Detection, classification and estimation of individual shapes in 2D and 3D point clouds

The problems of detecting, classifying, and estimating shapes in point cloud data are important due to their general applicability in image analysis, computer vision, and graphics. They are challenging because the data is typically noisy, cluttered, and unordered. We study these problems using a fully statistical model where the data is modeled using a Poisson process on the object's boundary (curves or surfaces), corrupted by additive noise and a clutter process. Using likelihood functions dictated by the model, we develop a generalized likelihood ratio test for detecting a shape in a point cloud. This ratio test is based on optimizing over some unknown parameters, including the pose and scale associated with hypothesized objects, and an empirical evaluation of the log-likelihood ratio distribution. Additionally, we develop a procedure for estimating most likely shapes in observed point clouds under given shape hypotheses. We demonstrate this framework using examples of 2D and 3D shape detection and estimation in both real and simulated data, and a usage of this framework in shape retrieval from a 3D shape database.