Narrow band region-based active contours and surfaces for 2D and 3D segmentation

We describe a narrow band region approach for deformable curves and surfaces in the perspective of 2D and 3D image segmentation. Basically, we develop a region energy involving a fixed-width band around the curve or surface. Classical region-based methods, like the Chan-Vese model, often make strong assumptions on the intensity distributions of the searched object and background. In order to be less restrictive, our energy achieves a trade-off between local features of gradient-like terms and global region features. Relying on the theory of parallel curves and surfaces, we perform a mathematical derivation to express the region energy in a curvature-based form allowing efficient computation on explicit models. We introduce two different region terms, each one being dedicated to a particular configuration of the target object. Evolution of deformable models is performed by means of energy minimization using gradient descent. We provide both explicit and implicit implementations. The explicit models are a parametric snake in 2D and a triangular mesh in 3D, whereas the implicit models are based on the level set framework, regardless of the dimension. Experiments are carried out on MRI and CT medical images, in 2D and 3D, as well as 2D color photographs.