A Variational Model Of Image Segmentation On Implicit Surfaces And Its Algorithms

Image segmentation is based on the characteristics of the edge, area, the noise distribution, color, texture, optical flow field and prior knowledge (such as a priori shape of image) to divide the image into different regions. With the variational level set method, variational level set model of image segmentation is developing and applying rapidly.Surface segmentation is a new problem in recent years in the field of surface image processing.The main difference of this kind of problem with the conventional planar image segmentation is that the division depends on the local geometry of the image. The surface expression is the important issues on the accuracy and complexity of mathematical model in surface image processing, thereby increasing the difficulty of image processing on the surface.This paper presents a variational model of image segmentation on implicit open surfaces and designs the corresponding dual method and Split Bregman algorithm. The surface with arbitrary topology is expressed using the intersection of zero level set of a continuous signed distance function and a binary label function. Characteristic functions for region division on a surface are designed based on the scheme partitioning n regions using n-1binary label functions. Variational models for multiphase image segmentation on implicit surfaces are proposed by making use of concepts of intrinsic gradients and intrinsic divergences. For the minimization with respect to binary label functions, we transform the original problems into convex optimization models by replacing the discrete label functions with continuous ones. In order to improve the computation efficiency, the corresponding dual method and Split Bregman algorithm are designed for the models via introducing auxiliary variables, dual variables and Bregman iterative parameters respectively. Some numerical examples validate the models and demonstrate the efficiency of the algorithms proposed in this paper.