A Unified Tensor Level Set Method for Image Segmentation

Abstract

This paper presents a new unified level set model for multiple regional image segmentation. This model builds a unified tensor representation for comprehensively depicting each pixel in the image to be segmented, by which the image aligns itself with a tensor field composed of the elements in form of high order tensor. Then the multi-phase level set functions are evolved in this tensor field by introducing a new weighted distance function. When the evolution converges, the tensor field is partitioned, and meanwhile the image is segmented. The proposed model has following main advantages. Firstly, the unified tensor representation integrates the information from Gaussian smoothed image, which results the model is robust against noise, especially the salt and pepper noise. Secondly, the local geometric features involved into the unified representation increase the weight of boundaries in energy functional, which makes the model more easily to detect the edges in the image and obtain better performance on non-homogenous images. Thirdly, the model offers a general formula for energy functional which can deal with the data type varying from scalar to vector then to tensor, and this formula also unifies single and multi-phase level set methods. We applied the proposed method to synthetic, medical and natural images respectively and obtained promising performance.