The shading zone problem in geodesic voting and its solutions for the segmentation of tree structures. Application to the segmentation of Microglia extensions

This paper presents a new method to segment thin tree structures, which are for example present in microglia extensions and cardiac or cerebral blood vessels. The minimal path method allows the segmentation of tubular structures between two points chosen by the user. A feature potential function is defined on the image domain. This corresponds to geodesic paths relatively to the metric weighted by the potential. We propose here to compute geodesics from a set of end points scattered in the image to a given source point. The target structure corresponds to image points with a high geodesic density. The geodesic density is defined at each pixel of the image as the number of geodesics that pass over this pixel. Since the potential takes low values on the tree structure, geodesics will locate preferably on this structure and thus the geodesic density should be high. The segmentation results depend on the distribution of the end points in the image. When only the image border is used to perform geodesic voting, the obtained geodesic density is contrasted and easy to use for image segmentation. However, when the tree to segment is complex a shading problem appears: some contours of the image can have a null density since geodesic have a better way around this region. To deal with this problem we propose several different strategies: we use several source points for the propagation by Fast Marching; a set of characteristic points or an adaptive set of points in the image or make successive segmentation in the shading zones. Numerical results on synthetic and microscopic images are presented.