A nonparametric statistical method for image segmentation using information theory and curve evolution

In this paper, we present a new information-theoretic approach to image segmentation. We cast the segmentation problem as the maximization of the mutual information between the region labels and the image pixel intensities, subject to a constraint on the total length of the region boundaries. We assume that the probability densities associated with the image pixel intensities within each region are completely unknown a priori, and we formulate the problem based on nonparametric density estimates. Due to the nonparametric structure, our method does not require the image regions to have a particular type of probability distribution and does not require the extraction and use of a particular statistic. We solve the information-theoretic optimization problem by deriving the associated gradient flows and applying curve evolution techniques. We use level-set methods to implement the resulting evolution. The experimental results based on both synthetic and real images demonstrate that the proposed technique can solve a variety of challenging image segmentation problems. Furthermore, our method, which does not require any training, performs as good as methods based on training.

I. Introduction

IMAGE segmentation is an important problem in image analysis, appearing in many applications including pattern recognition, object detection, and medical imaging. Some previous approaches to image segmentation, which provide the basis for a variety of more recent methods, include boundary-based segmentation such as Canny edge detection [1], region-based segmentation such as region growing [2], [3], and global optimization approaches such as those based on the Mumford–Shah functional [4] [5] [6]. Recently, there has been a considerable amount of work on image segmentation using curve evolution techniques [5], [7] [10] [10] [11] [12] [13] [14]. Some of these techniques, including the ones in [10] and [14] have relations to the approach we present here. In particular, Paragios et al. [10] developed a parametric model for supervised segmentation of textured images. Yezzi et al. [14] developed a segmentation technique using a particular discriminative statistical feature such as the mean or the variance of image regions. These, and many other recent methods (such as [12] and [15]) have been inspired by the region competition model of Zhu and Yuille [16].