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The Bas-Relief Ambiguity

Authors:

Peter N. Belhumeur,

David J. Kriegman,

Alan L. YuilleAuthors Info & Claims

International Journal of Computer Vision, Volume 35, Issue 1

Pages 33 - 44

https://doi.org/10.1023/A:1008154927611

Published: 01 November 1999 Publication History

Abstract

When an unknown object with Lambertian reflectance is viewed orthographically, there is an implicit ambiguity in determining its 3-d structure: we show that the object‘s visible surface f(x, y) is indistinguishable from a generalized bas-relief transformation of the object‘s geometry, \bar f (x, y) = ýf(x, y) + ýx + ýy, and a corresponding transformation on the object‘s albedo. For each image of the object illuminated by an arbitrary number of distant light sources, there exists an identical image of the transformed object illuminated by similarly transformed light sources. This result holds both for the illuminated regions of the object as well as those in cast and attached shadows. Furthermore, neither small motion of the object, nor of the viewer will resolve the ambiguity in determining the flattening (or scaling) ý of the object‘s surface. Implications of this ambiguity on structure recovery and shape representation are discussed.

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Cited By

Wu SRupprecht CVedaldi A(2023)Unsupervised Learning of Probably Symmetric Deformable 3D Objects From Images in the Wild (Invited Paper)IEEE Transactions on Pattern Analysis and Machine Intelligence10.1109/TPAMI.2021.307653645:4(5268-5281)Online publication date: 1-Apr-2023
https://dl.acm.org/doi/10.1109/TPAMI.2021.3076536
Quéau YBruneau RMélou JDurou JLauze F(2023)On Photometric Stereo in the Presence of a Refractive InterfaceScale Space and Variational Methods in Computer Vision10.1007/978-3-031-31975-4_53(691-703)Online publication date: 21-May-2023
https://dl.acm.org/doi/10.1007/978-3-031-31975-4_53
Gardner JEgger BSmith WKoyejo SMohamed SAgarwal ABelgrave DCho KOh A(2022)Rotation-equivariant conditional spherical neural fields for learning a natural illumination priorProceedings of the 36th International Conference on Neural Information Processing Systems10.5555/3600270.3602178(26309-26323)Online publication date: 28-Nov-2022
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Index Terms

The Bas-Relief Ambiguity
1. Computing methodologies
2. Theory of computation
  1. Randomness, geometry and discrete structures
    1. Computational geometry

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Information & Contributors

Information

Published In

cover image International Journal of Computer Vision

International Journal of Computer Vision Volume 35, Issue 1

Nov. 1999

101 pages

ISSN:0920-5691

Editors:
Takeo Kanade
Carnegie Mellon Univ., Pittsburgh, PA
,
Olivier Faugeras
INRIA, France

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Copyright © Copyright © 1999 Kluwer Academic Publishers.

Publisher

Kluwer Academic Publishers

United States

Publication History

Published: 01 November 1999

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Cited By

Wu SRupprecht CVedaldi A(2023)Unsupervised Learning of Probably Symmetric Deformable 3D Objects From Images in the Wild (Invited Paper)IEEE Transactions on Pattern Analysis and Machine Intelligence10.1109/TPAMI.2021.307653645:4(5268-5281)Online publication date: 1-Apr-2023
https://dl.acm.org/doi/10.1109/TPAMI.2021.3076536
Quéau YBruneau RMélou JDurou JLauze F(2023)On Photometric Stereo in the Presence of a Refractive InterfaceScale Space and Variational Methods in Computer Vision10.1007/978-3-031-31975-4_53(691-703)Online publication date: 21-May-2023
https://dl.acm.org/doi/10.1007/978-3-031-31975-4_53
Gardner JEgger BSmith WKoyejo SMohamed SAgarwal ABelgrave DCho KOh A(2022)Rotation-equivariant conditional spherical neural fields for learning a natural illumination priorProceedings of the 36th International Conference on Neural Information Processing Systems10.5555/3600270.3602178(26309-26323)Online publication date: 28-Nov-2022
https://dl.acm.org/doi/10.5555/3600270.3602178
Yang ZChen BZheng YChen XZhou K(2022)Human Bas-Relief Generation From a Single PhotographIEEE Transactions on Visualization and Computer Graphics10.1109/TVCG.2021.309287728:12(4558-4569)Online publication date: 1-Dec-2022
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Chen GHan KShi BMatsushita YWong K(2022)Deep Photometric Stereo for Non-Lambertian SurfacesIEEE Transactions on Pattern Analysis and Machine Intelligence10.1109/TPAMI.2020.300539744:1(129-142)Online publication date: 1-Jan-2022
https://dl.acm.org/doi/10.1109/TPAMI.2020.3005397
Bas ASmith W(2022)What Does 2D Geometric Information Really Tell Us About 3D Face Shape?International Journal of Computer Vision10.1007/s11263-019-01197-x127:10(1455-1473)Online publication date: 10-Mar-2022
https://dl.acm.org/doi/10.1007/s11263-019-01197-x
Li JLi H(2022)Self-calibrating Photometric Stereo by Neural Inverse RenderingComputer Vision – ECCV 202210.1007/978-3-031-20086-1_10(166-183)Online publication date: 23-Oct-2022
https://dl.acm.org/doi/10.1007/978-3-031-20086-1_10
Tiwari ARaman S(2022)DeepPS2: Revisiting Photometric Stereo Using Two Differently Illuminated ImagesComputer Vision – ECCV 202210.1007/978-3-031-20071-7_8(129-145)Online publication date: 23-Oct-2022
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Haefner BPeng SVerma AQuéau YCremers D(2020)Photometric Depth Super-ResolutionIEEE Transactions on Pattern Analysis and Machine Intelligence10.1109/TPAMI.2019.292362142:10(2453-2464)Online publication date: 2-Sep-2020
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