length of the edge of the cube is greater than the spacing between points for the signed distance grid. If so, a step 190 subdivides the cube in eight smaller cubes to refine the classification of the cubes as noted above. The logic then loops back to step 172, to identify the vertices of the corners for the next cube being evaluated. If the result of decision step 188 is negative, the current cube being examined is classified as an ON cube in a step 192--i.e., to provide an indication that part of the surface may be included in the cube. That result is also stored in data, in block 184. After storing a result in the data, while not shown, it will be understood that the process reiteratively continues with the next cube to be examined until all cubes that can be further subdivided have (in step 190), and all of the cubes that have been produced by subdividing larger cubes and are neither empty nor full have been examined.”; [0036] of Van Lierde “A preferred way of calculating the new signed distance values is based on the scanned point and its normal (i.e. the direction perpendicular to the surface of the body in said point, which is typically estimated). First, a plane is fitted through the scanned point and perpendicular to the normal of that point. For each corner point, the distance is then measured between the corner point and this normal plane as illustrated in FIG. 3. The sign of the distance value is determined by whether the scanned point is inside (a minus sign) or outside (a plus sign) of the body. The information on the location inside or outside the body can be derived from the scanned points, but can also be specified by the scanner device as extra information within the scanned point. [0037] A preferred way of calculating the new weight value of a corner point is assigning it a `1` when the scanned point will result in a modification of the signed distance value for this corner point and assigning it a `0` otherwise. In other words, the weight value of a corner point represents the number of scanned points that resulted in a signed distance value for this corner point.”; [0035] of Mecca “As mentioned above, in an embodiment, the photometric stereo approach determines the position of the surface of the object by using a signed distance function where the signed distance function determines the distance from a point to a surface, wherein the signed distance function is related to the surface normal: n(x)=∇d(x).(1) [0036] where n(x) is the surface normal at 3D point x, d(x) is the signed distance function at 3D point x and ∇ is the gradient operator, the signed distance function being substituted for the surface normal when modelling irradiance. [0037] By using the above, the surface is indicated when the signed distance function is at a minimum.”; [0094] In an embodiment, to provide suitable mathematical characterisation of a collection of solid objects, the implicit surface parameterisation is considered in terms of the signed distance function SDF …[0095] A signed distance function, when given the coordinates of a point x return the shortest distance between x and a defined surface. This parameterisation is suitable for this embodiment due to its practical way of describing the outgoing normal vector to a surface.”) In addition, the same motivation is used as the rejection for claim 1.
Regarding claim 6, Storti, Mecca and Van Lierde teach the computer implemented method according to claim 1, wherein each subgrid of the plurality of subgrids comprises a shape that includes a plurality of corner points, and wherein each subgrid of the plurality of subgrids comprises a plurality of edge points along one or more edges connecting a pair of corner points of the plurality of corner points, and wherein the plurality of corner points and/or the plurality of edge points includes the first point and the at least second point ([0141] Exemplary logical steps 170 illustrated in FIG. 14 can be employed for evaluating signed distance value data for signed distance grid 140 so that a region in which the object of interest is located can be divided into successively smaller cubes using the octree decomposition approach. A step 172 provides for identifying corner vertices of a cube (initially, a large cube that encompasses the region occupied by the object of interest), to produce vertex SDF values 174. Next, a step 176 applies local SDF bounds to the SDF values at the vertices of the cube to determine an interval SDF bound over the cube, D.sub.min.ltoreq.SDF.ltoreq.D.sub.max, as noted in a block 178. A decision step 180 then provides for examining the bounds to determine whether the cube being evaluated is empty of any portion of the object of interest, or may include a portion of the surface of the object, or may be fully occupied by a portion of the object. If the examination of the cube determines that D.sub.min>0, the result indicated in a block 182 is that the cube is empty, and the resulting data are stored in block 184. If the value of D.sub.max<0, then the result indicated in a block 194 is that the cube is fully occupied, and that result is stored as data in block 184. Finally, if D.sub.min.ltoreq.0.ltoreq.D.sub.max, the cube may contain part of the surface of the cube (and be partially occupied), as indicated in a block 186. A decision step then determines if the length of the edge of the cube is greater than the spacing between points for the signed distance grid. If so, a step 190 subdivides the cube in eight smaller cubes to refine the classification of the cubes as noted above. The logic then loops back to step 172, to identify the vertices of the corners for the next cube being evaluated. If the result of decision step 188 is negative, the current cube being examined is classified as an ON cube in a step 192--i.e., to provide an indication that part of the surface may be included in the cube. That result is also stored in data, in block 184. After storing a result in the data, while not shown, it will be understood that the process reiteratively continues with the next cube to be examined until all cubes that can be further subdivided have (in step 190), and all of the cubes that have been produced by subdividing larger cubes and are neither empty nor full have been examined.”; [0035] of Van Lierde “Signed distance and weight values are then related to the elementary spaces, for example by assigning values to the corner points (8) of these elementary spaces in step 203. Other specific points of said elementary spaces (e.g. midpoints of edges or faces, centre point of elementary space . . . ) can also be used for assigning distance and weight values, but are also referred to as corner points in the remainder of the text. When a new point is available from a scanning of the body, a new signed distance and weight value is calculated for every corner point in step 204. The current signed distance value of every corner point is then modified by replacing it with the weighted average of the new signed distance value and the current signed distance value, using the weight values as the weights for the average. The current weight value is then modified by replacing it with the sum of the current and new weight value. This means that when the calculated weight value is zero for a corner point, the new signed distance value will not be taken into account; hence there is no need to calculate a new signed distance value for this corner point. [0036] A preferred way of calculating the new signed distance values is based on the scanned point and its normal (i.e. the direction perpendicular to the surface of the body in said point, which is typically estimated). First, a plane is fitted through the scanned point and perpendicular to the normal of that point. For each corner point, the distance is then measured between the corner point and this normal plane as illustrated in FIG. 3. The sign of the distance value is determined by whether the scanned point is inside (a minus sign) or outside (a plus sign) of the body. The information on the location inside or outside the body can be derived from the scanned points, but can also be specified by the scanner device as extra information within the scanned point. [0037] A preferred way of calculating the new weight value of a corner point is assigning it a `1` when the scanned point will result in a modification of the signed distance value for this corner point and assigning it a `0` otherwise. In other words, the weight value of a corner point represents the number of scanned points that resulted in a signed distance value for this corner point.”; [0035] of Mecca “As mentioned above, in an embodiment, the photometric stereo approach determines the position of the surface of the object by using a signed distance function where the signed distance function determines the distance from a point to a surface, wherein the signed distance function is related to the surface normal: [0036] where n(x) is the surface normal at 3D point x, d(x) is the signed distance function at 3D point x and ∇ is the gradient operator, the signed distance function being substituted for the surface normal when modelling irradiance. [0037] By using the above, the surface is indicated when the signed distance function is at a minimum. [0038] In an embodiment, the processor processes the photometric stereo data using a volumetric approach, wherein the volume containing the object is subdivided into voxels and the signed distance function is calculated per voxel.) In addition, the same motivation is used as the rejection for claim 1.
Regarding claim 7, Storti, Mecca and Van Lierde teach the computer implemented method according to claim 6, wherein the plurality of edge points is uniformly distributed along an edge of at least a subgrid of the plurality of subgrids (see at least [0132]; [0141] of Storti “Recall the statement above that the local bounds can be applied to a grid at any scale. For example, consider a torus as a sample part or solid object. (A torus is selected for this example, because its exact SDF is available for comparison and verification.) When the torus SDF is sampled uniformly on a 129.times.129.times.129 grid, there are 1283 (somewhat more than 2.times.10.sup.6) cubes, each having an edge with a length l. A traditional approach to handling regularly sampled data in 3-D involves octrees, which are a multi-resolution spatial occupancy description that attempts to classify cubes as full, empty, or partially occupied (and which is appropriate for subdivision and inspection at finer resolution), based on detecting sign difference at cube vertices. With typical sample data, however, there is no guarantee that examining the grid at coarse resolution will not miss finer details that are hidden inside a large cube (e.g., all the vertex values may be positive, but there may be a region of negative values in the interior of the cube). The result is that a careful classification normally involves the expensive computation of inspecting all cubes at the smallest scale and then consolidating similar classifications where possible to obtain a condensed representation. Clearly, this complete evaluation would not provide any computational benefit.”; [0045] of Van Lierde “A preferred way of subdividing the sampling units is by using an octree, where each sampling unit is subdivided in eight equally-sized units. The new corner points are then generated on all the corners of the sampling unit itself and on the centre of the sampling unit itself, its edges and its faces (FIG. 4). The calculation of the initial signed distance and weight values can then be done as described in the embodiment above. When doing the calculation based on a predefined neighbourhood the calculation is preferably done in the following way. For a new corner point that is in the same place as the lower-level corner point, the initial values are those of the existing corner point. For a new corner point in the middle of an edge, the initial values are the average of the values of the 2 lower level corner points at the end of the edge. For a new corner point added in the middle of a face the initial values are the average of the values of the 4 lower level corner points of the face, and for a new corner point added in the middle of the sampling unit the initial values are the average of the values of the 8 lower-level corner points of the lower-level sampling unit. This means that for the calculation of the weight and signed distance values to be assigned to the new higher-level corner points, trilinear interpolation of the 8 lower-level corner points is used.”) In addition, the same motivation is used as the rejection for claim 1.
Regarding claim 8, Storti, Mecca and Van Lierde teach the computer implemented method according to claim 6, wherein the at least two computed signed distances for each of the plurality of subgrids are determined between a first corner point of the plurality of corner points and the digital 3D dental data and between a second corner point of the plurality of corner points and the digital 3D dental data ([0133] [0141] of Storti “However, the local bounds described above change the situation completely and provide a method for reliably creating octrees, starting at the coarsest level. Beginning with a cube containing the entire sample grid, it is only necessary to consider the extreme corner values (i.e., the vertices) and the edge length of 128. Since one of the corner values has magnitude less than 128 {square root over (3)}, the interval bound contains 0. Thus, the cube can next be divided into eight equal smaller cubes, each with an edge length equal to 64. The SDF values at the vertices of these smaller cubes are considered, interval bounds are computed for each, and the process continues until the smallest cubes are classified, or further subdivision is not possible with the given data.”; [0035] of Mecca “As mentioned above, in an embodiment, the photometric stereo approach determines the position of the surface of the object by using a signed distance function where the signed distance function determines the distance from a point to a surface, wherein the signed distance function is related to the surface normal: n(x)=∇d(x). (1) [0036] where n(x) is the surface normal at 3D point x, d(x) is the signed distance function at 3D point x and ∇ is the gradient operator, the signed distance function being substituted for the surface normal when modelling irradiance. [0037] By using the above, the surface is indicated when the signed distance function is at a minimum.”; [0094] In an embodiment, to provide suitable mathematical characterisation of a collection of solid objects, the implicit surface parameterisation is considered in terms of the signed distance function SDF …[0095] A signed distance function, when given the coordinates of a point x return the shortest distance between x and a defined surface. This parameterisation is suitable for this embodiment due to its practical way of describing the outgoing normal vector to a surface.” “;[0035] of Van Lierde “Signed distance and weight values are then related to the elementary spaces, for example by assigning values to the corner points (8) of these elementary spaces in step 203. Other specific points of said elementary spaces (e.g. midpoints of edges or faces, centre point of elementary space . . . ) can also be used for assigning distance and weight values, but are also referred to as corner points in the remainder of the text. When a new point is available from a scanning of the body, a new signed distance and weight value is calculated for every corner point in step 204. The current signed distance value of every corner point is then modified by replacing it with the weighted average of the new signed distance value and the current signed distance value, using the weight values as the weights for the average. The current weight value is then modified by replacing it with the sum of the current and new weight value. This means that when the calculated weight value is zero for a corner point, the new signed distance value will not be taken into account; hence there is no need to calculate a new signed distance value for this corner point.” [0041] In order to increase the level of detail of the model, a selection of elementary spaces (e.g. sampling units such as regular sampling units) with a related selection of corner points is subdivided into new and smaller elementary spaces (sampling units) in step 205. Regular sampling units are equally sized sampling units. These equally sized sampling units are not necessarily cube shaped for example, because they could also be rectangular. When subdividing an existing elementary space or lower-level elementary space into new elementary spaces or higher-level elementary spaces, corner points are generated at all the corners of the sampling unit itself and within that sampling unit. As these higher-level corner points are also corner points, they also need a signed distance and weight parameter to be assigned to. After creation of the higher-level corner point, its signed distance and weight parameters need to be initialized by assigning them an initial value. One preferred way to calculate the initial values is by giving them a default value, for example zero. [0042] Another preferred way to calculate the initial value for the signed distance and weight parameters is by calculating the average of the neighbouring corner points that already existed before the subdivision, referred to as the neighbouring lower-level corner points. [0043] Another preferred way to calculate the initial value for the signed distance and weight parameters is by using not only the values of the corner points of the sampling unit that is subdivided but also the values of the corner points of neighbouring sampling units (i.e. the same or higher or lower level corner points).”) In addition, the same motivation is used as the rejection for claim 1.
Regarding claim 9, Storti, Mecca and Van Lierde teach the computer implemented method according to claim 6, wherein the computed signed distance for each of the plurality of subgrids is determined between a first edge point of the plurality of edge points or a first corner point of the plurality of corner points and the digital 3D dental data, and between a second edge point of the plurality of edge points or a second corner point of the plurality of corner points and the digital 3D dental data (see at least [0141] of Storti “Exemplary logical steps 170 illustrated in FIG. 14 can be employed for evaluating signed distance value data for signed distance grid 140 so that a region in which the object of interest is located can be divided into successively smaller cubes using the octree decomposition approach. A step 172 provides for identifying corner vertices of a cube (initially, a large cube that encompasses the region occupied by the object of interest), to produce vertex SDF values 174. Next, a step 176 applies local SDF bounds to the SDF values at the vertices of the cube to determine an interval SDF bound over the cube, D.sub.min.ltoreq.SDF.ltoreq.D.sub.max, as noted in a block 178. A decision step 180 then provides for examining the bounds to determine whether the cube being evaluated is empty of any portion of the object of interest, or may include a portion of the surface of the object, or may be fully occupied by a portion of the object. If the examination of the cube determines that D.sub.min>0, the result indicated in a block 182 is that the cube is empty, and the resulting data are stored in block 184. If the value of D.sub.max<0, then the result indicated in a block 194 is that the cube is fully occupied, and that result is stored as data in block 184. Finally, if D.sub.min.ltoreq.0.ltoreq.D.sub.max, the cube may contain part of the surface of the cube (and be partially occupied), as indicated in a block 186. A decision step then determines if the length of the edge of the cube is greater than the spacing between points for the signed distance grid. If so, a step 190 subdivides the cube in eight smaller cubes to refine the classification of the cubes as noted above. The logic then loops back to step 172, to identify the vertices of the corners for the next cube being evaluated. If the result of decision step 188 is negative, the current cube being examined is classified as an ON cube in a step 192--i.e., to provide an indication that part of the surface may be included in the cube. That result is also stored in data, in block 184. After storing a result in the data, while not shown, it will be understood that the process reiteratively continues with the next cube to be examined until all cubes that can be further subdivided have (in step 190), and all of the cubes that have been produced by subdividing larger cubes and are neither empty nor full have been examined.”; [0035] of Mecca “As mentioned above, in an embodiment, the photometric stereo approach determines the position of the surface of the object by using a signed distance function where the signed distance function determines the distance from a point to a surface, wherein the signed distance function is related to the surface normal: n(x)=∇d(x). (1) [0036] where n(x) is the surface normal at 3D point x, d(x) is the signed distance function at 3D point x and ∇ is the gradient operator, the signed distance function being substituted for the surface normal when modelling irradiance. [0037] By using the above, the surface is indicated when the signed distance function is at a minimum.”; [0094] In an embodiment, to provide suitable mathematical characterisation of a collection of solid objects, the implicit surface parameterisation is considered in terms of the signed distance function SDF …[0095] A signed distance function, when given the coordinates of a point x return the shortest distance between x and a defined surface. This parameterisation is suitable for this embodiment due to its practical way of describing the outgoing normal vector to a surface.” [0045] of Van Lierde “ A preferred way of subdividing the sampling units is by using an octree, where each sampling unit is subdivided in eight equally-sized units. The new corner points are then generated on all the corners of the sampling unit itself and on the centre of the sampling unit itself, its edges and its faces (FIG. 4). The calculation of the initial signed distance and weight values can then be done as described in the embodiment above. When doing the calculation based on a predefined neighbourhood the calculation is preferably done in the following way. For a new corner point that is in the same place as the lower-level corner point, the initial values are those of the existing corner point. For a new corner point in the middle of an edge, the initial values are the average of the values of the 2 lower level corner points at the end of the edge. For a new corner point added in the middle of a face the initial values are the average of the values of the 4 lower level corner points of the face, and for a new corner point added in the middle of the sampling unit the initial values are the average of the values of the 8 lower-level corner points of the lower-level sampling unit. This means that for the calculation of the weight and signed distance values to be assigned to the new higher-level corner points, trilinear interpolation of the 8 lower-level corner points is used.”; [0062] According to another embodiment of the second aspect of the invention, a tooth stump and its marginal edge as well as the neighbouring teeth and the antagonists are digitized in order to design a crown restoration in a method 500 as shown in FIG. 10. At first an intra-oral scan is made of the tooth stump and the neighbouring teeth in step 501. All scanned data is loaded into a computer in step 502--such as computer 54 of FIG. 5. Thereto the scanner is moved along the teeth and the tooth stump in order to obtain a high resolution model of these. Especially at the marginal edge of the tooth stump a highly detailed surface representation is needed in order to be able to detect this marginal edge with high accuracy, needed to design a well-fitting crown. Secondly the antagonists, i.e. for the region of the tooth stump and the neighbouring teeth, are digitized at average resolution in step 503. Also a side scan is taken of this area while the patient bites in occlusion in step 504. The side scan is used for positioning the antagonists virtually in occlusion with the tooth stump and the neighbouring teeth in step 505. As such it is possible to shape the surface of the occlusion of the crown so that it occludes well with the antagonists.”) In addition, the same motivation is used as the rejection for claim 1.
Regarding claim 10, Storti, Mecca and Van Lierde teach the computer implemented method according to claim 1, wherein identifying the group of subgrids comprises identifying a subgrid when the at least two signed distances each determined at the first point and at the at least second point meet a selection criterion (see at least [0141] of Storti “Exemplary logical steps 170 illustrated in FIG. 14 can be employed for evaluating signed distance value data for signed distance grid 140 so that a region in which the object of interest is located can be divided into successively smaller cubes using the octree decomposition approach. A step 172 provides for identifying corner vertices of a cube (initially, a large cube that encompasses the region occupied by the object of interest), to produce vertex SDF values 174. Next, a step 176 applies local SDF bounds to the SDF values at the vertices of the cube to determine an interval SDF bound over the cube, D.sub.min.ltoreq.SDF.ltoreq.D.sub.max, as noted in a block 178. A decision step 180 then provides for examining the bounds to determine whether the cube being evaluated is empty of any portion of the object of interest, or may include a portion of the surface of the object, or may be fully occupied by a portion of the object. If the examination of the cube determines that D.sub.min>0, the result indicated in a block 182 is that the cube is empty, and the resulting data are stored in block 184. If the value of D.sub.max<0, then the result indicated in a block 194 is that the cube is fully occupied, and that result is stored as data in block 184. Finally, if D.sub.min.ltoreq.0.ltoreq.D.sub.max, the cube may contain part of the surface of the cube (and be partially occupied), as indicated in a block 186. A decision step then determines if the length of the edge of the cube is greater than the spacing between points for the signed distance grid. If so, a step 190 subdivides the cube in eight smaller cubes to refine the classification of the cubes as noted above. The logic then loops back to step 172, to identify the vertices of the corners for the next cube being evaluated. If the result of decision step 188 is negative, the current cube being examined is classified as an ON cube in a step 192--i.e., to provide an indication that part of the surface may be included in the cube. That result is also stored in data, in block 184. After storing a result in the data, while not shown, it will be understood that the process reiteratively continues with the next cube to be examined until all cubes that can be further subdivided have (in step 190), and all of the cubes that have been produced by subdividing larger cubes and are neither empty nor full have been examined. Regarding claim 11, Storti, Mecca and Van Lierde teach the computer implemented method according to claim 6,wherein identifying the group of subgrids comprises identifying a subgrid when the at least two signed distances each determined at the first corner point and at the at least second corner point meet a selection criterion (see at least [0141] of Storti “Exemplary logical steps 170 illustrated in FIG. 14 can be employed for evaluating signed distance value data for signed distance grid 140 so that a region in which the object of interest is located can be divided into successively smaller cubes using the octree decomposition approach. A step 172 provides for identifying corner vertices of a cube (initially, a large cube that encompasses the region occupied by the object of interest), to produce vertex SDF values 174. Next, a step 176 applies local SDF bounds to the SDF values at the vertices of the cube to determine an interval SDF bound over the cube, D.sub.min.ltoreq.SDF.ltoreq.D.sub.max, as noted in a block 178. A decision step 180 then provides for examining the bounds to determine whether the cube being evaluated is empty of any portion of the object of interest, or may include a portion of the surface of the object, or may be fully occupied by a portion of the object. If the examination of the cube determines that D.sub.min>0, the result indicated in a block 182 is that the cube is empty, and the resulting data are stored in block 184. If the value of D.sub.max<0, then the result indicated in a block 194 is that the cube is fully occupied, and that result is stored as data in block 184. Finally, if D.sub.min.ltoreq.0.ltoreq.D.sub.max, the cube may contain part of the surface of the cube (and be partially occupied), as indicated in a block 186. A decision step then determines if the length of the edge of the cube is greater than the spacing between points for the signed distance grid. If so, a step 190 subdivides the cube in eight smaller cubes to refine the classification of the cubes as noted above. The logic then loops back to step 172, to identify the vertices of the corners for the next cube being evaluated. If the result of decision step 188 is negative, the current cube being examined is classified as an ON cube in a step 192--i.e., to provide an indication that part of the surface may be included in the cube. That result is also stored in data, in block 184. After storing a result in the data, while not shown, it will be understood that the process reiteratively continues with the next cube to be examined until all cubes that can be further subdivided have (in step 190), and all of the cubes that have been produced by subdividing larger cubes and are neither empty nor full have been examined.”; [0035] of Van Lierde “Signed distance and weight values are then related to the elementary spaces, for example by assigning values to the corner points (8) of these elementary spaces in step 203. Other specific points of said elementary spaces (e.g. midpoints of edges or faces, centre point of elementary space . . . ) can also be used for assigning distance and weight values, but are also referred to as corner points in the remainder of the text. When a new point is available from a scanning of the body, a new signed distance and weight value is calculated for every corner point in step 204. The current signed distance value of every corner point is then modified by replacing it with the weighted average of the new signed distance value and the current signed distance value, using the weight values as the weights for the average. The current weight value is then modified by replacing it with the sum of the current and new weight value. This means that when the calculated weight value is zero for a corner point, the new signed distance value will not be taken into account; hence there is no need to calculate a new signed distance value for this corner point. [0036] A preferred way of calculating the new signed distance values is based on the scanned point and its normal (i.e. the direction perpendicular to the surface of the body in said point, which is typically estimated). First, a plane is fitted through the scanned point and perpendicular to the normal of that point. For each corner point, the distance is then measured between the corner point and this normal plane as illustrated in FIG. 3. The sign of the distance value is determined by whether the scanned point is inside (a minus sign) or outside (a plus sign) of the body. The information on the location inside or outside the body can be derived from the scanned points, but can also be specified by the scanner device as extra information within the scanned point.”) In addition, the same motivation is used as the rejection for claim 1.
Regarding claim 12, Storti, Mecca and Van Lierde teach the computer implemented method according to claim 6,wherein identifying the group of subgrids comprises identifying a subgrid when the at least two signed distances each determined at the first corner point or at the first edge point and at the at least second corner point or at the at least second edge point meet a selection criterion(see at least [0141] of Storti “Exemplary logical steps 170 illustrated in FIG. 14 can be employed for evaluating signed distance value data for signed distance grid 140 so that a region in which the object of interest is located can be divided into successively smaller cubes using the octree decomposition approach. A step 172 provides for identifying corner vertices of a cube (initially, a large cube that encompasses the region occupied by the object of interest), to produce vertex SDF values 174. Next, a step 176 applies local SDF bounds to the SDF values at the vertices of the cube to determine an interval SDF bound over the cube, D.sub.min.ltoreq.SDF.ltoreq.D.sub.max, as noted in a block 178. A decision step 180 then provides for examining the bounds to determine whether the cube being evaluated is empty of any portion of the object of interest, or may include a portion of the surface of the object, or may be fully occupied by a portion of the object. If the examination of the cube determines that D.sub.min>0, the result indicated in a block 182 is that the cube is empty, and the resulting data are stored in block 184. If the value of D.sub.max<0, then the result indicated in a block 194 is that the cube is fully occupied, and that result is stored as data in block 184. Finally, if D.sub.min.ltoreq.0.ltoreq.D.sub.max, the cube may contain part of the surface of the cube (and be partially occupied), as indicated in a block 186. A decision step then determines if the length of the edge of the cube is greater than the spacing between points for the signed distance grid. If so, a step 190 subdivides the cube in eight smaller cubes to refine the classification of the cubes as noted above. The logic then loops back to step 172, to identify the vertices of the corners for the next cube being evaluated. If the result of decision step 188 is negative, the current cube being examined is classified as an ON cube in a step 192--i.e., to provide an indication that part of the surface may be included in the cube. That result is also stored in data, in block 184. After storing a result in the data, while not shown, it will be understood that the process reiteratively continues with the next cube to be examined until all cubes that can be further subdivided have (in step 190), and all of the cubes that have been produced by subdividing larger cubes and are neither empty nor full have been examined.”; [0045] of Van Lierde “ A preferred way of subdividing the sampling units is by using an octree, where each sampling unit is subdivided in eight equally-sized units. The new corner points are then generated on all the corners of the sampling unit itself and on the centre of the sampling unit itself, its edges and its faces (FIG. 4). The calculation of the initial signed distance and weight values can then be done as described in the embodiment above. When doing the calculation based on a predefined neighbourhood the calculation is preferably done in the following way. For a new corner point that is in the same place as the lower-level corner point, the initial values are those of the existing corner point. For a new corner point in the middle of an edge, the initial values are the average of the values of the 2 lower level corner points at the end of the edge. For a new corner point added in the middle of a face the initial values are the average of the values of the 4 lower level corner points of the face, and for a new corner point added in the middle of the sampling unit the initial values are the average of the values of the 8 lower-level corner points of the lower-level sampling unit. This means that for the calculation of the weight and signed distance values to be assigned to the new higher-level corner points, trilinear interpolation of the 8 lower-level corner points is used.”; [0062] According to another embodiment of the second aspect of the invention, a tooth stump and its marginal edge as well as the neighbouring teeth and the antagonists are digitized in order to design a crown restoration in a method 500 as shown in FIG. 10. At first an intra-oral scan is made of the tooth stump and the neighbouring teeth in step 501. All scanned data is loaded into a computer in step 502--such as computer 54 of FIG. 5. Thereto the scanner is moved along the teeth and the tooth stump in order to obtain a high resolution model of these. Especially at the marginal edge of the tooth stump a highly detailed surface representation is needed in order to be able to detect this marginal edge with high accuracy, needed to design a well-fitting crown. Secondly the antagonists, i.e. for the region of the tooth stump and the neighbouring teeth, are digitized at average resolution in step 503. Also a side scan is taken of this area while the patient bites in occlusion in step 504. The side scan is used for positioning the antagonists virtually in occlusion with the tooth stump and the neighbouring teeth in step 505. As such it is possible to shape the surface of the occlusion of the crown so that it occludes well with the antagonists.”) In addition, the same motivation is used as the rejection for claim 1.
Regarding claim 13, Storti, Mecca and Van Lierde teach the computer implemented method according to claim 6,the selection criterion includes that the at least two signed distances include at least one positive signed distance and at least one negative signed distance (see at least [0141] of Storti “Exemplary logical steps 170 illustrated in FIG. 14 can be employed for evaluating signed distance value data for signed distance grid 140 so that a region in which the object of interest is located can be divided into successively smaller cubes using the octree decomposition approach. A step 172 provides for identifying corner vertices of a cube (initially, a large cube that encompasses the region occupied by the object of interest), to produce vertex SDF values 174. Next, a step 176 applies local SDF bounds to the SDF values at the vertices of the cube to determine an interval SDF bound over the cube, D.sub.min.ltoreq.SDF.ltoreq.D.sub.max, as noted in a block 178. A decision step 180 then provides for examining the bounds to determine whether the cube being evaluated is empty of any portion of the object of interest, or may include a portion of the surface of the object, or may be fully occupied by a portion of the object. If the examination of the cube determines that D.sub.min>0, the result indicated in a block 182 is that the cube is empty, and the resulting data are stored in block 184. If the value of D.sub.max<0, then the result indicated in a block 194 is that the cube is fully occupied, and that result is stored as data in block 184. Finally, if D.sub.min.ltoreq.0.ltoreq.D.sub.max, the cube may contain part of the surface of the cube (and be partially occupied), as indicated in a block 186. A decision step then determines if the length of the edge of the cube is greater than the spacing between points for the signed distance grid. If so, a step 190 subdivides the cube in eight smaller cubes to refine the classification of the cubes as noted above. The logic then loops back to step 172, to identify the vertices of the corners for the next cube being evaluated. If the result of decision step 188 is negative, the current cube being examined is classified as an ON cube in a step 192--i.e., to provide an indication that part of the surface may be included in the cube. That result is also stored in data, in block 184. After storing a result in the data, while not shown, it will be understood that the process reiteratively continues with the next cube to be examined until all cubes that can be further subdivided have (in step 190), and all of the cubes that have been produced by subdividing larger cubes and are neither empty nor full have been examined.” [0128] of Mecca “ In FIG. 8, a node simply contains the information of a 3D cube (position, size), a SDF value (coded with the grayscale here; light grey is positive, dark grey is negative) as well as pointers to next level nodes corresponding to subdividing the box in all 3 dimensions (this 2D figure only shows 4 children nodes but in reality they are 8). [0129] The initial voxel size is set in S401. In 403, the SDF is estimated. For the first time the algorithm is run, the SDF is estimated from the initial surface estimate from the MVS data. The process of estimating an SDF for a voxel is an iterative process. Using this SDF estimate, ray tracing is performed in step S405. [0036] of Van Lierde “A preferred way of calculating the new signed distance values is based on the scanned point and its normal (i.e. the direction perpendicular to the surface of the body in said point, which is typically estimated). First, a plane is fitted through the scanned point and perpendicular to the normal of that point. For each corner point, the distance is then measured between the corner point and this normal plane as illustrated in FIG. 3. The sign of the distance value is determined by whether the scanned point is inside (a minus sign) or outside (a plus sign) of the body. The information on the location inside or outside the body can be derived from the scanned points, but can also be specified by the scanner device as extra information within the scanned point. [0037] A preferred way of calculating the new weight value of a corner point is assigning it a `1` when the scanned point will result in a modification of the signed distance value for this corner point and assigning it a `0` otherwise. In other words, the weight value of a corner point represents the number of scanned points that resulted in a signed distance value for this corner point.” [0077] The software can be adapted such that when it is executed on a suitable processing engine said new signed distance value is the distance between a normal plane fitted through said scanned point and said elementary space; and wherein the sign of said new signed distance value is positive if said elementary space is located outside of said body and wherein the sign of said value is negative if said elementary space is located inside of said body.) In addition, the same motivation is used as the rejection for claim 1.
Regarding claim 16, Storti, Mecca and Van Lierde teach the computer implemented method according to claim 1, wherein the digitally designing of the dental appliance comprises performing volumetric operation based on the received digital 3D dental data for at least the identified group of subgrids (see at least [0014] of Storti “The step of processing the volumetric scan data with a computing device can include the step of segmenting the volumetric scan data to produce the signed distance grid of points and to determine the signed distance values specifying the distances from the points to the surface of the object.” Fig. 9, 10A-10D [0135] -[0141] A flowchart 130 shown in FIG. 13 illustrates exemplary steps for implementing different aspects of the novel approach discussed above. This approach is implemented using volumetric scan data that have been collected for an N-dimensional object, as indicated in a block 132. In some of the examples that are discussed herein, a 3-D object such as part of a patient's body is the object; however, it should be understood that the object is not limited to part of a body, but can be almost any type of object. Furthermore, the object can have more or fewer than three dimensions. A step 134 provides for carrying out an N-dimensional scan of the object, for example, using a CT, MR, PET, or other type of volumetric scanner. The result of this scan is an image stack 136, in which the object is delineated from surrounding material based on a characteristic, such as intensity. While the term "object" is used in the singular form, it will be understood that a plurality of objects of interest may be scanned so that a model can be produced for each object or group of objects using the present novel approach. For example, if an CT scanner is employed, the image stack may represent generally parallel contiguous "slices" through one or more objects (such as one or more bones) and any surrounding material (such as tissue), wherein the object is visually apparent in the images because it has a substantially different intensity or gray-scale value than the surrounding material. However, it must be stressed that segmentation of the raw image data, which is carried out in the following step, is not simply a matter of applying a threshold test. Indeed, a step 138 provides for converting the intensities (or other characteristic, such as color) of the voxels comprising the image stack data using segmentation (which may optionally use a level sets algorithm, such as the exemplary approach discussed above) to produce signed distance values on a signed distance grid 140. Based on the characteristic of the image stack data, this step determines the distance from the center of the voxels comprising the image stack data to the nearest point on the surface of the object. Voxels that have a positive signed distance value are thus outside the object, while those with a negative value are inside the object…[0141] Exemplary logical steps 170 illustrated in FIG. 14 can be employed for evaluating signed distance value data for signed distance grid 140 so that a region in which the object of interest is located can be divided into successively smaller cubes using the octree decomposition approach. A step 172 provides for identifying corner vertices of a cube (initially, a large cube that encompasses the region occupied by the object of interest), to produce vertex SDF values 174. Next, a step 176 applies local SDF bounds to the SDF values at the vertices of the cube to determine an interval SDF bound over the cube, D.sub.min.ltoreq.SDF.ltoreq.D.sub.max, as noted in a block 178. A decision step 180 then provides for examining the bounds to determine whether the cube being evaluated is empty of any portion of the object of interest, or may include a portion of the surface of the object, or may be fully occupied by a portion of the object. If the examination of the cube determines that D.sub.min>0, the result indicated in a block 182 is that the cube is empty, and the resulting data are stored in block 184. If the value of D.sub.max<0, then the result indicated in a block 194 is that the cube is fully occupied, and that result is stored as data in block 184. Finally, if D.sub.min.ltoreq.0.ltoreq.D.sub.max, the cube may contain part of the surface of the cube (and be partially occupied), as indicated in a block 186. A decision step then determines if the length of the edge of the cube is greater than the spacing between points for the signed distance grid. If so, a step 190 subdivides the cube in eight smaller cubes to refine the classification of the cubes as noted above. The logic then loops back to step 172, to identify the vertices of the corners for the next cube being evaluated. If the result of decision step 188 is negative, the current cube being examined is classified as an ON cube in a step 192--i.e., to provide an indication that part of the surface may be included in the cube. That result is also stored in data, in block 184. After storing a result in the data, while not shown, it will be understood that the process reiteratively continues with the next cube to be examined until all cubes that can be further subdivided have (in step 190), and all of the cubes that have been produced by subdividing larger cubes and are neither empty nor full have been examined.”; [[0137] of Mecca “The volumetric approach described herein allows for very fast visibility estimations, especially when implemented as an octree. Indeed, assuming a voxel grid of dimension N×N×N, then the number of voxels around the surface are expected to be (N.sup.2). Then, for each voxel, visibility calculations only require examining custom-character(logN) (as illustrated in the caption of FIG. 9(b)) as opposed to custom-character(N) operations for a dense volume/depth map parameterisation or custom-character(N.sup.2) operations required in a mesh-parameterisation framework (i.e. check all ray-box intersections); [0054] of Van Lierde “At any point in time, the corner points with their signed distance and weight values comprise a model of the body that is scanned taking into account the already scanned points. At any point in time, this model can be used to derive a surface or volume representation of the body. A typical example of a surface representation is a triangular mesh. Such a mesh can be obtained from the model of the body by state-of-the-art meshing techniques, like the Marching Cubes or the Marching Tetrahedra algorithm: see for example Lorensen, W. E.; Cline, Harvey E. (1987). "Marching cubes: A high resolution 3d surface construction algorithm". ACM Computer Graphics vol. 21 (4) pages 163-169 and for example Akio Doi and Akoi Koide, "An efficient method of triangulating equi-valued surfaces by using tetrahedral cells", IEICE Trans Commun. Elec. Inf. Syst, E-74(1) pages 213-224, 1991.. In addition, the same motivation is used as the rejection for claim 1.
Regarding claim 17, Storti, Mecca and Van Lierde teach the computer implemented method according to claim 1,wherein each of the identified group of subgrids includes a plurality of cells, and wherein at least two signed cell distances are determined for each of the plurality of cells, and based on the at least two signed cell distances a group of cells are identified, and wherein a volumetric operation is performed for each identified cells of the group of cells ([0090] of Storti “ In regard to the two-dimensional (2-D) case, the ideas remain the same as for the 1-D case, but the geometry becomes more complicated. The sample points now lie on a uniform 2-D grid so that the cells obtained by connecting neighboring sample points along the coordinate directions become squares; plots of the upper and lower bounds generated by each sample point become 45.degree. cones with vertical axes of symmetry; and most significantly, the direction of .gradient.f can lie anywhere in the plane and need not be aligned with a coordinate direction.”; 0108] A variety of traditional compression techniques have been applied to the raw scan data, but once segmentation has been performed and a signed distance grid has been obtained, more effective compression can be achieved using a variety of sparse representations. For example, model representations requiring less data storage can be obtained by keeping only a subset of the original data from which signed distance values can be computed at other locations. The key property of the SDF, f({right arrow over (r)}) is that (away from singular points, as described below) the magnitude of the gradient is unity. As noted above, in mathematical terms, the SDF satisfies a partial differential equation known as the eikonal equation, |.gradient.f|=1. By keeping only an appropriate subset of the original sample data, the remainder of the data can be reconstructed as a solution of the eikonal equation using a numerical partial differential equation solving algorithm, such as the "fast marching method." (The fast marching method was introduced by James A. Sethian as a numerical method for solving boundary value problems of the form F(x)|.gradient.T(x)|=1.)”; [0135] of Mecca “The zero level set of the SDF is then obtained in S415. Here, the voxels where the value of the SDF which is as close to zero as allowed by the resolution are taken to be the surface. The reconstructed surface is then computed in step S417 using for example a Marching cubes technique, for example the variant discussed in M. Kazhdan, A. Klein, K. Dalal, and H. Hoppe. Unconstrained isosurface extraction on arbitrary octrees. In ESGP, 2007. In Marching cubes The premise of algorithm is to divide the input volume into a discrete set of cubes. By assuming linear reconstruction filtering, each cube, which contains a piece of a given isosurface, can easily be identified because the sample values at the cube vertices must span the target isosurface value. For each cube containing a section of the isosurface, a triangular mesh that approximates the behavior of the trilinear interpolant in the interior cube is generated. [0137] “The volumetric approach described herein allows for very fast visibility estimations, especially when implemented as an octree. Indeed, assuming a voxel grid of dimension N×N×N, then the number of voxels around the surface are expected to be (N.sup.2). Then, for each voxel, visibility calculations only require examining custom-character(logN) (as illustrated in the caption of FIG. 9(b)) as opposed to custom-character(N) operations for a dense volume/depth map parameterisation or custom-character(N.sup.2) operations required in a mesh-parameterisation framework (i.e. check all ray-box intersections).; [0035] As mentioned above, in an embodiment, the photometric stereo approach determines the position of the surface of the object by using a signed distance function where the signed distance function determines the distance from a point to a surface, wherein the signed distance function is related to the surface normal:[0036] where n(x) is the surface normal at 3D point x, d(x) is the signed distance function at 3D point x and ∇ is the gradient operator, the signed distance function being substituted for the surface normal when modelling irradiance. [0037] By using the above, the surface is indicated when the signed distance function is at a minimum. [0038] In an embodiment, the processor processes the photometric stereo data using a volumetric approach, wherein the volume containing the object is subdivided into voxels and the signed distance function is calculated per voxel.”; [0055] of Van Lierde “Therefore meshing is done by extracting the 0-isosurface (i.e. the surface that goes through the points where distance equals 0) in the sampling units. For the evaluation of the signed distances there are different options, either all signed distance values (i.e. at all levels of subdivision) are used or only the highest level values are used, or any combination of different levels. A typical way to visualize volumetric data is volume rendering. This is done by state-of-the-art techniques, like the volume ray casting algorithm, which is based on the principle of shooting rays from the eye through each pixel of the image and finding the closest object blocking the path of that ray. The signed distance and weight values are used to determine the intersection between the ray and the volume and to determine the color of the corresponding pixel.”) In addition, the same motivation is used as the rejection for claim 1.
2. Claims 14-15 are rejected under 35 U.S.C. 103 as being unpatentable over Storti et al., IDS, U.S Patent Application Publication No.20009/0244065 (“Storti”) in view of Mecca et al. U.S Patent Application Publication No.2021/0044788 (“Mecca”) further in view of Van Lierde et al., U.S Patent Application Publication No.2015/0248538 (“Van Lierde”) further in view of Museth et al., U.S Patent Application Publication No.20040170302 (“Museth”)
Regarding claim 14, Storti, Mecca and Van Lierde teach the computer implemented method according to claim 1, comprising determining a bounding box comprising the digital 3D dental data, and at least a first set of subgrids of the plurality of subgrids, and wherein the first set of subgrids corresponds to subgrids that relate to an surface of either the first surface or the second surface, wherein the surface is determined to the digital 3D dental data that defines either the first surface or the second surface[0133] [0141] of Storti “However, the local bounds described above change the situation completely and provide a method for reliably creating octrees, starting at the coarsest level. Beginning with a cube containing the entire sample grid, it is only necessary to consider the extreme corner values (i.e., the vertices) and the edge length of 128. Since one of the corner values has magnitude less than 128 {square root over (3)}, the interval bound contains 0. Thus, the cube can next be divided into eight equal smaller cubes, each with an edge length equal to 64. The SDF values at the vertices of these smaller cubes are considered, interval bounds are computed for each, and the process continues until the smallest cubes are classified, or further subdivision is not possible with the given data.”; [0035] of Mecca “As mentioned above, in an embodiment, the photometric stereo approach determines the position of the surface of the object by using a signed distance function where the signed distance function determines the distance from a point to a surface, wherein the signed distance function is related to the surface normal: n(x)=∇d(x). (1) [0036] where n(x) is the surface normal at 3D point x, d(x) is the signed distance function at 3D point x and ∇ is the gradient operator, the signed distance function being substituted for the surface normal when modelling irradiance. [0037] By using the above, the surface is indicated when the signed distance function is at a minimum.”; [0094] In an embodiment, to provide suitable mathematical characterisation of a collection of solid objects, the implicit surface parameterisation is considered in terms of the signed distance function SDF …[0095] A signed distance function, when given the coordinates of a point x return the shortest distance between x and a defined surface. This parameterisation is suitable for this embodiment due to its practical way of describing the outgoing normal vector to a surface.” “;[0035] of Van Lierde “Signed distance and weight values are then related to the elementary spaces, for example by assigning values to the corner points (8) of these elementary spaces in step 203. Other specific points of said elementary spaces (e.g. midpoints of edges or faces, centre point of elementary space . . . ) can also be used for assigning distance and weight values, but are also referred to as corner points in the remainder of the text. When a new point is available from a scanning of the body, a new signed distance and weight value is calculated for every corner point in step 204. The current signed distance value of every corner point is then modified by replacing it with the weighted average of the new signed distance value and the current signed distance value, using the weight values as the weights for the average. The current weight value is then modified by replacing it with the sum of the current and new weight value. This means that when the calculated weight value is zero for a corner point, the new signed distance value will not be taken into account; hence there is no need to calculate a new signed distance value for this corner point.” [0041] In order to increase the level of detail of the model, a selection of elementary spaces (e.g. sampling units such as regular sampling units) with a related selection of corner points is subdivided into new and smaller elementary spaces (sampling units) in step 205. Regular sampling units are equally sized sampling units. These equally sized sampling units are not necessarily cube shaped for example, because they could also be rectangular. When subdividing an existing elementary space or lower-level elementary space into new elementary spaces or higher-level elementary spaces, corner points are generated at all the corners of the sampling unit itself and within that sampling unit. As these higher-level corner points are also corner points, they also need a signed distance and weight parameter to be assigned to. After creation of the higher-level corner point, its signed distance and weight parameters need to be initialized by assigning them an initial value. One preferred way to calculate the initial values is by giving them a default value, for example zero. [0042] Another preferred way to calculate the initial value for the signed distance and weight parameters is by calculating the average of the neighbouring corner points that already existed before the subdivision, referred to as the neighbouring lower-level corner points. [0043] Another preferred way to calculate the initial value for the signed distance and weight parameters is by using not only the values of the corner points of the sampling unit that is subdivided but also the values of the corner points of neighbouring sampling units (i.e. the same or higher or lower level corner points).In addition, the same motivation is used as the rejection for claim 1. Storti, Mecca and Van Lierde are understood to be silent on the remaining limitations of claim 14.
In the same field of endeavor, Museth teaches comprising determining a bounding box comprising the digital 3D dental data, and at least a first set of subgrids of the plurality of subgrids that is arranged outside the bounding box ([0020] The present invention further includes a method of mesh extraction that extensively utilizes bounding boxes and the active list of the level set solver to implement an incremental version of the Marching Cubes algorithm.”; [0212] One of the most effective techniques for increasing interactivity in the present level set editing system involves restricting computations to a subregion of the volume dataset. This is feasible because many of the editing operators by their very nature are local. The selection of the proper subvolume during the editing process is implemented with grid-aligned bounding boxes. Having the bounding boxes axis-aligned makes them straightforward to compute and manipulate, and having them grid-aligned guarantees that intersections directly correspond to valid subvolumes. The bounding box position and size are based on the geometric primitive, e.g. superellipsoid, triangle mesh or point set, utilized by a particular operator. [0213] Employing bounding boxes within the local level set editing operators (blending, smoothing, sharpening and embossing) significantly lessens the computation time during the editing process. These operators are defined by speed functions (F( )) that specify the speed of the deformation on the surface. For the smoothing, sharpening and embossing operators, the user specifies the portion of the model to be edited by positioning a region-of-influence (ROI) primitive. The speed function is defined to be zero outside of the ROI primitive. During a blending operation a set of intersection voxels (those containing both surfaces being blended) are identified and blending only occurs within a user-specified distance of these voxels. The speed function is zero beyond this distance. In both cases no level set computation is needed in the outer regions. Given the ROI primitive and the distance information from the set of intersection voxels, a grid/axis-aligned bounding box that contains only those regions where the speed function is non-zero can be defined. A subvolume is "carved" out from the complete model by performing a CSG intersection operation with the signed distance field associated with the bounding box and the model's volume. The resulting subvolume is then passed to the level set solver, and inserted back into the model's volume after processing.” 0222] The process starts by making the following observations about the bounding boxes introduced in Section 3.3.6. First, the definition of the speed functions that utilize bounding boxes guarantees that the mesh outside of the bounding boxes is unchanged after a local editing operation. Second, the bounding boxes are by definition grid-aligned and all vertices of a MC mesh lie, by construction, on grid edges. These observations lead to the following incremental mesh extraction algorithm. Given a complete global mesh the process first trims away all triangles with vertices inside a bounding box. Next, for each subsequent iteration of the level set calculation, new triangles are only extracted from the sub-volume defined by the bounding box. The resulting new triangles are then incrementally added to the trimmed mesh, which by construction properly connect without the need for additional triangle clipping.), and wherein the first set of subgrids corresponds to subgrids that relate to an expanded surface of either the first surface or the second surface ([0084] Automatic blending is demonstrated in FIG. 4. A wing model is positioned relative to a dragon model. The two models are pasted together and automatic mean curvature-based blending is applied to smooth the creased intersection region. In the left panel, the wing model is positioned onto the dragon model. In the middle panel, the models are pasted together (CSG union operation), producing sharp, undesirable creases, a portion of which is expanded in the box. Finally, the right panel shows the same region after automatic blending based on mean curvature. The blending is constrained to only move outwards. The models are rendered with flat-shading to highlight the details of the surface structure., wherein the expanded surface is determined by adding an offset value to the digital 3D dental data that defines either the first surface or the second surface ([0101] Morphological openings and closings consist of two fundamental operators, dilations D.sub..omega., and erosions E.sub..omega.. Dilation creates an offset surface a distance .omega. outwards from the original surface, and erosion creates an offset surface a distance .omega. inwards from the original surface. The morphological opening operator O.sub..omega. is an erosion followed by a dilation, i.e. O.sub..omega.=D.sub..omega..smallcircle.E.sub..omega., which removes small pieces or thin appendages. A closing is defined as C.sub..omega.=E.sub..omega..smallcircle.D.sub..omega., and closes small gaps or holes within objects. [0102] Morphological operators may be implemented by solving a special form of the level set equation, the Eikonal equation, .+-..differential..phi./.differential.t=.vertline..gradient..phi..vertlin- e.=1, up to a certain time t, utilizing Sethian's Fast Marching Method, as decribed by Sethian J. in A fast marching level set method for monotonically advancing fronts, in Proceedings of the National Academy of Science, vol. 93, 1591-1595. The value of t corresponds to the offset distance, .omega., from the original surface, .phi.(t=0). FIG. 9 contains a model from a laser scan reconstruction that has been smoothed with an opening operator with .omega. equal to 3.”)
Therefore, it would have been obvious to one of ordinary skill in the art before the effective filling date of claimed invention to modify the method of creating a model of an objection based on volumetric scan data including a signed distance grid of point to a surface of the object of Storti, Mecca and Van Lierde with applying bounding boxes as seen in Museth because this modification would optimize computations related to the editing operators (abstract of Museth)
Thus, the combination of Storti, Mecca , Van Lierde and Museth teaches comprising determining a bounding box comprising the digital 3D dental data, and at least a first set of subgrids of the plurality of subgrids that is arranged outside the bounding box, and wherein the first set of subgrids corresponds to subgrids that relate to an expanded surface of either the first surface or the second surface, wherein the expanded surface is determined by adding an offset value to the digital 3D dental data that defines either the first surface or the second surface.
Regarding claim 15, Storti, Mecca , Van Lierde and Museth teach the computer implemented method according to claim 14, comprising determining a second set of subgrids of the plurality of subgrids lying partly inside the bounding box, and wherein the second set of subgrids corresponds to the digital 3D dental data of either the first surface or the second surface ([0133] [0141] of Storti “However, the local bounds described above change the situation completely and provide a method for reliably creating octrees, starting at the coarsest level. Beginning with a cube containing the entire sample grid, it is only necessary to consider the extreme corner values (i.e., the vertices) and the edge length of 128. Since one of the corner values has magnitude less than 128 {square root over (3)}, the interval bound contains 0. Thus, the cube can next be divided into eight equal smaller cubes, each with an edge length equal to 64. The SDF values at the vertices of these smaller cubes are considered, interval bounds are computed for each, and the process continues until the smallest cubes are classified, or further subdivision is not possible with the given data.”; [0035] of Mecca “As mentioned above, in an embodiment, the photometric stereo approach determines the position of the surface of the object by using a signed distance function where the signed distance function determines the distance from a point to a surface, wherein the signed distance function is related to the surface normal: n(x)=∇d(x). (1) [0036] where n(x) is the surface normal at 3D point x, d(x) is the signed distance function at 3D point x and ∇ is the gradient operator, the signed distance function being substituted for the surface normal when modelling irradiance. [0037] By using the above, the surface is indicated when the signed distance function is at a minimum.”; [0094] In an embodiment, to provide suitable mathematical characterisation of a collection of solid objects, the implicit surface parameterisation is considered in terms of the signed distance function SDF …[0095] A signed distance function, when given the coordinates of a point x return the shortest distance between x and a defined surface. This parameterisation is suitable for this embodiment due to its practical way of describing the outgoing normal vector to a surface.” “;[0035] of Van Lierde “Signed distance and weight values are then related to the elementary spaces, for example by assigning values to the corner points (8) of these elementary spaces in step 203. Other specific points of said elementary spaces (e.g. midpoints of edges or faces, centre point of elementary space . . . ) can also be used for assigning distance and weight values, but are also referred to as corner points in the remainder of the text. When a new point is available from a scanning of the body, a new signed distance and weight value is calculated for every corner point in step 204. The current signed distance value of every corner point is then modified by replacing it with the weighted average of the new signed distance value and the current signed distance value, using the weight values as the weights for the average. The current weight value is then modified by replacing it with the sum of the current and new weight value. This means that when the calculated weight value is zero for a corner point, the new signed distance value will not be taken into account; hence there is no need to calculate a new signed distance value for this corner point.” [0041] In order to increase the level of detail of the model, a selection of elementary spaces (e.g. sampling units such as regular sampling units) with a related selection of corner points is subdivided into new and smaller elementary spaces (sampling units) in step 205. Regular sampling units are equally sized sampling units. These equally sized sampling units are not necessarily cube shaped for example, because they could also be rectangular. When subdividing an existing elementary space or lower-level elementary space into new elementary spaces or higher-level elementary spaces, corner points are generated at all the corners of the sampling unit itself and within that sampling unit. As these higher-level corner points are also corner points, they also need a signed distance and weight parameter to be assigned to. After creation of the higher-level corner point, its signed distance and weight parameters need to be initialized by assigning them an initial value. One preferred way to calculate the initial values is by giving them a default value, for example zero. [0042] Another preferred way to calculate the initial value for the signed distance and weight parameters is by calculating the average of the neighbouring corner points that already existed before the subdivision, referred to as the neighbouring lower-level corner points. [0043] Another preferred way to calculate the initial value for the signed distance and weight parameters is by using not only the values of the corner points of the sampling unit that is subdivided but also the values of the corner points of neighbouring sampling units (i.e. the same or higher or lower level corner points).”;[0052] of Museth “In the present invention, the assumption is that a positive-inside/negative-outside sign convention for .phi.(x, t), i.e. n points outwards. Eq. (3) introduces the speed function F, which is a user-defined scalar function that can depend on any number of variables including x, n, .phi. and its derivatives evaluated at x, as well as a variety of external data inputs. F( ) is a signed scalar function that defines the motion (i.e. speed) of the level set surface in the direction of the local normal n at x.; 0066] In Eq. (8a) d denotes the distance from a point on the level set surface to the closest point in the point set p. In Eq. (8b) d denotes a signed distance measure from a point on the level set surface to the implicit surface s. The signed distance measure does not necessarily have to be Euclidean distance--just a monotonic distance measure following the positive-inside/negative-outside convention. Note that D.sub.p(d) is one when the shortest distance, d, to the point set is smaller than d.sub.min, and decays smoothly to zero as d increases to d.sub.max, after which it is zero. D.sub.s(d), on the other hand, is zero everywhere outside, as well as on, the surface s (d.ltoreq.0), but one inside when the distance measure d is larger than d.sub.max. 0108] As for the level set deformation operators (blending, smoothing, sharpening and embossing), in one embodiment many of these operators use bounding boxes (further described in Section 3.3.6), numerical integration (further described in Section 3.3) and the sparse-field techniques (further described in Section 3.3.5). In one embodiment, the blending and embossing operators use K-D trees (further described in Section 3.2.5) to quickly find closest points. The smoothing, sharpening and embossing operators utilize shortest distance calculations (further described in Section 3.2.3) for localizing computation. In another embodiment, the morphological operators employ the Fast Marching Method (further described in Section 3.2.6) to calculate the needed distance information. In one embodiment, the mesh extraction algorithm also extensively utilizes bounding boxes and the active list of the level set solver to implement an incremental version of the Marching Cubes algorithm.”) In addition, the same motivation is used as the rejection for claim 14.
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/SARAH LE/Primary Examiner, Art Unit 2614
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