PDE-based modeling of image segmentation using volumic flooding

The classical case of morphological segmentation is based on the watershed transform, constructed by flooding the gradient image, which is seen as a topographic surface, with constant height speed. Changing the flooding criteria, (e.g. constant-speed height, area or volume) yields different segmentation results. In the field of PDEs and curve evolution the classic watershed transform can be modelled as the solution of an eikonal PDE. In this paper we model the watershed segmentation based on a volume flooding criterion via a different eikonal PDE. Then we solve this PDE using the fast marching method, which is a specific algorithm from the methodology of level sets. In addition, we attempt to exploit the advantages of image segmentation using PDE-based volume flooding over the classic height flooding.

1 INTRODUCTION

Segmentation is one of the most difficult tasks in image processing, as it is application dependent and requires to some extent a semantic understanding of the image. The morphological segmentation methodology, based on the watershed transform and markers, has been successfully used, both for interactive as for automated segmentation ([1], [13]). The segmentation process starts with creating flooding waves that emanate from the set of markers and flood the image gradient surface. The points where the emanating waves meet each other form the segmentation boundaries. The simplest markers are the regional minima of the gradient image. Very often, the minima are extremely numerous, leading to an oversegmentation. For this reason, in many practical cases, the watershed will take as sources of the flooding a smaller set of markers, which have been identified by a preliminary analysis step as inside particles of the regions or objects that need to be extracted via segmentation. The advantage of the aforementioned method is robustness: the result is independent of the shape or the placement of the markers in the zones of interest. The result is obtained by a global minimization implying both the topography of the surface and the complete set of markers.