In many disciplines, it is becoming common to scan and analyze 3D data from large sets of physical specimens with the goal of discovering semantic properties and functional relationships between them. A key challenge then is to provide effective algorithms for shape analysis that can extract salient features, discover similarities, extract repeating patterns, and provide functional descriptions of the data.
In this talk, I will describe recent efforts to provide shape analysis algorithms for projects in structural bioinformatics, paleontology, archaeology, and urban modeling. I will specifically focus on the fundamental problem of finding correspondences between points on 3D surfaces, which is at the core of analyzing modes of variation, measuring shape similarities, transferring surface properties, and many other shape analysis tasks. Recently, we have proposed tractable algorithms for finding point correspondences between surfaces differing by large non-rigid deformations, levaraging the low-dimensionality of M\"{o}bius transformations to search the space of conformal maps. I will describe the ideas behind these algorithms and provide results of applications in symmetry detection and inter-surface mapping.
This work was done jointly by Yaron Lipman (post-doc) and Vladimir Kim (Ph.D. student) at Princeton University.