Level set evolution model for image segmentation based on variable exponent p-Laplace equation

Abstract

In this paper, we proposed a modified active contour model based on p-Laplace equation for image segmentation. By combining the region information with the variable exponent p-Laplace energy, the modified model can fast and accurately segment the image with complex topological changes with flexible scheme of level set function initialization. Firstly, the region information is used to find the contours nearby the object boundaries. Secondly, the variable exponent p-Laplace energy is used for the regularization of the zero level contours that move to the accurate object boundaries with complex topological changes and deep depression. In addition, the Gaussian filter is used to keep the level set smoothing in the evolution process. Finally, the numerical scheme of the partial difference equation (PDE) based modified model is implemented via a simple finite difference method. And the scheme of level set function initialization can be chosen flexibly (i.e. a bounded constant function, a signed distance function(SDF) or a piecewise constant function). The experiment results on some synthetic and real images show that the modified model can segment complex object boundaries and the evolution of contours do not sensitive to the scheme of the level set function initialization.