Image Segmentation Using Active Contours Driven by the Bhattacharyya Gradient Flow

Abstract

This paper addresses the problem of image segmentation by means of active contours, whose evolution is driven by the gradient flow derived from an energy functional that is based on the Bhattacharyya distance. In particular, given the values of a photometric variable (or of a set thereof), which is to be used for classifying the image pixels, the active contours are designed to converge to the shape that results in maximal discrepancy between the empirical distributions of the photometric variable inside and outside of the contours. The above discrepancy is measured by means of the Bhattacharyya distance that proves to be an extremely useful tool for solving the problem at hand. The proposed methodology can be viewed as a generalization of the segmentation methods, in which active contours maximize the difference between a finite number of empirical moments of the "inside" and "outside" distributions. Furthermore, it is shown that the proposed methodology is very versatile and flexible in the sense that it allows one to easily accommodate a diversity of the image features based on which the segmentation should be performed. As an additional contribution, a method for automatically adjusting the smoothness properties of the empirical distributions is proposed. Such a procedure is crucial in situations when the number of data samples (supporting a certain segmentation class) varies considerably in the course of the evolution of the active contour. In this case, the smoothness properties of the empirical distributions have to be properly adjusted to avoid either over-or underestimation artifacts. Finally, a number of relevant segmentation results are demonstrated and some further research directions are discussed.

Statistical shape learning for 3D tracking

“…We follow here the approach in [7] to which we refer the interested reader for all of the details. The overall method is based on active contours implemented via level set techniques [10], [15], [14], [2].…”

“…In particular, given the values of a photometric variable, which is to be used for classifying the image pixels, the active contours are designed to converge to the shape that results in maximal discrepancy between the distributions of the photometric variable inside and outside of the contours. This discrepancy is measured by means of the Bhattacharyya distance that proves to be an extremely useful tool for solving the problem at hand [7].…”

“…Thus the functions the functions P − (x | Ψ(z)) and P + (x | Ψ(z)) given by (2) and (3) are kernel-based estimates of the probability density functions pdf of the image features observed over the sub-domains Ω − and Ω + . The key idea underpinning the segmentation approach of [7] is that for a properly selected subset of image features, the "overlap" between the informational contents of the object and of the background has to be minimal. In other words, if one thinks of the active contour as a discriminator that separates the image pixels into two subsets, then the optimal contour should minimize the mutual information between these subsets.…”

“…We propose to employ the geometric active contour (GAC) framework [15], [10], [14], whereby a curve is evolved continuously until it satisfies a stopping criterion that coincides with the object's boundaries. The model used will be based on statistical information theory, in particular, the Bhattarcharyya coefficient from information theory [7]. Although this improves segmentation results, one still may encounter problems with tracking in cluttered adversarial scenarios.…”

Global Region Based Segmentation of Satellite and Medical Imagery with Active Contours and Level Set Evolution on Noisy Images

“…The foremost essential goal of the segmentation process is to partition an image into regions that are homogeneous (uniform) with respect to one or more self characteristics and features. Active contour methods are applied in a wide range of problems including visual tracking and image segmentation [11]- [14]. The basic idea is to allow a contour to deform so as to minimize a given energy functional in order to produce the desired segmentation.…”