Abstract (EN)

We present a new method for segmenting closed curves or surfaces from a single point. Our work builds on a variant of the Fast Marching algorithm and an implicit approach which solves a transport equation. The goal is to define the curve as a series of minimal paths linking successive keypoints. First, an initial point on the desired boundary is chosen by the user. Next, new keypoints are detected automatically using a front propagation approach. Since the desired object has a closed boundary, a relevant criterion for stopping the keypoint detection and front propagation is used. 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 curve in 2D or a network of minimal paths from a 3D image called Geodesic Mesh. To obtain a complete 3D surface that contains the mesh, we introduce an implicit approach that, through a linear partial differential equation, generates a function whose zero level set is the final segmentation. The proposed method has been successfully applied to 2D and 3D synthetic and real biological data.