# US 12,762,787 B2 · Method, electronic device, and computer program product for generating three-dimensional image > Agents: this data is available as JSON from the patentgrep API and MCP server — see https://patentgrep.com/llms.txt - Number: US 12,762,787 B2 - Document ID: US12762787B2 - Status: Granted - Kind: B2 - Application number: 18/510,122 - Filed: 2023-11-15 - Published: 2025-05-01 - Granted: 2026-10-13 - Earliest claimed: 2023-10-27 - Assignees: Dell Products L.P. - Applicants: Dell Products L.P. - Inventors: Zijia Wang; Zhisong Liu; Zhen Jia - Web page: https://patentgrep.com/patent/US12762787B2 ## CPC - G06T 15/205: {Image-based rendering} - G06T 19/20: Editing of three-dimensional [3D] images, e.g. changing shapes or colours, aligning objects or positioning parts - G06V 10/7715: {Feature extraction, e.g. by transforming the feature space, e.g. multi-dimensional scaling [MDS]; Mappings, e.g. subspace methods} - G06V 10/774: Generating sets of training patterns; Bootstrap methods, e.g. bagging or boosting - G06V 10/82: using neural networks - G06T 2219/2016: Rotation, translation, scaling - G06T: IMAGE DATA PROCESSING OR GENERATION, IN GENERAL - G06V: IMAGE OR VIDEO RECOGNITION OR UNDERSTANDING ## Abstract Embodiments of the present disclosure relate to a method, an electronic device, and a computer program product for generating a three-dimensional image. The method includes: receiving a first image presenting a target object at a first viewing angle, wherein the first image is a two-dimensional image; determining a transformed image of the first image at a target viewing angle, wherein the target viewing angle is the same as or different from the first viewing angle. The method further includes: generating a first representation using a first feature extraction layer corresponding to the first viewing angle in an encoder based on the transformed image; and generating a second image based on the first representation, wherein the second image is a three-dimensional image and presents the target object at the target viewing angle. ## Claims ### Claim 1 A method for generating a three-dimensional image, comprising: receiving a first image presenting a target object at a first viewing angle, wherein the first image is a two-dimensional image; determining a transformed image of the first image at a target viewing angle, wherein the target viewing angle is the same as or different from the first viewing angle, wherein determining the transformed image of the first image at the target viewing angle comprises generating a plurality of transformed images based on the first image utilizing a transformation group comprising a dihedral group, the dihedral group including rotation transformations at a plurality of angles and reflection transformations at a plurality of angles, the transformed image of the first image being determined based on the plurality of transformed images generated utilizing the transformation group comprising the dihedral group; generating a first representation using a first feature extraction layer corresponding to the first viewing angle in an encoder based on the transformed image; and generating a second image based on the first representation, wherein the second image is a three-dimensional image and presents the target object at the target viewing angle. ### Claim 2 (depends on 1) The method according to claim 1, wherein determining the transformed image of the first image further comprises: determining a plurality of weights corresponding to the plurality of transformed images based on the target viewing angle; and determining the transformed image based on the plurality of transformed images and the plurality of weights. ### Claim 3 (depends on 1) The method according to claim 1, wherein the rotation transformations at the plurality of angles comprise a plurality of rotation transformations that rotate the target object at different angles, respectively, and the reflection transformations at the plurality of angles comprise a plurality of reflection transformations that reflect the target object in different directions, respectively. ### Claim 4 (depends on 1) The method according to claim 1, wherein the encoder further comprises a second feature extraction layer corresponding to a second viewing angle, a third feature extraction layer corresponding to a third viewing angle, and a fourth feature extraction layer corresponding to a fourth viewing angle, wherein the first viewing angle, the second viewing angle, the third viewing angle, and the fourth viewing angle are different from one another. ### Claim 5 (depends on 4) The method according to claim 4, the method further comprising: generating a second representation based on the first image and with the second feature extraction layer; generating a third representation based on the first image and with the third feature extraction layer; generating a fourth representation based on the first image and with the fourth feature extraction layer; and generating a fifth representation based on the first representation, the second representation, the third representation, and the fourth representation, and wherein generating the second image based on the first representation comprises: generating the second image based on the fifth representation. ### Claim 6 (depends on 5) The method according to claim 5, wherein the encoder is part of a group-equivariant convolutional neural network obtained via pre-training, and the first feature extraction layer, the second feature extraction layer, the third feature extraction layer, and the fourth feature extraction layer are respectively at least one layer in the group-equivariant convolutional neural network. ### Claim 7 (depends on 6) The method according to claim 6, wherein the pre-training comprises: determining, based on a set of sample two-dimensional images, a first loss function corresponding to the set of sample two-dimensional images with an inverse transformation network, wherein the first loss function represents a degree to which the encoder reserves relative transformations between multiple images at different viewing angles; and determining, based on the set of sample two-dimensional images, a second loss function corresponding to the set of sample two-dimensional images with a differentiable renderer, and the second loss function represents a matching degree of a generated plurality of training three-dimensional images and a plurality of reference three-dimensional images in terms of appearance similarity. ### Claim 8 (depends on 7) The method according to claim 7, wherein the first loss function comprises a set of distances between respective ones of: a plurality of training transformed images generated by the inverse transformation network and based on a plurality of representations determined by a feature extraction layer corresponding to a plurality of sample transformed images in the encoder; and a plurality of reference transformed images. ### Claim 9 (depends on 7) The method according to claim 7, wherein the second loss function comprises a set of distances between respective ones of: a plurality of training three-dimensional images generated by the differentiable renderer and based on a plurality of representations generated by a feature extraction layer corresponding to a plurality of sample transformed images in the encoder, the target viewing angle, and a background image; and a plurality of reference three-dimensional images. ### Claim 10 (depends on 7) The method according to claim 7, wherein the pre-training further comprises: determining a first weight corresponding to the first loss function and a second weight corresponding to the second loss function; determining a third loss function based on the first weight and the second weight; and adjusting at least one parameter of the third loss function. ### Claim 11 An electronic device, comprising: at least one processor; and memory coupled to the at least one processor and having instructions stored therein, wherein the instructions, when executed by the at least one processor, cause the electronic device to perform actions, the actions comprising: receiving a first image presenting a target object at a first viewing angle, wherein the first image is a two-dimensional image; determining a transformed image of the first image at a target viewing angle, wherein the target viewing angle is the same as or different from the first viewing angle, wherein determining the transformed image of the first image at the target viewing angle comprises generating a plurality of transformed images based on the first image utilizing a transformation group comprising a dihedral group, the dihedral group including rotation transformations at a plurality of angles and reflection transformations at a plurality of angles, the transformed image of the first image being determined based on the plurality of transformed images generated utilizing the transformation group comprising the dihedral group; generating a first representation using a first feature extraction layer corresponding to the first viewing angle in an encoder based on the transformed image; and generating a second image based on the first representation, wherein the second image is a three-dimensional image and presents the target object at the target viewing angle. ### Claim 12 (depends on 11) The electronic device according to claim 11, wherein determining the transformed image of the first image further comprises: determining a plurality of weights corresponding to the plurality of transformed images based on the target viewing angle; and determining the transformed image based on the plurality of transformed images and the plurality of weights. ### Claim 13 (depends on 11) The electronic device according to claim 11, wherein the rotation transformations at the plurality of angles comprise a plurality of rotation transformations that rotate the target object at different angles, respectively, and the reflection transformations at the plurality of angles comprise a plurality of reflection transformations that reflect the target object in different directions, respectively. ### Claim 14 (depends on 11) The electronic device according to claim 11, wherein the encoder further comprises a second feature extraction layer corresponding to a second viewing angle, a third feature extraction layer corresponding to a third viewing angle, and a fourth feature extraction layer corresponding to a fourth viewing angle, wherein the first viewing angle, the second viewing angle, the third viewing angle, and the fourth viewing angle are different from one another. ### Claim 15 (depends on 14) The electronic device according to claim 14, wherein the actions further comprise: generating a second representation based on the first image and with the second feature extraction layer; generating a third representation based on the first image and with the third feature extraction layer; generating a fourth representation based on the first image and with the fourth feature extraction layer; and generating a fifth representation based on the first representation, the second representation, the third representation, and the fourth representation, and wherein generating the second image based on the first representation comprises: generating the second image based on the fifth representation. ### Claim 16 (depends on 15) The electronic device according to claim 15, wherein the encoder is part of a group-equivariant convolutional neural network obtained via pre-training, and the first feature extraction layer, the second feature extraction layer, the third feature extraction layer, and the fourth feature extraction layer are respectively at least one layer in the group-equivariant convolutional neural network. ### Claim 17 (depends on 16) The electronic device according to claim 16, wherein the pre-training comprises: determining, based on a set of sample two-dimensional images, a first loss function corresponding to the set of sample two-dimensional images with an inverse transformation network, wherein the first loss function represents a degree to which the encoder reserves relative transformations between multiple images at different viewing angles; and determining, based on the set of sample two-dimensional images, a second loss function corresponding to the set of sample two-dimensional images with a differentiable renderer, and the second loss function represents a matching degree of a generated plurality of training three- dimensional images and a plurality of reference three-dimensional images in terms of appearance similarity. ### Claim 18 (depends on 17) The electronic device according to claim 17, wherein the first loss function comprises a set of distances between respective ones of: a plurality of training transformed images generated by the inverse transformation network and based on a plurality of representations determined by a feature extraction layer corresponding to a plurality of sample transformed images in the encoder; and a plurality of reference transformed images, and the second loss function comprises a set of distances between respective ones of: a plurality of training three-dimensional images generated by the differentiable renderer and based on a plurality of representations generated by a feature extraction layer corresponding to a plurality of sample transformed images in the encoder, the target viewing angle, and a background image; and a plurality of reference three-dimensional images. ### Claim 19 (depends on 17) The electronic device according to claim 17, wherein the pre-training further comprises: determining a first weight corresponding to the first loss function and a second weight corresponding to the second loss function; determining a third loss function based on the first weight and the second weight; and adjusting at least one parameter of the third loss function. ### Claim 20 A computer program product comprising a non-transitory computer-readable medium having computer-executable instructions stored therein, wherein the computer-executable instructions, when executed by a device, cause the device to perform actions, the actions comprising: receiving a first image presenting a target object at a first viewing angle, wherein the first image is a two-dimensional image; determining a transformed image of the first image at a target viewing angle, wherein the target viewing angle is the same as or different from the first viewing angle, wherein determining the transformed image of the first image at the target viewing angle comprises generating a plurality of transformed images based on the first image utilizing a transformation group comprising a dihedral group, the dihedral group including rotation transformations at a plurality of angles and reflection transformations at a plurality of angles, the transformed image of the first image being determined based on the plurality of transformed images generated utilizing the transformation group comprising the dihedral group; generating a first representation using a first feature extraction layer corresponding to the first viewing angle in an encoder based on the transformed image; and generating a second image based on the first representation, wherein the second image is a three-dimensional image and presents the target object at the target viewing angle.