In this paper, we present a new distribution metric for image segmentation that arises as a result in prediction
theory. Forming a natural geodesic, our metric quantifies "distance" for two density functionals as the standard
deviation of the difference between logarithms of those distributions. Using level set methods, we incorporate an
energy model based on the metric into the Geometric Active Contour framework. Moreover, we briefly provide a
theoretical comparison between the popular Fisher Information metric, from which the Bhattacharyya distance
originates, with the newly proposed similarity metric. In doing so, we demonstrate that segmentation results are
directly impacted by the type of metric used. Specifically, we qualitatively compare the Bhattacharyya distance
and our algorithm on the Kaposi Sarcoma, a pathology that infects the skin. We also demonstrate the algorithm
on several challenging medical images, which further ensure the viability of the metric in the context of image
segmentation.
Tracking involves estimating not only the global motion but also local perturbations or deformations corresponding to a specified object of interest. From this, motion can be decoupled into a finite dimensional state space (the global motion) and the more interesting infinite dimensional state space (deformations). Recently, the incorporation of the particle filter with geometric active contours which use first and second moments has shown robust tracking results. By generalizing the statistical inference to entire probability distributions, we introduce a new distribution metric for tracking that is naturally able to better model the target. Also, due to the multiple hypothesis nature of particle filtering, it can be readily seen that if the background resembles the foreground,
then one might lose track. Even though this can be described as a finite dimensional problem where global motion can be modeled and learned online through a filtering process, we approach this task by incorporating a separate energy term in the deformable model that penalizes large centroid displacements. Robust results are
obtained and demonstrated on several surveillance sequences.
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