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What shadows reveal about object structure.

D J Kriegman¹, P N Belhumeur

¹Beckman Institute, Department of Computer Science, University of Illinois, Urbana-Champaign, Urbana 61801, USA. kriegman@uiuc.edu

Journal of the Optical Society of America. A, Optics, Image Science, and Vision

|August 8, 2001

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Object shape and light source direction can be reconstructed from shadows alone. This is possible because equivalent object shapes produce identical shadows under specific transformations, allowing for 3D reconstruction from multiple images.

Area of Science:

Computer Vision
Computational Geometry
3D Reconstruction

Background:

Shadow boundaries in images vary with light source position.
Understanding shape from shadows is crucial for 3D scene analysis.

Purpose of the Study:

To establish an equivalence class of object shapes that produce identical shadows.
To identify transformations that preserve shadow information.
To enable 3D surface and light source reconstruction from shadows.

Main Methods:

Analysis of shadow boundaries under orthographic and perspective projection.
Investigation of projective transformations and their effect on shadows.
Demonstration of the generalized bas-relief (GBR) transformation.

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Main Results:

An equivalence class of object shapes exists for a given set of shadows.
Shadows are invariant under a four-parameter family of projective transformations.
The GBR transformation is the unique shape transformation preserving all shadows under orthographic projection.
Reconstruction of object surface and light source direction is possible from multiple shadow images.

Conclusions:

Shadows provide sufficient information for 3D shape and light source reconstruction.
The GBR transformation defines the ambiguity in shape reconstruction from shadows.
This work advances understanding of shape-from-shadows techniques.