Abstract
In a scene observed from a fixed viewpoint, the set of shadow curves 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 per- spective 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. Furthermore, for objects with Lambertian surfaces illuminated by dis- tant light sources, the equivalence class of object shapes which preserves shadows also preserves surface shading. Finally, we show that given mul- tiple images under differing and unknown light source directions, it is possible to reconstruct an object’s shape up to these transformations from the shadows alone.
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© 1999 Springer-Verlag Berlin Heidelberg
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Belhumeur, P.N., Kriegman, D.J., Yuille, A.L. (1999). Shadows, Shading, and Projective Ambiguity. In: Shape, Contour and Grouping in Computer Vision. Lecture Notes in Computer Science, vol 1681. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-46805-6_8
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DOI: https://doi.org/10.1007/3-540-46805-6_8
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