Finding a Closed Boundary by Growing Minimal Paths from a Single Point on 2D or 3D Images

In this paper, we present a new method for segmenting closed contours and surfaces. Our work builds on a variant of the Fast Marching algorithm. First, an initial point on the desired contour is chosen by the user. Next, new keypoints are detected automatically using a front propagation approach. We assume that the desired object has a closed boundary. This a-priori knowledge on the topology is used to devise a relevant criterion for stopping the keypoint detection and front propagation. The final domain visited by the front will yield a band surrounding the object of interest. Linking pairs of neighboring keypoints with minimal paths allows us to extract a closed contour from a 2D image. Detection of a variety of objects on real images is demonstrated. Using a similar same idea, we can extract networks of minimal paths from a 3D image called Geodesic Meshing. The proposed method is applied to 3D data with promising results.