In this paper, we describe a set of robust algorithms for group-wise registration using both rigid and non-rigid transformations of multiple unlabelled point-sets with no bias toward a given set. These methods mitigate the need to establish a correspondence among the point-sets by representing them as probability density functions where the registration is treated as a multiple distribution alignment. Holder's and Jensen's inequalities provide a notion of similarity/distance among point-sets and Rényi's second order entropy yields a closed-form solution to the cost function and update equations. We also show that the methods can be improved by normalizing the entropy with a scale factor. These provide simple, fast and accurate algorithms to compute the spatial transformation function needed to register multiple point-sets. The algorithms are compared against two well-known methods for group-wise point-set registration. The results show an improvement in both accuracy and computational complexity.

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.

Dictionary.com defines learning as the process of acquiring knowledge. In psychology, learning is defined as the modification of behavior through training. In our work, we combine these definitions to define learning as the modification of a system model to incorporate the knowledge acquired by new observations. During learning, the system creates and modifies a model to improve its performance. As new samples are introduced, the system updates its model based on the new information provided by the samples. However, this update may not necessarily improve the model. We propose a Bayesian surprise metric to differentiate good data (beneficial) from outliers (detrimental), and thus help to selectively adapt the model parameters. The surprise metric is calculated based on the difference between the prior and the posterior distributions of the model when a new sample is introduced. The metric is useful not only to identify outlier data, but also to differentiate between the data carrying useful information for improving the model and those carrying no new information (redundant). Allowing only the relevant data to update the model would speed up the learning process and prevent the system from overfitting. The method is demonstrated in all three learning procedures: supervised, semi-supervised and unsupervised. The results show the benefit of surprise in both clustering and outlier detection.

This paper presents an efficient approach to calculate the difference between two probability density functions (pdfs), each of which is a mixture of Gaussians (MoG). Unlike Kullback-Leibler divergence (DKL), the authors propose that the Cauchy-Schwarz (CS) pdf divergence measure (DCS) can give an analytic, closed-form expression for MoG. This property of the DCSmakes fast and efficient calculations possible, which is tremendously desired in real-world applications where the dimensionality of the data/features is very high. We show that DCSfollows similar trends to DKL, but can be computed much faster, especially when the dimensionality is high. Moreover, the proposed method is shown to significantly outperform DKLin classifying real-world 2D and 3D objects, and static hand posture recognition based on distances alone.

In this paper, we describe a new method for performing kernel principal component analysis which is online and also has a fast convergence rate. The method follows the Rayleigh quotient to obtain a fixed point update rule to extract the leading eigenvalue and eigenvector. Online deflation is used to estimate the remaining components. These operations are performed in reproducing kernel Hilbert space (RKHS) with linear order memory and computation complexity. The derivation of the method and several applications are presented.

This paper presents an automated way of classifying mines in sidescan sonar imagery. A nonlinear extension to the matched filter is introduced using a new metric called correntropy. This method features high order moments in the decision statistic showing improvements in classification especially in the presence of noise. Templates have been designed using prior knowledge about the objects in the dataset. During classification, these templates are linearly transformed to accommodate for the shape variability in the observation. The template resulting in the largest correntropy cost function is chosen as the object category. The method is tested on real sonar images producing promising results considering the low number of images required to design the templates.