Level set active contours on unstructured point cloud

We present a novel level set representation and front propagation scheme for active contours where the analysis/evolution domain is sampled by unstructured point cloud. These sampling points are adaptively distributed according to both local data and level set geometry, hence allow extremely convenient enhancement/reduction of local front precision by simply putting more/fewer points on the computation domain without grid refinement (as the cases in finite difference schemes) or remeshing (typical infinite element methods). The front evolution process is then conducted on the point-sampled domain, without the use of computational grid or mesh, through the precise but relatively expensive moving least squares (MLS) approximation of the continuous domain, or the faster yet coarser generalized finite difference (GFD) representation and calculations. Because of the adaptive nature of the sampling point density, our strategy performs fast marching and level set local refinement concurrently. We have evaluated the performance of the method in image segmentation and shape recovery applications using real and synthetic data.