Topological Active Nets are promising parametric deformable models that integrate features of region-based and boundary-based segmentation techniques. Problems associated with the complexity of the model, however, have limited their utility. This paper introduces an extension of the model, defining a new behavior for changing its topology, as well as a novel external force definition and a new local search optimization procedure. In particular, we propose a new automatic pre-processing phase, a new external energy term based on the Extended Vector Field Convolution, node movement constraints to avoid crossing links, and different procedures to perform link cuts and hole detection. Moreover, the new local search procedure also incorporates heuristics to correct the position of eventually misplaced nodes. The proposal has been tested on 18 synthetic images which present different segmentation difficulties along with 3 real medical images. Its performance has been compared with that of the original Topological Active Net optimization approach along with both state-of-the-art parametric and geometric active contours: two snakes (based on Gradient Vector Flow and Vector Field Convolution), and two level sets (Chan and Vese, and Geodesic Active Contour). Our new method outperforms all the others for the given image sets, in terms of segmentation accuracy measured by using four standard segmentation metrics. 
Extended Topological Active Nets