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Mathematical Aspects of Shape Reconstruction from an Image Sequence

Atsushi Imiya Kazuhiko Kawamoto

Presented at 1st International Symposium on 3D Data Processing Visualization and Transmission (3DPVT 2002), Padova, Italy, Jun 19-21, 2002


Abstract

This paper clarifies a sufficient condition for the reconstruction of an object from its shadows. The objects considered are finite closed convex regions in three-dimensional Euclidean space. First we show a negative result that a series of shadows measured using a camera moving along a circle on a plane is insufficient for the full reconstruction of an object even if the object is convex.Then, we show a positive result that a series of pairs of shadows measured using a general stereo system with some geometrical assumptions is sufficient for full reconstruction of a convex object. Furthermore, we show that a class of non-convex objects, which we define as slice convex objects, are also reconstractable from a series of shadows.


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