Technical Report PHD-2011-06

Title: General Techniques for Interpolation, Reconstruction and Morphing of Polyhedral Surfaces
Authors: Amir Vaxman
Supervisors: Gill Barequet
Abstract: The topics of shape reconstruction from samples, and of morphing between objects are two of the major research branches of geometric processing. The two major problems in reconstruction which are commonly researched are reconstruction of two and three-dimensional objects from point sets, and reconstruction from cross-sections. The major issue of morphing between objects is usually the determination of correspondence between shapes, and of intrinsic symmetry. In this work we develop three techniques to assist in the solutions of these major problems. We first develop a unique three-dimensional structure to find correspondences between arbitrarily-aligned planes, and on top of that we develop a geometric algorithm for reconstruction between partial slices. We continue by developing an algorithm to efficiently compute the heat kernel, which has been recently given much attention, as a quality descriptor in the study of the intrinsic properties of shapes.
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