Statistical active grid for segmentation refinement

Abstract

We present a new statistical method, based on a deformable partition called “active grid” for the semi-supervised segmentation of an image composed of several homogeneous regions. This approach allows one to efficiently refine a rough pre-segmentation with a computing time below half a second for 256×256 images (on a standard 700 MHz PC).

Introduction

Since the work of Geman and Geman (1984), there has been a growing interest in statistical techniques for image segmentation. Recently, deformable models have been coupled with the statistical approach to provide efficient estimation and regularization of the contours. Some of these methods aim at segmenting a unique object in the scene (Staib and Duncan, 1992, Kervrann and Heitz, 1994, Storvik, 1994, Nguyen et al., 1992, Figueiredo et al., 2000), while others are able to segment the scene into several regions. For example, in (Zhu and Yuille, 1996), a global technique which allows region growing and competition has been proposed in order to segment complex images. We propose here, an analogous but simpler technique, which leads to a fast algorithm based on rigorous statistical criterion but which needs a more supervised approach. In a recent paper (Germain and Réfrégier, 1996), we have presented a method based on active contours (snakes) to estimate the contour of an object in a statistical framework. The contour deformation was driven by the optimization of a closed-form criterion that is optimal for given models of the scene. It has been shown that this technique is efficient when the edges are difficult to detect (Chenaud et al., 1999) and that it could be used to correct the bias observed in SAR edge location (Germain and Réfrégier, 2000). However, the main limitation of this approach was the assumption that the image is only made of two regions. If the background of the scene is not homogeneous, this assumption is violated and thus, the method can fail in this case.

In this letter, we propose an original statistical method to segment images made of several (more than two) homogeneous regions, when the number of regions as well as their approximate positions are known a priori. The aim is then to refine and regularize an initial rough segmentation with a deformable partition that we call “active grid”. Note that contour regularization is classical (Chenaud et al., 1999) and will not be detailed here. In the following, we will focus on two original points: the active grid and its fast implementation. In Section 2, we give the mathematical formulation of the problem and study the solution in the case where the pdf of the intensities belong to the exponential family. In Section 3, we address the implementation of the method and we show that a fast algorithm, analogous to the one proposed in (Chenaud et al., 1999) can be applied. Finally, some segmentation results with computing times are presented in Section 4.