Curvature Fields from Shading Fields

Xinran Han, Todd Zickler
Proceedings of the 2nd NeurIPS Workshop on Symmetry and Geometry in Neural Representations, PMLR 228:232-254, 2024.

Abstract

We re-examine the estimation of 3D shape from images that are caused by shading of diffuse Lambertian surfaces. We propose a neural model that is motivated by the well-documented perceptual effect in which shape is perceived from shading without a precise perception of lighting. Our model operates independently in each receptive field and produces a scalar statistic of surface curvature for that field. The model’s architecture builds on previous mathematical analyses of lighting-invariant shape constraints, and it leverages geometric structure to provide equivariance under image rotations and translations. Applying our model in parallel across a dense set of receptive fields produces a curvature field that we show is quite stable under changes to a surface’s albedo pattern (texture) and also to changes in lighting, even when lighting varies spatially across the surface.

Cite this Paper

BibTeX
@InProceedings{pmlr-v228-han24a, title = {Curvature Fields from Shading Fields}, author = {Han, Xinran and Zickler, Todd}, booktitle = {Proceedings of the 2nd NeurIPS Workshop on Symmetry and Geometry in Neural Representations}, pages = {232--254}, year = {2024}, editor = {Sanborn, Sophia and Shewmake, Christian and Azeglio, Simone and Miolane, Nina}, volume = {228}, series = {Proceedings of Machine Learning Research}, month = {16 Dec}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v228/main/assets/han24a/han24a.pdf}, url = {https://proceedings.mlr.press/v228/han24a.html}, abstract = {We re-examine the estimation of 3D shape from images that are caused by shading of diffuse Lambertian surfaces. We propose a neural model that is motivated by the well-documented perceptual effect in which shape is perceived from shading without a precise perception of lighting. Our model operates independently in each receptive field and produces a scalar statistic of surface curvature for that field. The model’s architecture builds on previous mathematical analyses of lighting-invariant shape constraints, and it leverages geometric structure to provide equivariance under image rotations and translations. Applying our model in parallel across a dense set of receptive fields produces a curvature field that we show is quite stable under changes to a surface’s albedo pattern (texture) and also to changes in lighting, even when lighting varies spatially across the surface.} }
Endnote
%0 Conference Paper %T Curvature Fields from Shading Fields %A Xinran Han %A Todd Zickler %B Proceedings of the 2nd NeurIPS Workshop on Symmetry and Geometry in Neural Representations %C Proceedings of Machine Learning Research %D 2024 %E Sophia Sanborn %E Christian Shewmake %E Simone Azeglio %E Nina Miolane %F pmlr-v228-han24a %I PMLR %P 232--254 %U https://proceedings.mlr.press/v228/han24a.html %V 228 %X We re-examine the estimation of 3D shape from images that are caused by shading of diffuse Lambertian surfaces. We propose a neural model that is motivated by the well-documented perceptual effect in which shape is perceived from shading without a precise perception of lighting. Our model operates independently in each receptive field and produces a scalar statistic of surface curvature for that field. The model’s architecture builds on previous mathematical analyses of lighting-invariant shape constraints, and it leverages geometric structure to provide equivariance under image rotations and translations. Applying our model in parallel across a dense set of receptive fields produces a curvature field that we show is quite stable under changes to a surface’s albedo pattern (texture) and also to changes in lighting, even when lighting varies spatially across the surface.
APA
Han, X. & Zickler, T.. (2024). Curvature Fields from Shading Fields. Proceedings of the 2nd NeurIPS Workshop on Symmetry and Geometry in Neural Representations, in Proceedings of Machine Learning Research 228:232-254 Available from https://proceedings.mlr.press/v228/han24a.html.

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