Looking for Shapes in Cluttered Point Clouds
by
Anuj Srivastava
Florida State University

The problem of recognizing shapes in given images is present in many branches of science. A subproblem in that area is study point clouds - a collection of points in a Euclidean space - and form interesting shapes by connecting suitable subsets of points. We model these clouds as sampled contours that are corrupted by clutter and observation noise. Taking an analysis-by-synthesis approach, we simulate high-probability configurations of sampled contours using shape models learnt from training data to evaluate the given test data. To facilitate simulations, we develop statistical models for sources of (nuisance) variability: (i) shape variations within classes, (ii) variability in sampling continuous curves, (iii) pose and scale variability, (iv) observation noise, and (v) points introduced by clutter. The variability in sampling closed curves into finite points is represented by positive diffeomorphisms of a unit circle. We derive probability models on these functions using their square-root forms and the Fisher-Rao metric. Using a Monte Carlo approach, we simulate configurations from a joint prior on the shape-sample space and compare them to the data using a likelihood function. Average likelihoods of simulated configurations lead to estimates of posterior probabilities of different classes and, hence, Bayesian classification.

Date received: February 24, 2009