Information theoretic shape matching

In this paper, we describe two related algorithms that provide both rigid and non-rigid point set registration with different computational complexity and accuracy. The first algorithm utilizes a nonlinear similarity measure known as correntropy. The measure combines second and high order moments in its decision statistic showing improvements especially in the presence of impulsive noise. The algorithm assumes that the correspondence between the point sets is known, which is determined with the surprise metric. The second algorithm mitigates the need to establish a correspondence by representing the point sets as probability density functions (PDF). The registration problem is then treated as a distribution alignment. The method utilizes the Cauchy-Schwarz divergence to measure the similarity/distance between the point sets and recover the spatial transformation function needed to register them. Both algorithms utilize information theoretic descriptors; however, correntropy works at the realizations level, whereas Cauchy-Schwarz divergence works at the PDF level. This allows correntropy to be less computationally expensive, and for correct correspondence, more accurate. The two algorithms are robust against noise and outliers and perform well under varying levels of distortion. They outperform several well-known and state-of-the-art methods for point set registration.