A New Implicit Method for Surface Segmentation by Minimal Paths: Applications in 3D Medical Images

Abstract

We introduce a novel implicit approach for single object segmentation in 3D images. The boundary surface of this object is assumed to contain two known curves (the constraining curves), given by an expert. The aim of our method is to find this surface by exploiting as much as possible the information given in the supplied curves. As for active surfaces, we use a cost potential which penalizes image regions of low interest (most likely areas of low gradient or away from the surface to be extracted). In order to avoid local minima, we introduce a new partial differential equation and use its solution for segmentation. We show that the zero level set of this solution contains the constraining curves as well as a set of paths joining them. These paths globally minimize an energy which is defined from the cost potential. Our approach is in fact an elegant, implicit extension to surfaces of the minimal path framework already known for 2D image segmentation. As for this previous approach, and unlike other variational methods, our method is not prone to local minima traps of the energy. We present a fast implementation which has been successfully applied to 3D medical and synthetic images.