Coupled Geodesic Active Regions for Image Segmentation: A Level Set Approach

Abstract

This paper presents a novel variational method for im age segmentation that unifies boundary and region-based information sources under the Geodesic Active Region framework. A statistical analysis based on the Minimum Description Length criterion and the Maximum Likelihood Principle for the observed density function (image histogram) using a mixture of Gaussian elements, indicates the number of the different regions and their intensity properties. Then, the boundary information is determined using a probabilistic edge detector, while the region information is estimated using the Gaussian components of the mixture model. The defined objective function is mini mized using a gradientdescent method where a level set approach is used to implement the resulting PDE system. According to the motion equations, the set of initial curves is propagated toward the segmentation result under the influence of boundary and region-based segmentation forces, and being constrained by a regularity force. The changes of topology are naturally handled thanks to the level set implementation, while a coupled multi-phase propagation is adopted that increases the robustness and the convergence rate by imposing the idea of mutually exclusive propagating curves. Finally, to reduce the required computational cost and the risk of convergence to local minima, a multi-scale approach is also considered. The performance of our method is demonstrated on a variety of real images.