Functional data analysis and partial shape matching in the square root velocity framework.

摘要

We investigate two problems in elastic curve shape analysis, working within the context of the square root velocity (SRV) framework. The first of these is to develop specialized algorithms for the analysis of one-dimensional curves, which are just real-valued functions. In this particularly simple case, the elastic matching problem can be stated as a finite combinatorial problem in which the optimal solution can be found exactly. We also develop a method for groupwise alignment, and use it to compute Karcher means of collections of functions. Second, we consider the problem of finding optimal partial matches between curves in Euclidean space within the SRV framework, and present algorithms and heuristics to solve this problem. Finally, we give a brief overview of libsrvf, an open-source software library providing implementations of the algorithms developed in the course of this work.