What shadows reveal about object structure
- 1 August 2001
- journal article
- Published by Optica Publishing Group in Journal of the Optical Society of America A
- Vol. 18 (8), 1804-1813
- https://doi.org/10.1364/josaa.18.001804
Abstract
In a scene observed from a fixed viewpoint, the set of shadow boundaries in an image changes as a point light source (nearby or at infinity) assumes different locations. We show that for any finite set of point light sources illuminating an object viewed under either orthographic or perspective projection, there is an equivalence class of object shapes having the same set of shadows. Members of this equivalence class differ by a four-parameter family of projective transformations, and the shadows of a transformed object are identical when the same transformation is applied to the light source locations. Under orthographic projection, this family is the generalized bas-relief (GBR) transformation, and we show that the GBR transformation is the only family of transformations of an object’s shape for which the complete set of imaged shadows is identical. Finally, we show that given multiple images under differing and unknown light source directions, it is possible to reconstruct both an object’s surface and the light source locations up to this family of transformations from the shadows alone.Keywords
This publication has 13 references indexed in Scilit:
- The Bas-Relief AmbiguityInternational Journal of Computer Vision, 1999
- Singularities of Illuminated SurfacesInternational Journal of Computer Vision, 1997
- 3D Motion recovery via affine Epipolar geometryInternational Journal of Computer Vision, 1995
- Stratification of three-dimensional vision: projective, affine, and metric representationsJournal of the Optical Society of America A, 1995
- Delimiting the building heights in a city from the shadow in a panchromatic SPOT-image—Part 1. Test of forty-two buildingsInternational Journal of Remote Sensing, 1995
- Affine structure from motionJournal of the Optical Society of America A, 1991
- Recognition by linear combinations of modelsIEEE Transactions on Pattern Analysis and Machine Intelligence, 1991
- Methods for exploiting the relationship between buildings and their shadows in aerial imageryIEEE Transactions on Systems, Man, and Cybernetics, 1989
- The Entry-Exit Method of Shadow Boundary SegmentationIEEE Transactions on Pattern Analysis and Machine Intelligence, 1987
- Using shadows in finding surface orientationsComputer Vision, Graphics, and Image Processing, 1983