Gaussian mixture model-signature quadratic form distance based point set registration

Abstract

Point set registration is a long addressed problem in lots of pattern recognition tasks. This paper presents a robust point set registration algorithm based on optimization of distance between two probability distributions. A major problem encountered in the point to point algorithms is the definition of correspondence between two point sets. This paper follows the idea of some probability based point set registration methods and the point set is represented as Gaussian Mixture Models (GMMs). Through optimizing distance between the two GMMs, the rigid transformation (rotation and translation) between two point sets will be obtained while averting the trouble of finding correspondence. Previous studies used L2 distance, KL distance, etc. to measure similarity between two GMMs, the problem therein is the robustness to noise and outliers, especially when the covariance matrix is large or there exists local minimum. So in this work, the signature quadratic form distance is derived for the distribution similarity measurement. The contribution of this paper is as follows. First, we derive the signature quadratic form distance for GMMs similarity measurement. Second, the signature quadratic form distance is adopted to the point set registration algorithm. And performance of the proposed method compared with some existing widely used point set registration algorithms is also presented. Experimental results show precision and robustness of this algorithm. The results also demonstrate this algorithm outperforms some state-of-the-art point set registration algorithms in terms of noise, outliers, partial structures and misalignment initialization, etc.