# US 12,182,933 B2 · Methods and systems for rendering subsurface scattering > Agents: this data is available as JSON from the patentgrep API and MCP server — see https://patentgrep.com/llms.txt - Number: US 12,182,933 B2 - Document ID: US12182933B2 - Status: Granted - Kind: B2 - Application number: 18/152,630 - Filed: 2023-01-10 - Published: 2024-07-11 - Granted: 2024-12-31 - Earliest claimed: 2023-01-10 - Assignees: Huawei Cloud Computing Technologies Co., Ltd. - Applicants: Wei Sen Loi; Li Li - Inventors: Wei Sen Loi; Li Li - Web page: https://patentgrep.com/patent/US12182933B2 ## CPC - G06T 15/506: {Illumination models} - G06T 2200/24: involving graphical user interfaces [GUIs] - G06T: IMAGE DATA PROCESSING OR GENERATION, IN GENERAL ## Abstract A method and computing system for rendering subsurface scattering are provided. An optical property and a thickness are received for each of a plurality of material layers. A latent space is trained for each of the plurality of material layers. A global transfer matrix is generated for at least one multi-layer material, each of the at least one multi-layer material including an ordered set of material layers selected from the plurality of material layers, by determining a transfer matrix for each adjacent pair of material layers in the ordered set of material layers using the latent space for each material layer in the adjacent pair of material layers, the transfer matrix describing angular and azimuthal reflectance and angular and azimuthal transmittance, and determining the global transfer matrix as a product of the transfer matrices of each adjacent pair of material layers. ## Claims ### Claim 1 A computer-implemented method for rendering subsurface scattering, comprising: receiving an optical property and a thickness for each of a plurality of material layers; training a latent space for each of the plurality of material layers; generating a global transfer matrix for at least one multi-layer material, each of the at least one multi-layer material including an ordered set of material layers selected from the plurality of material layers, by: determining a transfer matrix for each adjacent pair of material layers in the ordered set of material layers using the latent space for each material layer in the adjacent pair of material layers, the transfer matrix describing angular and azimuthal reflectance and angular and azimuthal transmittance; and determining the global transfer matrix as a product of the transfer matrices of each adjacent pair of material layers; and storing the transfer matrix for each of the at least one multi-layer material in memory of a computing system. ### Claim 2 The computer-implemented method for rendering subsurface scattering, further comprising: rendering subsurface scattering in a rendered image using at least one of the transfer matrices. ### Claim 3 (depends on 1) The computer-implemented method of claim 1, wherein the optical property is a refractive index. ### Claim 4 (depends on 1) The computer-implemented method of claim 1, further comprising: determining a bidirectional scattering distribution function for each of the plurality of material layers using the optical property and the thickness thereof, wherein the training is performed using the bidirectional scattering distribution function. ### Claim 5 (depends on 1) The computer-implemented method of claim 1, further comprising: determining a bidirectional reflectance distribution function and a bidirectional transmittance distribution function for each of the plurality of material layers; and storing the bidirectional reflectance distribution function and the bidirectional transmittance distribution function for each of the plurality of material layers in memory, wherein the determining of the transfer matrix for each adjacent pair of material layers is based on the bidirectional reflectance distribution function and the bidirectional transmittance distribution function for each of the material layers in the adjacent pair. ### Claim 6 (depends on 1) The computer-implemented method of claim 1, wherein the bidirectional scattering distribution function is determined using a Monte Carlo subsurface scattering method. ### Claim 7 (depends on 6) The computer-implemented method of claim 6, wherein the Monte Carlo subsurface scattering method is a ground truth Monte Carlo subsurface scattering method. ### Claim 8 (depends on 1) The computer-implemented method of claim 1, wherein during the receiving of the optical property and the thickness of each of the plurality of material layers, a graphical user interface is generated to enable specification of the optical property and the thickness for each of the plurality of material layers. ### Claim 9 (depends on 8) The computer-implemented method of claim 8, further comprising: receiving, for each of the at least one multi-layer material, an identification of each of the material layers in the ordered set, and an order of the material layers in the ordered set, via the graphical user interface. ### Claim 10 (depends on 9) The computer-implemented method of claim 9, wherein, upon the identification of each of the material layers in the ordered set for one of the at least one multi-layer material, the graphical user interface presents a rendered view of the one of the at least one multi-layer material with subsurface scattering generated using the global transfer matrix. ### Claim 11 A computing system for rendering subsurface scattering, the computing system comprising: one or processors; a memory storing machine-readable instructions that, when executed by the one or more processors, cause the one or more processors to: receive an optical property and a thickness for each of a plurality of material layers; train a latent space for each of the plurality of material layers; generate a global transfer matrix for at least one multi-layer material, each of the at least one multi-layer material including an ordered set of material layers selected from the plurality of material layers, by: determining a transfer matrix for each adjacent pair of material layers in the ordered set of material layers using the latent space for each material layer in the adjacent pair of material layers, the transfer matrix describing angular and azimuthal reflectance and angular and azimuthal transmittance; and determining the global transfer matrix as a product of the transfer matrices of each adjacent pair of material layers; and store the transfer matrix for each of the at least one multi-layer material in memory of a computing system. ### Claim 12 (depends on 11) The computing system for rendering subsurface scattering of claim 11, wherein the machine-readable instructions, when executed by the one or more processors, cause the one or more processors to: generate subsurface scattering in a rendered image using at least one of the transfer matrices. ### Claim 13 (depends on 11) The computing system for rendering subsurface scattering of claim 11, wherein the optical property is a refractive index. ### Claim 14 (depends on 11) The computing system for rendering subsurface scattering of claim 11, wherein the machine-readable instructions, when executed by the one or more processors, cause the one or more processors to: determine a bidirectional scattering distribution function for each of the plurality of material layers using the optical property and the thickness thereof, wherein the training is performed using the bidirectional scattering distribution function. ### Claim 15 (depends on 11) The computing system for rendering subsurface scattering of claim 11, wherein the machine-readable instructions, when executed by the one or more processors, cause the one or more processors to: determine a bidirectional reflectance distribution function and a bidirectional transmittance distribution function for each of the plurality of material layers; and store the bidirectional reflectance distribution function and the bidirectional transmittance distribution function for each of the plurality of material layers in memory, wherein the determining of the transfer matrix for each adjacent pair of material layers is based on the bidirectional reflectance distribution function and the bidirectional transmittance distribution function for each of the material layers in the adjacent pair. ### Claim 16 (depends on 11) The computing system for rendering subsurface scattering of claim 11, wherein the bidirectional scattering distribution function is determined using a Monte Carlo subsurface scattering method. ### Claim 17 (depends on 16) The computing system for rendering subsurface scattering of claim 16, wherein the Monte Carlo subsurface scattering method is a ground truth Monte Carlo subsurface scattering method. ### Claim 18 (depends on 11) The computing system for rendering subsurface scattering of claim 11, wherein the machine-readable instructions, when executed by the one or more processors, cause the one or more processors to: generate a graphical user interface to enable specification of the optical property and the thickness for each of the plurality of material layers. ### Claim 19 (depends on 18) The computing system for rendering subsurface scattering of claim 18, wherein the machine-readable instructions, when executed by the one or more processors, cause the one or more processors to: receive, for each of the at least one multi-layer material, an identification of each of the material layers in the ordered set, and an order of the material layers in the ordered set, via the graphical user interface. ### Claim 20 (depends on 19) The computing system for rendering subsurface scattering of claim 19, wherein, upon the identification of each of the material layers in the ordered set for one of the at least one multi-layer material, the machine-readable instructions, when executed by the one or more processors, cause the one or more processors to present a rendered view of the one of the at least one multi-layer material with subsurface scattering generated using the global transfer matrix with the graphical user interface.