Active Contour Without Edges using Chan-Vese
A class project for CSE 577 (Medical Imaging), Spring '23, Stony Brook University
The landscape of mathematical models addressing this task has evolved since the 1970s. Notably, the Chan-Vese segmentation model, conceived during this period, stands out by not incorporating edge information in its solution to the segmentation problem. Originally designed for two-phase segmentation and grayscale images, the Chan-Vese algorithm laid the foundation for subsequent advancements. This report delves into the exploration of the original Chan-Vese model and its adaptations for multi-phase segmentation and RGB images. Although the initial Chan-Vese framework is tailored for grayscale images, it can be effortlessly extended to handle 3-D images. The model can be applied individually to each 2-D slice of a 3-D image, computing the resultant forces F1 and F2, which collectively influence the boundary movement.
The intuitive explanation of the Chan-Vese model reveals a dynamic interplay of two forces: one compelling the boundary inwards and the other exerting an outward pull. Extending the algorithm beyond binary segmentation, the report demonstrates its versatility in accommodating multi-phase segmentation. In this context, the algorithm groups regions based on their mean values, effectively distinguishing colors and facilitating the grouping of closely related hues. By assigning regions to their respective mean values, the algorithm adapts to scenarios where two regions possess mean values closer to each other than to the rest, resulting in their amalgamation. This extension broadens the applicability of the Chan-Vese model and is exemplified with insightful examples to enhance understanding.