From a single point to a surface patch by growing minimal paths

Abstract

We introduce a novel implicit approach for surface patch segmentation in 3D images starting from a single point. Since the boundary surface of an object is locally homeomorphic to a disc, we know that the boundary of a small neighboring domain intersects the surface of interest on a single closed curve. Similarly to active surfaces, we use a cost potential which penalizes image regions of low interest. First, Using a front propagation approach from the source point chosen by the user, one can see that the closed curve corresponds to a valley line of the arrival time from the source point. Next, we use an implicit 3D segmentation method. It assumes that the object boundary contains two known constraining curves. In our case, the first curve is reduced to a point and the other one is automatically detected by our approach. A partial differential equation is introduced and its solution is used for segmentation. The zero level set of this solution contains the valley line and the source point as well as the set of minimal paths joining them. We present a fast implementation which has been successfully applied to 3D biomedical and synthetic images. © 2009 Springer Berlin Heidelberg.