Simultaneous segmentation and approximation of complex patterns

Deformable model have been widely used to approximate objects from collected data points, but most algorithms based on the deformable model can only handle geometrically and topologically simple objects. They are inadequate for objects with deep cavities or multi-part objects. Furthermore, they always assume there is only one underlying object for the collected data, which means the segmentation has been done ahead of time. Unlike most deformable algorithms which approximate one object at a time, our proposed approach can apply simultaneously more than one curve to approximate multiple objects. Using (1) the residual data points, (2) the bad parts of the fitting curve, and (3) appropriate Boolean operations, our approach is able to detect patterns with holes or cavities, and can perform segmentation by itself for more than one underlying object. We currently present experiments mainly on 2D data. These 2D algorithms can be extended to 3D without theoretical difficulties. An experiment on 3D data, composed of two genus I toruses, is also presented. Also, a new method for defining the external energy is presented, which helps capture the shape more accurately with low time and reasonable space complexities, and a method to prevent self-intersection of the curve during evolution is also introduced