Analysis of Numerical Methods for Level Set Based Image Segmentation

In this paper we analyze numerical optimization procedures in the context of level set based image segmentation. The Chan-Vese functional for image segmentation is a general and popular variational model. Given the corresponding Euler-Lagrange equation to the ChanVese functional the region based segmentation is usually done by solving a differential equation as an initial value problem. While most works use the standard explicit Euler method, we analyze and compare this method with two higher order methods (second and third order RungeKutta methods). The segmentation accuracy and the dependence of these methods on the involved parameters are analyzed by numerous experiments on synthetic images as well as on real images. Furthermore, the performance of the approaches is evaluated in a segmentation benchmark containing 1023 images. It turns out, that our proposed higher order methods perform more robustly, more accurately and faster compared to the commonly used Euler method.