A Two-Sample Test for Statistical Comparisons of Shape Populations

摘要

This paper develops a formal test to compare populations of shapes of objects given these population samples. The setup involves sets of shapes extracted from different images, and the goal is to equate the underlying populations and not just the individual shapes. While past works have successfully derived shape metrics and individual shape models, the problem of comparing populations using sampled shapes remains relatively unexplored. We use a novel combination of tools - elastic shape analysis of planar closed curves, spherical MDS for dimension reduction, kernel density-estimation on a unit sphere, the Fisher-Rao distance for density comparisons, and, finally, a bootstrap technique for performing a two-sample test - to reach a novel solution for population comparison. We demonstrate these ideas using some practical datasets: image-based biological cell comparisons, nano-manufacturing analysis, coffee-bean classification, and so on. This method is found to be useful in discriminating between shape sets, even those containing visually similar shapes.