Prosecution Insights
Last updated: April 19, 2026
Application No. 18/528,670

NULL-DENSITY-BASED SAMPLING FOR VOLUMETRIC RENDERING

Non-Final OA §103§Other
Filed
Dec 04, 2023
Examiner
CHEN, BIAO
Art Unit
2611
Tech Center
2600 — Communications
Assignee
Disney Enterprises Inc.
OA Round
2 (Non-Final)
84%
Grant Probability
Favorable
2-3
OA Rounds
2y 5m
To Grant
99%
With Interview

Examiner Intelligence

Grants 84% — above average
84%
Career Allow Rate
27 granted / 32 resolved
+22.4% vs TC avg
Strong +26% interview lift
Without
With
+26.3%
Interview Lift
resolved cases with interview
Typical timeline
2y 5m
Avg Prosecution
25 currently pending
Career history
57
Total Applications
across all art units

Statute-Specific Performance

§101
4.7%
-35.3% vs TC avg
§103
69.1%
+29.1% vs TC avg
§102
9.8%
-30.2% vs TC avg
§112
15.7%
-24.3% vs TC avg
Black line = Tech Center average estimate • Based on career data from 32 resolved cases

Office Action

§103 §Other
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 . 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. Claims 1 and 5-9 are rejected under 35 U.S.C. 103 as being unpatentable over APPA (Applicant Admitted Prior Art, Applicant’s specification for this application, hereinafter “AAPA”, and all the paragraph numbers used in citations is from PGPub “US 20250182383 A1”) in view of Miller et al. (A null-scattering path integral formulation of light transport, ACM Trans. Graph., Vol. 38, No. 4, Article 44. Publication date: July 2019, hereinafter “Miller”). Regarding claim 1, AAPA discloses A computer-implemented method for rendering a volumetric medium, the method comprising: (AAPA, para. [0002], “Volumetric rendering refers to the process of generating images that depict the propagation of light within a three-dimensional (3D) volumetric medium occupied by a certain type of material or object”). determining a null density for the volumetric medium based on a real density of the volumetric medium and an upper bound on a density of the volumetric medium; (AAPA, para. [0003], “Certain state-of-the-art techniques for performing volumetric rendering, which are referred to as null-collision approaches, determine absorption, emission, scattering, and/or other interactions between light and matter using predefined upper bounds (which can also be referred to as "majorants" or "bounding extinctions") on the density of the volumetric media at various points or regions in the 3D volume”). Note that: (1) the "majorants" or "bounding extinctions" are the predefined upper bounds of the density for the volumetric medium; (2) the combination of densities for absorption and scattering is a real density for the volumetric medium; and (3) a null density is the difference between a predefined upper bound and the real density. However, AAPA does not discloses, but in the same art of computer graphics, Miller discloses determining a distance associated with a ray based on the null density; (Miller, page 44:3, col. left, para. 1, “Formally, we introduce the combined extinction medium coefficient PNG media_image1.png 32 208 media_image1.png Greyscale ”; page 44:8, col. left, para. 4, “Kutz et al. [2017] proposed sampling distances according to a combined extinction PNG media_image2.png 28 24 media_image2.png Greyscale that bounds the extinctions of all color components along with carefully chosen event type probabilities to limit the variance of the estimate ⟨Ic ⟩ of each component. This conservative technique eliminates the color noise, but the dense sampling can significantly increase the computational cost when one channel has medium density significantly higher than the rest. Our framework allows us to track all color components together using distances sampled from extinctions that bound only an individual channel, while mitigating the potential for higher variance using MIS”). Note that: distances (or a distance) along a ray can be sampled or determined by a combined extinction PNG media_image2.png 28 24 media_image2.png Greyscale that bounds the extinctions of all color components while PNG media_image2.png 28 24 media_image2.png Greyscale includes the null density PNG media_image3.png 36 60 media_image3.png Greyscale . computing a transmittance associated with the distance; and (Miller, page 44:2, col. right, para. 2, “ PNG media_image4.png 198 652 media_image4.png Greyscale ”). Note that: a transmittance T(x,y) can be computed by the exponential function of the integral of PNG media_image5.png 22 26 media_image5.png Greyscale with the distance between points x and y while the distance is sampled or determined above. rendering the volumetric medium based on the transmittance. (Miller, page 44:2, col. right, para. 2, “ PNG media_image6.png 580 658 media_image6.png Greyscale ”). Note that: (1) Equation 3 above is the volume rendering equation (VRE) for a volumetric rendering of the volumetric medium; and (2) the transmittance indicated by Equation 5 above is a part of Equation 3. AAPA and Miller are in the same field of endeavor, namely computer graphics. Before the effective filing date of the claimed invention, it would have been obvious to apply determining distance based on null density, computing transmittance, and rendering a volumetric medium, as taught by Miller into AAPA. The motivation would have been “We demonstrate the practicality of our theory by combining, for the first time, several path sampling techniques in spatially and spectrally varying media, generalizing and outperforming the prior state of the art.” (Miller, page 33:1, col. left, para. 1). The suggestion for doing so would allow to improve rendering quality and speed and outperforming the prior state of the art. Therefore, it would have been obvious to combine AAPA and Miller. Regarding claim 5, AAPA in view of Miller discloses The computer-implemented method of claim 1, further comprising: sampling an additional distance associated with the ray based on an additional null density for the volumetric medium; and (Miller, “Formally, we introduce the combined extinction medium coefficient PNG media_image1.png 32 208 media_image1.png Greyscale ”; page 44:8, col. left, para. 4, “Kutz et al. [2017] proposed sampling distances according to a combined extinction PNG media_image2.png 28 24 media_image2.png Greyscale that bounds the extinctions of all color components along with carefully chosen event type probabilities to limit the variance of the estimate ⟨Ic ⟩ of each component. This conservative technique eliminates the color noise, but the dense sampling can significantly increase the computational cost when one channel has medium density significantly higher than the rest. Our framework allows us to track all color components together using distances sampled from extinctions that bound only an individual channel, while mitigating the potential for higher variance using MIS”). Note that: (1) distances (or a distance) along a ray can be sampled or determined by a combined extinction PNG media_image2.png 28 24 media_image2.png Greyscale that bounds the extinctions of all color components while PNG media_image2.png 28 24 media_image2.png Greyscale includes the null density PNG media_image3.png 36 60 media_image3.png Greyscale ; and (2) it is obvious to one having ordinary skills in the art that an additional distance can be sampled or determined with an additional combined extinction PNG media_image2.png 28 24 media_image2.png Greyscale that bounds the extinctions of all color components while PNG media_image2.png 28 24 media_image2.png Greyscale includes a corresponding additional null density PNG media_image3.png 36 60 media_image3.png Greyscale . updating the transmittance based on the additional distance. (Miller, page 44:2, col. right, para. 2, “ PNG media_image4.png 198 652 media_image4.png Greyscale ”). Note that: an additional transmittance T(x,y) can be updated or multiplied by the exponential function of the integral of PNG media_image5.png 22 26 media_image5.png Greyscale with the additional distance between additional points x and y while the additional distance is sampled or determined above. The motivation to combine AAPA and Miller given in claim 1 is incorporated here. Regarding claim 6, AAPA in view of Miller discloses The computer-implemented method of claim 5, further comprising determining the additional null density based on an additional real density of the volumetric medium at a location corresponding to the distance. (AAPA, para. [0003], “Certain state-of-the-art techniques for performing volumetric rendering, which are referred to as null-collision approaches, determine absorption, emission, scattering, and/or other interactions between light and matter using predefined upper bounds (which can also be referred to as "majorants" or "bounding extinctions") on the density of the volumetric media at various points or regions in the 3D volume”). Note that: (1) the "majorants" or "bounding extinctions" are the predefined upper bounds of the density for the volumetric medium; (2) the combination of densities for absorption and scattering is a real density for the volumetric medium; (3) a null density is the difference between a predefined upper bound and the real density at a point x in the medium; and (4) it is obvious to one having ordinary skills in the art that the additional null density can be determined at a location or a point x in the medium while the point x is corresponding to the distance. In other words, the null density is location-based and point is on the path of the ray. Regarding claim 7, AAPA in view of Miller discloses The computer-implemented method of claim 1, further comprising: sampling an additional distance associated with an additional ray based on an additional null density for the volumetric medium; (Miller, page 44:3, col. left, para. 1, “Formally, we introduce the combined extinction medium coefficient PNG media_image1.png 32 208 media_image1.png Greyscale ”; page 44:8, col. left, para. 4, “Kutz et al. [2017] proposed sampling distances according to a combined extinction PNG media_image2.png 28 24 media_image2.png Greyscale that bounds the extinctions of all color components along with carefully chosen event type probabilities to limit the variance of the estimate ⟨Ic ⟩ of each component. This conservative technique eliminates the color noise, but the dense sampling can significantly increase the computational cost when one channel has medium density significantly higher than the rest. Our framework allows us to track all color components together using distances sampled from extinctions that bound only an individual channel, while mitigating the potential for higher variance using MIS”). Note that: (1) distances (or a distance) along a ray can be sampled or determined by a combined extinction PNG media_image2.png 28 24 media_image2.png Greyscale that bounds the extinctions of all color components while PNG media_image2.png 28 24 media_image2.png Greyscale includes the null density PNG media_image3.png 36 60 media_image3.png Greyscale ; and (2) it is obvious to one having ordinary skills in the art that an additional distance can be sampled or determined with an additional combined extinction PNG media_image2.png 28 24 media_image2.png Greyscale that bounds the extinctions of all color components while PNG media_image2.png 28 24 media_image2.png Greyscale includes a corresponding additional null density PNG media_image3.png 36 60 media_image3.png Greyscale . computing an additional transmittance using the additional distance; and (Miller, page 44:2, col. right, para. 2, “ PNG media_image4.png 198 652 media_image4.png Greyscale ”). Note that: an additional transmittance T(x,y) can be updated or multiplied by the exponential function of the integral of PNG media_image5.png 22 26 media_image5.png Greyscale with the additional distance between additional points x and y while the additional distance is sampled or determined above. further rendering the volumetric medium based on the additional transmittance. (Miller, page 44:2, col. right, para. 2, “ PNG media_image6.png 580 658 media_image6.png Greyscale ”). Note that: (1) Equation 3 above is the volume rendering equation (VRE) for a volumetric rendering of the volumetric medium; (2) the transmittance indicated by Equation 5 above is a part of Equation 3; and (3) after the additional transmittance has been updated, the rendering by Equation 3 is can be further performed. The motivation to combine AAPA and Miller given in claim 1 is incorporated here. Regarding claim 8, AAPA in view of Miller discloses The computer-implemented method of claim 1, wherein computing the transmittance comprises evaluating an exponential function using the null density. (Miller, page 44:2, col. right, para. 2, “ PNG media_image4.png 198 652 media_image4.png Greyscale ”). Note that: a transmittance T(x,y) can be computed by the exponential function of the integral of PNG media_image5.png 22 26 media_image5.png Greyscale with the distance between points x and y while the distance is sampled or determined above. The motivation to combine AAPA and Miller given in claim 1 is incorporated here. Regarding claim 9, AAPA in view of Miller discloses The computer-implemented method of claim 1, wherein determining the distance comprises limiting the distance to a remaining distance between a current location associated with the ray and an end of the volumetric medium. (Miller, page 44:3, col. left, para. 1, “Formally, we introduce the combined extinction medium coefficient PNG media_image1.png 32 208 media_image1.png Greyscale ”; page 44:8, col. left, para. 4, “Kutz et al. [2017] proposed sampling distances according to a combined extinction PNG media_image2.png 28 24 media_image2.png Greyscale that bounds the extinctions of all color components along with carefully chosen event type probabilities to limit the variance of the estimate ⟨Ic ⟩ of each component. This conservative technique eliminates the color noise, but the dense sampling can significantly increase the computational cost when one channel has medium density significantly higher than the rest. Our framework allows us to track all color components together using distances sampled from extinctions that bound only an individual channel, while mitigating the potential for higher variance using MIS”). Note that: (1) distances (or a distance) along a ray can be sampled or determined by a combined extinction PNG media_image2.png 28 24 media_image2.png Greyscale that bounds the extinctions of all color components while PNG media_image2.png 28 24 media_image2.png Greyscale includes the null density PNG media_image3.png 36 60 media_image3.png Greyscale ; and (2) it obvious to one having ordinary skills in the art that the distances are sampled or determined so that the sampled distance should along the ray and within the volumetric volume. Since the previous sampled distance has been used for calculation of transmittance, the to-be-sampled distance along the ray should be within the remaining distance between a current point and the intersection point of the ray and end of the volumetric medium. The motivation to combine AAPA and Miller given in claim 1 is incorporated here. Claim 10 is rejected under 35 U.S.C. 103 as being unpatentable over AAPA in view of Miller, and further in view of ARCHIVE_ORG (The inverse CDF is x = –log(1–u), https://web.archive.org/web/20150905193736/https://blogs.sas.com/content/iml/2013/07/22/the-inverse-cdf-method.html, hereinafter “ARCHIVE_ORG”). Regarding claim 10, AAPA in view of Miller discloses The computer-implemented method of claim 1, wherein the distance is sampled (Miller, page 44:3, col. left, para. 1, “Formally, we introduce the combined extinction medium coefficient PNG media_image1.png 32 208 media_image1.png Greyscale ”; page 44:8, col. left, para. 4, “Kutz et al. [2017] proposed sampling distances according to a combined extinction PNG media_image2.png 28 24 media_image2.png Greyscale that bounds the extinctions of all color components along with carefully chosen event type probabilities to limit the variance of the estimate ⟨Ic ⟩ of each component. This conservative technique eliminates the color noise, but the dense sampling can significantly increase the computational cost when one channel has medium density significantly higher than the rest. Our framework allows us to track all color components together using distances sampled from extinctions that bound only an individual channel, while mitigating the potential for higher variance using MIS”). Note that: distances (or a distance) along a ray can be sampled or determined by a combined extinction PNG media_image2.png 28 24 media_image2.png Greyscale that bounds the extinctions of all color components while PNG media_image2.png 28 24 media_image2.png Greyscale includes the null density PNG media_image3.png 36 60 media_image3.png Greyscale . However, AAPA in view Miller fails to disclose, but in the same art of computer graphics, ARCHIVE_ORG discloses from an inverted cumulative distribution function (ARCHIVE_ORG, page 1, lines 6-10, “To illustrate the inverse CDF sampling technique (also called the inverse transformation algorithm), consider sampling from a standard exponential distribution. The exponential distribution has probability density f(x) = e–x, x ≥ 0, and therefore the cumulative distribution is the integral of the density: F(x) = 1 – e–x. This function can be explicitly inverted by solving for x in the equation F(x) = u. The inverse CDF is x = –log(1–u)”). Note that: (1) The inverse CDF is the same as an inverted cumulative distribution function; and (2) the inverse CDF is –log(1–u), can be used for sampling distances. AAPA in view Miller, and ARCHIVE_ORG, are in the same field of endeavor, namely computer graphics. Before the effective filing date of the claimed invention, it would have been obvious to apply the inverted cumulative distribution function, as taught by ARCHIVE_ORG into AAPA in view Miller. The motivation would have been “The inverse CDF is x = –log(1–u)” (ARCHIVE_ORG, page 1, line 10). The suggestion for doing so would allow them to sample distances from an inverted cumulative distribution function that is parameterized using the null density. Therefore, it would have been obvious to combine AAPA, Miller, and ARCHIVE_ORG. Claims 11, 14, and 18-20 are rejected under 35 U.S.C. 103 as being unpatentable over AAPA in view of Miller, and further in view of Peng et al. (US 20200007914 A1, hereinafter “Peng”). Claim 11 reciting “One or more non-transitory computer-readable media storing instructions that, when executed by one or more processors, cause the one or more processors to perform the steps of:” is corresponding to the method of claims 1. Therefore, claim 11 is rejected with the same prior art and citations for claim 1. However, AAPA in view of Miller fails to disclose, but in the same art of computer graphics, Peng discloses One or more non-transitory computer-readable media storing instructions that, when executed by one or more processors, cause the one or more processors to perform the steps of: (Peng, page 8, para. [0123], “A non-transitory computer readable storage medium is provided. The non-transitory computer readable storage medium is configured to store a computer program which, when executed by a processor, causes the processor to carry out following actions”). AAPA in view of Miller, and Peng, are in the same field of endeavor, namely computer graphics. Before the effective filing date of the claimed invention, it would have been obvious to apply a non-transitory computer-readable media storing instructions, as taught by Peng into AAPA in view of Miller. The motivation would have been “A non-transitory computer readable storage medium is provided. The non-transitory computer readable storage medium is configured to store a computer program which, when executed by a processor, causes the processor to carry out following actions” (Peng, page 8, para. [0123]). The suggestion for doing so would allow to have a non-transitory computer-readable media storing instructions. Therefore, it would have been obvious to combine AAPA, Miller, and Peng. Regarding claim 14, the combination of AAPA, Miller, and Peng discloses The one or more non-transitory computer-readable media of claim 11, wherein the instructions further cause the one or more processors to perform the steps of: determining an additional null density for the volumetric medium based on an additional real density of the volumetric medium and an additional upper bound on the density of the volumetric medium; and (AAPA, para. [0003], “Certain state-of-the-art techniques for performing volumetric rendering, which are referred to as null-collision approaches, determine absorption, emission, scattering, and/or other interactions between light and matter using predefined upper bounds (which can also be referred to as "majorants" or "bounding extinctions") on the density of the volumetric media at various points or regions in the 3D volume”). Note that: (1) the "majorants" or "bounding extinctions" are the predefined upper bounds of the density for the volumetric medium; (2) the combination of densities for absorption and scattering is a real density for the volumetric medium; (3) a null density is the difference between a predefined upper bound and the real density; and (4) In the same fashion one can determine an additional null density for the volumetric medium based on an additional real density of the volumetric medium and an additional upper bound on the density of the volumetric medium for the points at additional distance. further rendering the volumetric medium based on an additional transmittance (Miller, page 44:2, col. right, para. 2, “ PNG media_image6.png 580 658 media_image6.png Greyscale ”). Note that: (1) Equation 3 above is the volume rendering equation (VRE) for a volumetric rendering of the volumetric medium; (2) the transmittance indicated by Equation 5 above is a part of Equation 3; and (3) In the same fashion one can render the volumetric medium based on an additional transmittance computed or determined with using the additional null density. that is determined using the additional null density (Miller, page 44:3, col. left, para. 1, “Formally, we introduce the combined extinction medium coefficient PNG media_image1.png 32 208 media_image1.png Greyscale ”; page 44:8, col. left, para. 4, “Kutz et al. [2017] proposed sampling distances according to a combined extinction PNG media_image2.png 28 24 media_image2.png Greyscale that bounds the extinctions of all color components along with carefully chosen event type probabilities to limit the variance of the estimate ⟨Ic ⟩ of each component. This conservative technique eliminates the color noise, but the dense sampling can significantly increase the computational cost when one channel has medium density significantly higher than the rest. Our framework allows us to track all color components together using distances sampled from extinctions that bound only an individual channel, while mitigating the potential for higher variance using MIS”). Note that: (1) distances (or a distance) along a ray can be sampled or determined by a combined extinction PNG media_image2.png 28 24 media_image2.png Greyscale that bounds the extinctions of all color components while PNG media_image2.png 28 24 media_image2.png Greyscale includes the null density PNG media_image3.png 36 60 media_image3.png Greyscale ; and (2) in the same fashion one can compute or determine the additional transmittance using the additional null density. Claim 18 is corresponding to the method of claim 9. Therefore, claim 18 is rejected for the same rationale for claim 9. Regarding claim 19, the combination of AAPA, Miller, and Peng discloses The one or more non-transitory computer-readable media of claim 11, wherein computing the transmittance comprises evaluating an exponential function using the null density and the distance. (Miller, page 44:3, col. left, para. 1, “Formally, we introduce the combined extinction medium coefficient PNG media_image1.png 32 208 media_image1.png Greyscale ”; page 44:2, col. right, para. 2, “ PNG media_image4.png 198 652 media_image4.png Greyscale ”). Note that: (1) an transmittance T(x,y) can be computed or evaluated by the exponential function of the integral of PNG media_image5.png 22 26 media_image5.png Greyscale (x) (= PNG media_image7.png 26 52 media_image7.png Greyscale - PNG media_image3.png 36 60 media_image3.png Greyscale ) with the distance between additional points x and y while the additional distance is sampled or determined above; (2) Since PNG media_image5.png 22 26 media_image5.png Greyscale (x) = PNG media_image7.png 26 52 media_image7.png Greyscale - PNG media_image3.png 36 60 media_image3.png Greyscale , where PNG media_image7.png 26 52 media_image7.png Greyscale is combined extinction and PNG media_image3.png 36 60 media_image3.png Greyscale is the null density, the exponential function uses both of the null density and the distance. Claim 20 reciting “A system, comprising: one or more memories that store instructions, and one or more processors that are coupled to the one or more memories and, when executing the instructions, are configured to perform the steps of:”, is corresponding to the method of claim 1. Therefore, claim 20 is rejected with the prior art and corresponding citations for claim 1. In addition, the combination of AAPA, Miller, and Peng discloses A system, comprising: one or more memories that store instructions, and one or more processors that are coupled to the one or more memories and, when executing the instructions, are configured to perform the steps of: (Peng, page 9, claim 8, “An electronic device, comprising: at least one processor; and a computer readable storage, coupled to the at least one processor and storing at least one computer executable instruction thereon which, when executed by the at least one processor, causes the at least one processor to”). Note that: the electronic system cited here is an apparatus. AAPA in view of Miller, and Peng, are in the same field of endeavor, namely computer graphics. Before the effective filing date of the claimed invention, it would have been obvious to apply a system comprising memories and processors executing instructions in memories, as taught by Peng into AAPA in view of Miller. The motivation would have been “An electronic device, comprising: at least one processor; and a computer readable storage, coupled to the at least one processor and storing at least one computer executable instruction thereon which, when executed by the at least one processor, causes the at least one processor to” (Peng, page 9, claim 8). The suggestion for doing so would allow to have a system comprising memories and processors executing instructions in memories. Therefore, it would have been obvious to combine AAPA, Miller and Peng. Claim 17 is rejected under 35 U.S.C. 103 as being unpatentable over AAPA in view of Miller and Peng, and further in view of ARCHIVE_ORG. Regarding claim 17, the combination of AAPA, Miller, and Peng discloses The one or more non-transitory computer-readable media of claim 11, wherein the distance is sampled (Miller, page 44:3, col. left, para. 1, “Formally, we introduce the combined extinction medium coefficient PNG media_image1.png 32 208 media_image1.png Greyscale ”; page 44:8, col. left, para. 4, “Kutz et al. [2017] proposed sampling distances according to a combined extinction PNG media_image2.png 28 24 media_image2.png Greyscale that bounds the extinctions of all color components along with carefully chosen event type probabilities to limit the variance of the estimate ⟨Ic ⟩ of each component. This conservative technique eliminates the color noise, but the dense sampling can significantly increase the computational cost when one channel has medium density significantly higher than the rest. Our framework allows us to track all color components together using distances sampled from extinctions that bound only an individual channel, while mitigating the potential for higher variance using MIS”). Note that: distances (or a distance) along a ray can be sampled or determined by a combined extinction PNG media_image2.png 28 24 media_image2.png Greyscale that bounds the extinctions of all color components while PNG media_image2.png 28 24 media_image2.png Greyscale includes the null density PNG media_image3.png 36 60 media_image3.png Greyscale . However, the combination of AAPA, Miller, and Peng fails to disclose, but in the same art of computer graphics, ARCHIVE_ORG discloses from an exponential distribution (ARCHIVE_ORG, page 1, lines 5-6, “consider sampling from a standard exponential distribution. The exponential distribution has probability density f(x) = e–x, x ≥ 0”). Note that: sampling from a standard exponential distribution is taught here. The combination of AAPA, Miller, and Peng, and ARCHIVE_ORG, are in the same field of endeavor, namely computer graphics. Before the effective filing date of the claimed invention, it would have been obvious to apply sampling from a standard exponential distribution, as taught by ARCHIVE_ORG into the combination of AAPA, Miller, and Peng. The motivation would have been “consider sampling from a standard exponential distribution. The exponential distribution has probability density f(x) = e–x, x ≥ 0” (ARCHIVE_ORG, page 1, lines 5-6). The suggestion for doing so would allow them to sample distances from an exponential distribution that is parameterized using the null density. Therefore, it would have been obvious to combine AAPA, Miller, Peng, and ARCHIVE_ORG. Allowable Subject Matter Claims 2-4, 12-13, and 15-16 are objected to as being dependent upon a rejected base claim, but would be allowable if rewritten in independent form including all of the limitations of the base claim and any intervening claims. Regarding dependent claim 2, in the context of claim as a whole, the prior art either alone or in combination does not teach or suggest the additional elements of: “computing a clamped real density as a lower of the real density and the upper bound; and computing the null density as a difference between the upper bound and the clamped real density”. Regarding dependent claim 3, in the context of claim as a whole, the prior art either alone or in combination does not teach or suggest the additional elements of: “computing the upper bound as a higher of (i) an additional upper bound on the density of the volumetric medium and (ii) a sum of an additional real density of the volumetric medium and a positive constant”. Claim 4 depends from claim 3. Regarding dependent claim 12, in the context of claim as a whole, the prior art either alone or in combination does not teach or suggest the additional elements of: “computing a clamped real density as a lower of the real density and the upper bound; and computing the null density as a difference between the upper bound and the clamped real density”. Claim 13 depends from claim 12. Regarding dependent claim 15, in the context of claim as a whole, the prior art either alone or in combination does not teach or suggest the additional elements of: “the volumetric medium is rendered as an average of a first set of pixel values associated with the upper bound and a second set of pixel values associated with the additional upper bound”. Regarding dependent claim 16, in the context of claim as a whole, the prior art either alone or in combination does not teach or suggest the additional elements of: “computing the upper bound as a maximum of (i) an additional upper bound on the density of the volumetric medium and (ii) a sum of an additional real density of the volumetric medium and a positive constant”. Response to Arguments Applicant's arguments with respect to claim rejection 35 U.S.C. 102 and claim rejection 35 U.S.C. 103 have been fully considered but they are not persuasive. Applicant alleges, “The disclosure of Misso et al. was made on August 6-10, 2023, less than one year before the effective filing date of the claimed invention. The joint inventors are coauthors of the cited reference, and the subject matter disclosed in the cited reference was obtained from one or more joint inventors of the claimed invention. Applicant is submitting a declaration under 37 C.F.R. § 1.130(a) herewith to invoke the exception provided by 35 U.S.C. § 102(b)(1)(A), thereby disqualifying the cited reference as prior art. Accordingly, Applicant submits that independent claims 1, 11, and 20, and the corresponding dependent claims, are in condition for allowance.” (page 6 / line 26 - page 7 / line 5). Examiner agrees that Misso fails to be qualified as a prior art due to a declaration under 37 C.F.R. § 1.130(a) from Applicant. However, Examiner respectfully disagrees about the respective allegations as whole because: AAPA discloses A computer-implemented method for rendering a volumetric medium, the method comprising: (AAPA, para. [0002], “Volumetric rendering refers to the process of generating images that depict the propagation of light within a three-dimensional (3D) volumetric medium occupied by a certain type of material or object”). determining a null density for the volumetric medium based on a real density of the volumetric medium and an upper bound on a density of the volumetric medium; (AAPA, para. [0003], “Certain state-of-the-art techniques for performing volumetric rendering, which are referred to as null-collision approaches, determine absorption, emission, scattering, and/or other interactions between light and matter using predefined upper bounds (which can also be referred to as "majorants" or "bounding extinctions") on the density of the volumetric media at various points or regions in the 3D volume”). Note that: (1) the "majorants" or "bounding extinctions" are the predefined upper bounds of the density for the volumetric medium; (2) the combination of densities for absorption and scattering is a real density for the volumetric medium; and (3) a null density is the difference between a predefined upper bound and the real density. However, AAPA does not discloses, but in the same art of computer graphics, Miller discloses determining a distance associated with a ray based on the null density; (Miller, page 44:3, col. left, para. 1, “Formally, we introduce the combined extinction medium coefficient PNG media_image1.png 32 208 media_image1.png Greyscale ”; page 44:8, col. left, para. 4, “Kutz et al. [2017] proposed sampling distances according to a combined extinction PNG media_image2.png 28 24 media_image2.png Greyscale that bounds the extinctions of all color components along with carefully chosen event type probabilities to limit the variance of the estimate ⟨Ic ⟩ of each component. This conservative technique eliminates the color noise, but the dense sampling can significantly increase the computational cost when one channel has medium density significantly higher than the rest. Our framework allows us to track all color components together using distances sampled from extinctions that bound only an individual channel, while mitigating the potential for higher variance using MIS”). Note that: distances (or a distance) along a ray can be sampled or determined by a combined extinction PNG media_image2.png 28 24 media_image2.png Greyscale that bounds the extinctions of all color components while PNG media_image2.png 28 24 media_image2.png Greyscale includes the null density PNG media_image3.png 36 60 media_image3.png Greyscale . computing a transmittance associated with the distance; and (Miller, page 44:2, col. right, para. 2, “ PNG media_image4.png 198 652 media_image4.png Greyscale ”). Note that: a transmittance T(x,y) can be computed by the exponential function of the integral of PNG media_image5.png 22 26 media_image5.png Greyscale with the distance between points x and y while the distance is sampled or determined above. rendering the volumetric medium based on the transmittance. (Miller, page 44:2, col. right, para. 2, “ PNG media_image6.png 580 658 media_image6.png Greyscale ”); Note that: (1) Equation 3 above is the volume rendering equation (VRE) for a volumetric rendering of the volumetric medium; and (2) the transmittance indicated by Equation 5 above is a part of Equation 3. AAPA and Miller are in the same field of endeavor, namely computer graphics. Before the effective filing date of the claimed invention, it would have been obvious to apply determining distance based on null density, computing transmittance, and rendering a volumetric medium, as taught by Miller into AAPA. The motivation would have been “We demonstrate the practicality of our theory by combining, for the first time, several path sampling techniques in spatially and spectrally varying media, generalizing and outperforming the prior state of the art.” (Miller, page 33:1, col. left, para. 1). The suggestion for doing so would allow to improve rendering quality and speed and outperforming the prior state of the art. Therefore, it would have been obvious to combine AAPA and Miller. AAPA in view of Miller discloses all limitations of independent claim 1 for claim rejection 35 U.S.C. Independent claims 11 and 20 are corresponding to the method of claim 1, respectively. Therefore, claim 11 and 20 are rejected for the same rationale for claim 1, respectively. Please see the details of prior art and citations for claim rejection of claims 11 and 20 above, respectively. The arguments are not persuasive. Conclusion Any inquiry concerning this communication or earlier communications from the examiner should be directed to BIAO CHEN whose telephone number is (703)756-1199. The examiner can normally be reached M-F 8am-5pm ET. Examiner interviews are available via telephone, in-person, and video conferencing using a USPTO supplied web-based collaboration tool. To schedule an interview, applicant is encouraged to use the USPTO Automated Interview Request (AIR) at http://www.uspto.gov/interviewpractice. If attempts to reach the examiner by telephone are unsuccessful, the examiner’s supervisor, Kee M Tung can be reached at (571)272-7794. The fax phone number for the organization where this application or proceeding is assigned is 571-273-8300. Information regarding the status of published or unpublished applications may be obtained from Patent Center. Unpublished application information in Patent Center is available to registered users. To file and manage patent submissions in Patent Center, visit: https://patentcenter.uspto.gov. Visit https://www.uspto.gov/patents/apply/patent-center for more information about Patent Center and https://www.uspto.gov/patents/docx for information about filing in DOCX format. For additional questions, contact the Electronic Business Center (EBC) at 866-217-9197 (toll-free). If you would like assistance from a USPTO Customer Service Representative, call 800-786-9199 (IN USA OR CANADA) or 571-272-1000. /Biao Chen/ Patent Examiner, Art Unit 2611 /KEE M TUNG/Supervisory Patent Examiner, Art Unit 2611
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Prosecution Timeline

Dec 04, 2023
Application Filed
Aug 14, 2025
Non-Final Rejection — §103, §Other
Nov 19, 2025
Response after Non-Final Action
Nov 19, 2025
Response Filed
Jan 15, 2026
Non-Final Rejection — §103, §Other (current)

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Study what changed to get past this examiner. Based on 5 most recent grants.

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2-3
Expected OA Rounds
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99%
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2y 5m
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