Bayesian Classification of Shapes Hidden in Point Cloud Data

An interesting challenge in image processing is to classify shapes of polygons formed by selecting and ordering points in a 2D cluttered point cloud. This kind of data can result, for example, from a simple preprocessing of images containing objects with prominent boundaries. Taking an analysis-by-synthesis approach, we simulate high-probability configurations of sampled contours using models learnt from the training data to evaluate the given test data. To facilitate simulations, we develop statistical models for sources of (nuisance) variability: (i) shape variations of contours within classes, (ii) variability in sampling continuous curves into points, (iii) pose and scale variability, (iv) observation noise, and (v) points introduced by clutter. Finally, using a Monte Carlo approach, we estimate the posterior probabilities of different classes which leads to a Bayesian classification.