Shape and Topology Constraints on Parametric Active Contours

In recent years, the field of active contour-based image segmentation has seen the emergence of two competing approaches. The first and oldest approach represents active contours in an explicit (or parametric) manner corresponding to the Lagrangian formulation. The second approach represents active contours in an implicit manner corresponding to the Eulerian framework. After comparing these two approaches, we describe several new topological and physical constraints applied to parametric active contours in order to combine the advantages of these two contour representations. More precisely, we introduce three algorithms related to the control of the contour topology, geometry, and deformation. The first algorithm controls both vertex spacing and contour smoothness in an independent and intrinsic manner. The second algorithm controls the contour resolution (number of vertices) while the third algorithm automatically creates or fuses connected components on closed or opened contours. The efficiency of these algorithms is demonstrated on several images including medical images and a comparison with the level-sets method is also provided.