前向后向扩散的距离正则模型应用于图像分割*

针对在演化过程中水平集函数震荡问题，提出前向后向扩散的距离正则模型应用于图像分割。新的距离正则项由一个势函数定义，推导的演化方程以唯一的方式前向后向扩散，即：水平集函数在其陡峭区域前向扩散，降低函数的梯度模直至为1，反之它后向扩散，提高梯度模直至1。演化结果是水平集函数收敛于符号距离函数，这是水平集函数稳定演化所希望保持的状态。为了阐述距离正则项的有效性，本文将其和基于边缘信息的外能量项相结合。实验结果表明，该模型能够好的完成图像分割，对噪声和弱目标图像鲁棒。

Forward-and-Backward Diffusion-Based Distance Regularized model for Image Segmentation

A forward-and-backward diffusion-based distance regularized model for image segmentation is introduced to deal with the problem of irregularities that commonly appears in level set evolution. The distance regularization term (DRT) is defined with a potential function such as the derived level set evolution has a unique forward-and-backward diffusion effect, i.e., the diffusion is forward for steep shape region of the level set function(LSE), which keeps decreasing the gradient magnitude until it approaches 1 , otherwise, the diffusion becomes backward and increases the gradient magnitude back to 1. As a result, the LSE converges to sign distance function which is a desired shape of level set evolution. To demonstrate the effectiveness of the DRT, we apply it to an edge-based external energy for image segmentation. Experimental results show a good performance of the distance regularized model, and the proposed method is robust for noisy and/or weak object images.