Total variance based feature point selection and applications

Abstract

Feature points are used to capture geometric characteristics of an object and are usually associated with certain anatomical significance or geometric meaning. The selection of feature points is a fundamental problem with various applications, for example, in shape registration, cross-parameterization, sparse shape reconstruction, parametric shape design, and dimension construction.In the literature, feature points are usually selected on a single shape by their differential property or saliency, and the information of similar shapes in the population are not considered. Though carefully chosen feature points can represent the corresponding shape well, the variations among different shapes within the population are overlooked.In this paper, through statistical shape modeling, we evaluate the feature points by the amount of variance they capture of the shape population, which leads to an algorithm that sequentially selects and ranks the feature points. In this way, the selected feature points explicitly incorporate the population information of the shapes. Then, we demonstrate how the proposed feature point selection approach can be integrated in the applications of sparse shape reconstruction, construction of new dimensions and shape classification through sparse measurements.The numerical examples have validated the effectiveness and efficiency of the proposed approach.