Compactly Supported Radial Basis Functions Based Collocation Method for Level-Set Evolution in Image Segmentation

The partial differential equation driving level-set evolution in segmentation is usually solved using finite differences schemes. In this paper, we propose an alternative scheme based on radial basis functions (RBFs) collocation. This approach provides a continuous representation of both the implicit function and its zero level set. We show that compactly supported RBFs (CSRBFs) are particularly well suited to collocation in the framework of segmentation. In addition, CSRBFs allow us to reduce the computation cost using a kd-tree-based strategy for neighborhood representation. Moreover, we show that the usual reinitialization step of the level set may be avoided by simply constraining the l₁-norm of the CSRBF parameters. As a consequence, the final solution is topologically more flexible, and may develop new contours (i.e., new zero-level components), which are difficult to obtain using reinitialization. The behavior of this approach is evaluated from numerical simulations and from medical data of various kinds, such as 3-D CT bone images and echocardiographic ultrasound images.