DETAILED ACTION
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 .
This communication is in response to Application No. 19/052,503 filed 02/13/2025. Claims 1-12 are pending.
Information Disclosure Statement
The information disclosure statement(s) (IDS) submitted on 04/23/2025 have been entered and considered. Initialed copies of the PTO-1449 by the examiner are attached.
Drawings
The drawings are objected to because at Figure 1, #42 should recite “backward differentiator 42” to avoid clarity issues. Corrected drawing sheets in compliance with 37 CFR 1.121(d) are required in reply to the Office action to avoid abandonment of the application. Any amended replacement drawing sheet should include all of the figures appearing on the immediate prior version of the sheet, even if only one figure is being amended. The figure or figure number of an amended drawing should not be labeled as “amended.” If a drawing figure is to be canceled, the appropriate figure must be removed from the replacement sheet, and where necessary, the remaining figures must be renumbered and appropriate changes made to the brief description of the several views of the drawings for consistency. Additional replacement sheets may be necessary to show the renumbering of the remaining figures. Each drawing sheet submitted after the filing date of an application must be labeled in the top margin as either “Replacement Sheet” or “New Sheet” pursuant to 37 CFR 1.121(d). If the changes are not accepted by the examiner, the applicant will be notified and informed of any required corrective action in the next Office action. The objection to the drawings will not be held in abeyance.
Claim Objections
Claims 4 and 12 are objected to because of the following informalities:
Claim 12 should recite, in part, “A non-transitory computer readable medium” to avoid clarity issues.
Claim 4 should read, in part, “The system of claim 1, wherein the renderer” to avoid typographical and/or clarity issues.
Appropriate correction is required.
Claim Interpretation
The following is a quotation of 35 U.S.C. 112(f):
(f) Element in Claim for a Combination. – An element in a claim for a combination may be expressed as a means or step for performing a specified function without the recital of structure, material, or acts in support thereof, and such claim shall be construed to cover the corresponding structure, material, or acts described in the specification and equivalents thereof.
The following is a quotation of pre-AIA 35 U.S.C. 112, sixth paragraph:
An element in a claim for a combination may be expressed as a means or step for performing a specified function without the recital of structure, material, or acts in support thereof, and such claim shall be construed to cover the corresponding structure, material, or acts described in the specification and equivalents thereof.
The claims in this application are given their broadest reasonable interpretation using the plain meaning of the claim language in light of the specification as it would be understood by one of ordinary skill in the art. The broadest reasonable interpretation of a claim element (also commonly referred to as a claim limitation) is limited by the description in the specification when 35 U.S.C. 112(f) or pre-AIA 35 U.S.C. 112, sixth paragraph, is invoked.
As explained in MPEP § 2181, subsection I, claim limitations that meet the following three-prong test will be interpreted under 35 U.S.C. 112(f) or pre-AIA 35 U.S.C. 112, sixth paragraph:
(A) the claim limitation uses the term “means” or “step” or a term used as a substitute for “means” that is a generic placeholder (also called a nonce term or a non-structural term having no specific structural meaning) for performing the claimed function;
(B) the term “means” or “step” or the generic placeholder is modified by functional language, typically, but not always linked by the transition word “for” (e.g., “means for”) or another linking word or phrase, such as “configured to” or “so that”; and
(C) the term “means” or “step” or the generic placeholder is not modified by sufficient structure, material, or acts for performing the claimed function.
Use of the word “means” (or “step”) in a claim with functional language creates a rebuttable presumption that the claim limitation is to be treated in accordance with 35 U.S.C. 112(f) or pre-AIA 35 U.S.C. 112, sixth paragraph. The presumption that the claim limitation is interpreted under 35 U.S.C. 112(f) or pre-AIA 35 U.S.C. 112, sixth paragraph, is rebutted when the claim limitation recites sufficient structure, material, or acts to entirely perform the recited function.
Absence of the word “means” (or “step”) in a claim creates a rebuttable presumption that the claim limitation is not to be treated in accordance with 35 U.S.C. 112(f) or pre-AIA 35 U.S.C. 112, sixth paragraph. The presumption that the claim limitation is not interpreted under 35 U.S.C. 112(f) or pre-AIA 35 U.S.C. 112, sixth paragraph, is rebutted when the claim limitation recites function without reciting sufficient structure, material or acts to entirely perform the recited function.
Claim limitations in this application that use the word “means” (or “step”) are being interpreted under 35 U.S.C. 112(f) or pre-AIA 35 U.S.C. 112, sixth paragraph, except as otherwise indicated in an Office action. Conversely, claim limitations in this application that do not use the word “means” (or “step”) are not being interpreted under 35 U.S.C. 112(f) or pre-AIA 35 U.S.C. 112, sixth paragraph, except as otherwise indicated in an Office action.
Claim(s) 1, 4, 5, 7 and 8 recite limitations that use words like “means” (or “step”) or similar terms with functional language and do invoke 35 U.S.C. 112(f):
Claims 1, 4 and 7; recites the limitation, “renderer is configured to …,”.
Claims 1 and 8; recites the limitation, “forward differentiator is configured to …,”.
Claim 1; recites the limitation, “backward differentiator configured to …,”.
Claim 5; recites the limitation, “optimizer is configured to …,”.
Because this/these claim limitation(s) is/are being interpreted under 35 U.S.C. 112(f) or pre-AIA 35 U.S.C. 112, sixth paragraph, it/they is/are being interpreted to cover the corresponding structure described in the specification as performing the claimed function, and equivalents thereof.
After a careful analysis, as disclosed above, and a careful review of the specification the following limitations in claim(s) 1, 4, 5, 7 and 8:
“Renderer” (Fig. 1, #36. Paragraph [0028 and 0057 and 0059]- “The rendering processes described herein are neural rendering processes, in which AI techniques such as neural networks are used to aid the rendering process” and “The features described herein may be implemented in software, firmware, hardware, or a combination thereof. In the case of a software implementation, features could be embodied in program code that performs specified tasks when executed on a processor (e.g. CPU or CPUs)” thus, have sufficient structure or material wherein is any kind of neural network implemented on a processor).
“forward differentiator” (Fig. 1, #40. Paragraph [0023 and 0057 and 0059]- “The renderer 36 comprises functional sub-components that are configured to carry out the rendering, including a forwards differentiator 40, a backwards differentiator 42, an optimizer 44 and a loss function” and “The rendering processes described herein are neural rendering processes, in which AI techniques such as neural networks are used to aid the rendering process” and “The features described herein may be implemented in software, firmware, hardware, or a combination thereof. In the case of a software implementation, features could be embodied in program code that performs specified tasks when executed on a processor (e.g. CPU or CPUs)” thus, have sufficient structure or material wherein is any kind of neural network implemented on a processor).
“backward differentiator” (Fig. 1, #42. Paragraph [0023 and 0057 and 0059]- “The renderer 36 comprises functional sub-components that are configured to carry out the rendering, including a forwards differentiator 40, a backwards differentiator 42, an optimizer 44 and a loss function” and “The rendering processes described herein are neural rendering processes, in which AI techniques such as neural networks are used to aid the rendering process” and “The features described herein may be implemented in software, firmware, hardware, or a combination thereof. In the case of a software implementation, features could be embodied in program code that performs specified tasks when executed on a processor (e.g. CPU or CPUs)” thus, have sufficient structure or material wherein is any kind of neural network implemented on a processor).
“optimizer” (Fig. 1, #44. Paragraph [0023 and 0057 and 0059]- “The renderer 36 comprises functional sub-components that are configured to carry out the rendering, including a forwards differentiator 40, a backwards differentiator 42, an optimizer 44 and a loss function” and “The rendering processes described herein are neural rendering processes, in which AI techniques such as neural networks are used to aid the rendering process” and “The features described herein may be implemented in software, firmware, hardware, or a combination thereof. In the case of a software implementation, features could be embodied in program code that performs specified tasks when executed on a processor (e.g. CPU or CPUs)” thus, have sufficient structure or material wherein is any kind of neural network implemented on a processor).
If applicant does not intend to have this/these limitation(s) interpreted under 35 U.S.C. 112(f) or pre-AIA 35 U.S.C. 112, sixth paragraph, applicant may: (1) amend the claim limitation(s) to avoid it/them being interpreted under 35 U.S.C. 112(f) or pre-AIA 35 U.S.C. 112, sixth paragraph (e.g., by reciting sufficient structure to perform the claimed function); or (2) present a sufficient showing that the claim limitation(s) recite(s) sufficient structure to perform the claimed function so as to avoid it/them being interpreted under 35 U.S.C. 112(f) or pre-AIA 35 U.S.C. 112, sixth paragraph.
Claim Rejections - 35 USC § 102
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 the appropriate paragraphs of 35 U.S.C. 102 that form the basis for the rejections under this section made in this Office action:
A person shall be entitled to a patent unless –
(a)(1) the claimed invention was patented, described in a printed publication, or in public use, on sale, or otherwise available to the public before the effective filing date of the claimed invention.
Claim(s) 1-12 are rejected under 35 U.S.C. 102(a)(1) as being anticipated by Weiss et al. (“Differentiable direct volume rendering”, 2021, hereinafter referred to as “Weiss”).
Regarding claim 1, Weiss teaches a medical imaging system for rendering medical images comprising: a renderer configured to receive medical imaging data and render medical images using the medical imaging data, the renderer comprising (Weiss, Fig. 1 medical images are used in a fully differentiable direct volume renderer):
a forwards differentiator configured to perform differentiable rendering using forward differentiation to create samples, wherein the samples created by the forwards differentiator are colour and/or intensity samples (“As an example (see Fig. 2 for a schematics), let us assume that derivatives should be computed with respect to a single entry in a 1D texture-based TF, e.g., the red channel of the first texel T0,red. When loading the TF from memory, T0,red is replaced by T~0,red=⟨T0,red,1⟩, i.e., it is wrapped in an instance of fvar with the derivative for that parameter set to 1... It is worth noting that in the above example only the derivative of one single texel in the TF is computed. This process needs to be repeated for each texel, respectively each color component of each texel, by extending the array fvar:: derivatives to store the required number of p parameters” Weiss, pg. 565 Col 1, section 4.2 forward differentiation, Fig. 2; here, forward differentiation is used create color samples, e.g., derive color for each texel); and
a backwards differentiator configured to perform differentiable rendering using backwards differentiation on samples to generate at least one of: intensity projection, composition and/or rendering integration (“Adjoint differentiation, also called the adjoint method, backward or reverse mode differentiation, or backpropagation, evaluates the chain rule in the inverse order than forward differentiation... For each variable xi, the associated adjoint variable [eq. (6)] stores the derivative of the final output with respect to the current variable” Weiss, pg. 565 Col 1-2, section 4.3 Adjoint differentiation; here, adjoint differentiation obtains a final output, i.e., eq. (6), in which a parameter, or parameter(s) if used multiple times, are obtained once again, see Weiss pg. 565 Col 2. The parameters include that of color samples. Fig. 3 illustrates gradients in the adjoint variables (red) are propagated backward through algorithm 1, including summation of color blending; and wherein a composition is generated through algorithm 1 Direct Volume Rending Algorithm line 7 blending of the sample, and “a Riemann sum which can be computed in front-to-back order using iterative application of alpha-blending” Weiss, pg. 564 Col 1);
wherein the samples from the forwards differentiator and the output of the backwards differentiator are used to form the rendered medical images (Weiss, Fig. 3 illustrates a schematic representation of the adjoint method for density and TF reconstruction. Gradients in the adjoint variables (red) are propagated backward through the algorithm. A circled + indicates the summation of the gradients over all steps and rays; wherein the TF reconstruction is that of a forwards differentiator and a volume is rendered).
Regarding claim 2, Weiss teaches the system of claim 1, wherein the samples used by the backwards differentiator are created using the forwards differentiator (“the blending operation (line 7 in Algorithm 1) is defined as follows: Let α,C be the opacity and rgb-emission at the current sample, i.e., the components of ci, and let α(i),C(i) be the accumulated opacity and emission up to the current sample, i.e., the components of colori in Algorithm 1” Weiss, pg. 566 Col 1; wherein the sample is from the forward differentiator, see Weiss pg. 564 Col 2 “the pixel color represents the accumulated attenuated emissions at the sampling points along the view rays. In the model of the Wengert list (see Equation 2), a function fi is computed for each sample. Hence, the number of operations k is proportional to the overall number of samples along the rays. The intermediate results xi are rgb α images of the rendered object up to the i-th sample”).
Regarding claim 3, Weiss teaches the system of claim 1, wherein the samples used by the backwards differentiator are recreated by rendering from the original data separately from any samples created by the forwards differentiator (“a method that avoids storing the intermediate colors after each step and, thus, has a constant memory requirement. We exploit that the blending step is invertible (see Fig. 4): If α(i+1),C(i+1) are given and the current sample is recomputed to obtain α and C,α(i),C(i) can be reconstructed as [eq (10)] With Equation 10 and α<1, the adjoint pass can be computed with constant memory by re-evaluating the current sample ci and reconstructing colori instead of storing the intermediate results. Thus, only the output color used in the loss function needs to be stored, while all intermediate values are recomputed on-the-fly” Weiss, pg. 566 Col 1-2, section 4.4 The Inversion Trick, Fig. 4).
Regarding claim 4, Weiss teaches the system of claim 1 wherein the renderer is configured to create a 3D volume model representative of the rendered medical images (Weiss, Fig. 1, volume renderer; Fig. 9).
Regarding claim 5, Weiss teaches the system of claim 1, further comprising at least one optimizer, wherein the at least one optimizer is configured to optimize one or both of: the output of the backwards differentiator and/or the samples from the forwards differentiator (“In direct volume rendering, the pixel color represents the accumulated attenuated emissions at the sampling points along the view rays. In the model of the Wengert list (see Equation 2), a function fi is computed for each sample. Hence, the number of operations k is proportional to the overall number of samples along the rays... The last operation fk in the optimization process is the evaluation of a scalar-valued loss function” Weiss, pg. 564 Col 2, section 4.1 The Direct Volume Rendering Algorithm).
Regarding claim 6, Weiss teaches the system of claim 5, wherein the output of the optimizer is used to update a 3D volume model representative of the rendered medical images according to the output of the optimizer (“When Algorithm 1 is executed, the operations form the computational graph. AD considers this graph to compute the derivatives of xout with respect to the parameters Δt, cam, T, and V, so that the changes that should be applied to the parameters to optimize the loss function can be computed automatically. Our implementation allows for computing derivatives with respect to all parameters, yet due to space limitations, we restrict the discussion to the computation of derivatives of xout with respect to the camera cam, the TF T and the volume densities V” Weiss, pg. 564 Col 2, section 4.1 The Direct Volume Rendering Algorithm).
Regarding claim 7, Weiss teaches the system of claim 6, wherein the renderer is configured to apply a loss function to calculate losses and/or accuracy of the output of the forwards differentiator relative to one or more source images from the medical imaging data (“When Algorithm 1 is executed, the operations form the computational graph. AD considers this graph to compute the derivatives of xout with respect to the parameters Δt, cam, T, and V, so that the changes that should be applied to the parameters to optimize the loss function can be computed automatically. Our implementation allows for computing derivatives with respect to all parameters, yet due to space limitations, we restrict the discussion to the computation of derivatives of xout with respect to the camera cam, the TF T and the volume densities V” Weiss, pg. 564 Col 2, section 4.1 The Direct Volume Rendering Algorithm), and the losses and/or accuracy from the loss function is used by the optimizer to optimize the 3D volume model representative of the rendered medical images (Weiss, Fig. 2 and Fig. 3 Loss; pg. 566 Col 1, Algorithm 2 Adjoint Code of the DVR Algorithm. Each line corresponds to a line in Algorithm 1 in reverse order).
Regarding claim 8, Weiss teaches the system of claim 6, wherein the forwards differentiator is configured to perform differentiable rendering using forward differentiation of a rendering function of the 3D volume model to create the samples (“As an example (see Fig. 2 for a schematics), let us assume that derivatives should be computed with respect to a single entry in a 1D texture-based TF, e.g., the red channel of the first texel T0,red. When loading the TF from memory, T0,red is replaced by T~0,red=⟨T0,red,1⟩, i.e., it is wrapped in an instance of fvar with the derivative for that parameter set to 1... It is worth noting that in the above example only the derivative of one single texel in the TF is computed. This process needs to be repeated for each texel, respectively each color component of each texel, by extending the array fvar:: derivatives to store the required number of p parameters” Weiss, pg. 565 Col 1, section 4.2 forward differentiation, Fig. 2; wherein the texel(s) are color samples mapped onto 3D surface).
Regarding claim 9, Weiss teaches the system of any of claim 7, wherein the optimizer optimizes the 3D volume model representative of the rendered medical images based in part on the losses and/or accuracy of the output of the forwards differentiator (“When Algorithm 1 is executed, the operations form the computational graph. AD considers this graph to compute the derivatives of xout with respect to the parameters Δt, cam, T, and V, so that the changes that should be applied to the parameters to optimize the loss function can be computed automatically. Our implementation allows for computing derivatives with respect to all parameters, yet due to space limitations, we restrict the discussion to the computation of derivatives of xout with respect to the camera cam, the TF T and the volume densities V” Weiss, pg. 564 Col 2, section 4.1 The Direct Volume Rendering Algorithm; Weiss, Fig. 2 and Fig. 3 Loss).
Regarding claim 10, Weiss teaches the system of claim 1, wherein the renderer is operable to train a neural network representing or outputting some or all the rendering parameters (“This makes DiffDVR in particular interesting in combination with neural networks. Such networks might be used as loss functions - providing blackboxes, which steer DiffDVR to an optimal output for training purposes, e.g., to synthesize volume-rendered imagery for transfer learning tasks” Weiss, Pg. 570 Col 2, Conclusion).
Regarding claim 11, Weiss teaches a method of rendering medical images, the method comprising: receiving medical imaging data; and rendering medical images using the medical imaging data, wherein the rendering comprises (Weiss, Fig. 1 medical images are used in a fully differentiable direct volume renderer):
performing differentiable rendering using forward differentiation to create samples, wherein the samples created by the forward differentiation are colour and/or intensity samples (“As an example (see Fig. 2 for a schematics), let us assume that derivatives should be computed with respect to a single entry in a 1D texture-based TF, e.g., the red channel of the first texel T0,red. When loading the TF from memory, T0,red is replaced by T~0,red=⟨T0,red,1⟩, i.e., it is wrapped in an instance of fvar with the derivative for that parameter set to 1... It is worth noting that in the above example only the derivative of one single texel in the TF is computed. This process needs to be repeated for each texel, respectively each color component of each texel, by extending the array fvar:: derivatives to store the required number of p parameters” Weiss, pg. 565 Col 1, section 4.2 forward differentiation, Fig. 2; here, forward differentiation is used create color samples, e.g., derive color for each texel); and
performing differentiable rendering using backward differentiation on samples to generate at least one of: intensity projection, composition and/or rendering integration (“Adjoint differentiation, also called the adjoint method, backward or reverse mode differentiation, or backpropagation, evaluates the chain rule in the inverse order than forward differentiation... For each variable xi, the associated adjoint variable [eq. (6)] stores the derivative of the final output with respect to the current variable” Weiss, pg. 565 Col 1-2, section 4.3 Adjoint differentiation; here, adjoint differentiation obtains a final output, i.e., eq. (6), in which a parameter, or parameter(s) if used multiple times, are obtained once again, see Weiss pg. 565 Col 2. The parameters include that of color samples. Fig. 3 illustrates gradients in the adjoint variables (red) are propagated backward through algorithm 1, including summation of color blending; and wherein a composition is generated through algorithm 1 Direct Volume Rending Algorithm line 7 blending of the sample, and “a Riemann sum which can be computed in front-to-back order using iterative application of alpha-blending” Weiss, pg. 564 Col 1);
wherein the samples from the forward differentiable rendering and the output of the backwards differentiable rendering are used to form the rendered medical imaging data (Weiss, Fig. 3 illustrates a schematic representation of the adjoint method for density and TF reconstruction. Gradients in the adjoint variables (red) are propagated backward through the algorithm. A circled + indicates the summation of the gradients over all steps and rays; wherein the TF reconstruction is that of a forwards differentiator and a volume is rendered).
Regarding claim 12, Weiss teaches a non-transient computer readable medium comprising a computer program product, the computer program product being configured such that, when executed by a computer system, causes the computer system to perform a process comprising receiving medical imaging data (“performed on a system running Windows 10 and CUDA 11.1 with an Intel Xeon 8x@3.60Ghz CPU, 64GB RAM, and an NVIDIA RTX 2070” Weiss, pg. 566 Col 2); and rendering medical images using the medical imaging data, wherein the rendering comprises (Weiss, Fig. 1 medical images are used in a fully differentiable direct volume renderer):
performing differentiable rendering using forward differentiation to create samples, wherein the samples created by the forward differentiation are colour and/or intensity samples (“As an example (see Fig. 2 for a schematics), let us assume that derivatives should be computed with respect to a single entry in a 1D texture-based TF, e.g., the red channel of the first texel T0,red. When loading the TF from memory, T0,red is replaced by T~0,red=⟨T0,red,1⟩, i.e., it is wrapped in an instance of fvar with the derivative for that parameter set to 1... It is worth noting that in the above example only the derivative of one single texel in the TF is computed. This process needs to be repeated for each texel, respectively each color component of each texel, by extending the array fvar:: derivatives to store the required number of p parameters” Weiss, pg. 565 Col 1, section 4.2 forward differentiation, Fig. 2; here, forward differentiation is used create color samples, e.g., derive color for each texel); and
performing differentiable rendering using backward differentiation on samples to generate at least one of: intensity projection, composition and/or rendering integration (“Adjoint differentiation, also called the adjoint method, backward or reverse mode differentiation, or backpropagation, evaluates the chain rule in the inverse order than forward differentiation... For each variable xi, the associated adjoint variable [eq. (6)] stores the derivative of the final output with respect to the current variable” Weiss, pg. 565 Col 1-2, section 4.3 Adjoint differentiation; here, adjoint differentiation obtains a final output, i.e., eq. (6), in which a parameter, or parameter(s) if used multiple times, are obtained once again, see Weiss pg. 565 Col 2. The parameters include that of color samples. Fig. 3 illustrates gradients in the adjoint variables (red) are propagated backward through algorithm 1, including summation of color blending; and wherein a composition is generated through algorithm 1 Direct Volume Rending Algorithm line 7 blending of the sample, and “a Riemann sum which can be computed in front-to-back order using iterative application of alpha-blending” Weiss, pg. 564 Col 1);
wherein the samples from the forward differentiable rendering and the output of the backwards differentiable rendering are used to form the rendered medical imaging data (Weiss, Fig. 3 illustrates a schematic representation of the adjoint method for density and TF reconstruction. Gradients in the adjoint variables (red) are propagated backward through the algorithm. A circled + indicates the summation of the gradients over all steps and rays; wherein the TF reconstruction is that of a forwards differentiator and a volume is rendered).
Conclusion
The prior art made of record and not relied upon is considered pertinent to applicant's disclosure.
Remi B (“An overview of differential rendering”, 2022) – discloses differentiable rendering techniques including optimizations and integration to neural network pipelines, solve inverse graphics problems such as 3D reconstruction from 2D images.
Zhang (“Medical volume reconstruction techniques”, 2018) – optimization of volume rendering techniques including alpha-blending rendering, maximum intensity projection (MIP) and direct volume rendering, the scalar value given at a sample point is virtually mapped to physical quantities that describe the emission and absorption of light at that point.
Spielberg et al. (“Differentiable Visual Computing for Inverse Problems and Machine Learning”, 2023) – Fig. 2 forward pass and backward pass, automatic differentiation to transform forward models into backward models useful for gradient-based optimization.
BUDZ et al. (US 20220122717 A1) – 3D medical data comprising volumetric data rendered from a set of two-dimensional (2D) images in one or more imaging planes, determining a composite representation of volume rendering; Along rays, RGBA values are determined for sampling points from the voxels and combined to form pixels for a two-dimensional image by way of alpha compositing or alpha blending.
Hasselgren et al. (US 20230316631 A1) – 3D model optimization system 100 finds a global texture and a constructed 3D model 130, that when rendered from a camera position 114 associated with the reference image 112, produce a rendered image 115 that matches the reference image 112.
Sudarsky et al. (US 20190147639 A1) – a multi-dimensional transfer function are determined based on one or more (e.g., different) characteristics of the intensities of the voxels of the subset. For example, the scalar values, local gradients of the scalar values, and curvature represented by the scalar values of the voxels of the subset are mapped or related by a function to the transfer function. Different transfer functions are provided for different combinations of distribution of scalar values, gradients, and/or curvature.
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/EMMANUEL SILVA-AVINA/Examiner, Art Unit 2673
/CHINEYERE WILLS-BURNS/Supervisory Patent Examiner, Art Unit 2673
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