Geometric deformable model in the confidence field

The geometric deformable model (GDM) determines object boundaries by evolving initial interfaces along the normal direction. A speed function controls how fast the interfaces move. When the speed function is zero or sufficiently small, the evolution stops or slows down significantly. Because the gradient flow equation that governs a GDM's evolution can be easily implemented with the level set technique, the GDM has the distinct advantage of being topologically flexible. Since its inception, the GDM has been successfully applied to many applications in medical imaging where variable geometry and topology of the model is crucial. Although much work has been done to improve and extend this method, little attention has been paid to the formulation of the speed function. Most existing GDMs use a fixed form of speed function for all applications. They also don't explicitly take noise into consideration. In this paper, we address these problems by formalizing the meaning of speed function. We believe that the speed of interface evolution should be determined by the confidence (or lack of) that the interface is on the boundary of interest. We describe two new speed functions based on this concept and demonstrate their effectiveness with both simulated and actual medical data. Our results show that the new speed functions are less sensitive to noise, allow faster evolution, and provide a better stopping power.