Image segmentation by geodesic voting. Application to the extraction of tree structures from confocal microscope images

This paper presents a new method to segment thin tree structures, such as extensions of microglia and cardiac or cerebral blood vessels. The Fast Marching method allows the segmentation of tree structures from a single point chosen by the user when a priori information is available about the length of the tree. In our case, no a priori information about the length of the tree structure to extract is available. We propose here to compute geodesics from a set of points scattered in the image. The targeted structure corresponds to image points with a high geodesic density. To compute the geodesic density we propose two methods. The first method defines the geodesic density of pixels in the image as the number of geodesics that cross this pixel. The second method consists in solving the transport equation with a velocity computed from the gradient of the distance map. In this method, the geodesic density is computed by integrating in short time the solution of the transport equation. To our knowledge this is the first time that geodesic voting is introduced. Numerical results from confocal microscope images are presented and show the interest of our approach.