Non-Rigid Motion and Regge Calculus.
MASSACHUSETTS INST OF TECH CAMBRIDGE ARTIFICIAL INTELLIGENCE LAB
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This document studies the problem of recovering the structure from motion of figures which are allowed to perform a controlled non-rigid motion. The authors use Regge Calculus to approximate a general surface by a net of triangles. The non-rigid flexing motion they deal with corresponds to keeping the triangles rigid and allowing bending only at the joins between triangles. Such motion has been studied by Koenderink and van Doorn 1986. It is shown that this motion keeps the Gaussian curvature of the surface constant but changes the principal curvatures. The authors show that depth information of the vertices of the triangles can be obtained by using a modified version of the Incremental Rigidity Scheme devised by Ullman 1984. In cases where the motion of the figure displays fundamentally different views at each frame presentation the algorithm works well, not only for strictly rigid motion Ullman 1984, Grzwacz and Hildreth 1985 but also for a limited amount of bending deformation. This scheme is modified to allow for flexing motion in the sense defined abovel this version is called the Incremental Semirigidity Scheme. Keywords Rigidity Computations.
- Numerical Mathematics