The motivating application for this research is the problem of recognizing a planar object consisting of points from a noisy observation of that object. Given is a planar Gaussian mixture model T (x) representing an object along with a noise model for the observation process (the template). Also given are points representing the observation of the object (the query). We propose a method to determine if these points were drawn from a Gaussian mixture Q(x) with the same shape as the template. The method consists in comparing samples from the distribution of distances of T (x) and Q(x), respectively. The distribution of distances is a faithful representation of the shape of generic Gaussian mixtures. Since it is invariant under rotations and translations of the Gaussian mixture, it provides a workaround to the problem of aligning objects before recognizing their shape without sacrificing accuracy. Experiments using synthetic data show a robust performance against type I errors, and few type II errors when the given template Gaussian mixtures are well distinguished.
Gaussian processes, information retrieval, object detection, shape recognition, sparse matrices
Date of this Version
Proc. SPIE - Int. Soc. Opt. Eng. (USA) 7533,(2010) 753305 (9 pp.)-753305 (9 pp.);