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Lambertian reflectance and linear subspaces
Abstract
We prove that the set of all reflectance functions (the mapping from surface normals to intensities) produced by Lambertian objects under distant, isotropic lighting lies close to a 9D linear subspace. This implies that the images of a convex Lambertian object obtained under a wide variety of lighting conditions can be approximated accurately with a low-dimensional linear subspace, explaining prior empirical results. We also provide a simple analytic characterization of this linear space. We obtain these results by representing lighting using spherical harmonics and describing the effects of Lambertian materials as the analog of a convolution. These results allow us to construct algorithms for object recognition based on linear methods as well as algorithms that use convex optimization to enforce non-negative lighting functions.
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Turk, M., & Pentland, A. (1991) · Journal of Cognitive Neuroscience · doi:10.1162/jocn.1991.3.1.71 · Cited by 13,733
Cited by
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Ramamoorthi, R., & Hanrahan, P. (2001) · Proceedings of the 28th annual conference on Computer graphics and interactive techniques · doi:10.1145/383259.383317 · Cited by 769
A signal-processing framework for inverse rendering
Ramamoorthi, R., & Hanrahan, P. (2001) · Proceedings of the 28th annual conference on Computer graphics and interactive techniques · doi:10.1145/383259.383271 · Cited by 577
Clustering appearances of objects under varying illumination conditions
Ho, J., Yang, M.-H., Lim, J., Lee, K.-C., & Kriegman, D. (2003) · 2003 IEEE Computer Society Conference on Computer Vision and Pattern Recognition, 2003. Proceedings. · doi:10.1109/cvpr.2003.1211332 · Cited by 521
Ramamoorthi, R., & Hanrahan, P. (2001) · Journal of the Optical Society of America A · doi:10.1364/josaa.18.002448 · Cited by 377
A ray tracing solution for diffuse interreflection
Ward, G. J., Rubinstein, F. M., & Clear, R. D. (2007) · ACM SIGGRAPH 2007 courses · doi:10.1145/1281500.1281626 · Cited by 373
Metadata
- Authors
- Basri, R., & Jacobs, D.
- Venue
- Proceedings Eighth IEEE International Conference on Computer Vision. ICCV 2001
- Publisher
- IEEE Comput. Soc
- Published
- 2002-11-13
- Volume
- 2
- Pages
- 383-390
- OpenAlex
- W2143915994
- Cited by
- 277
- References
- 1
- FWCI
- 15.45
- Type
- conference paper
- Language
- en
- Open access
- closed
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