基于改进符号距离函数的变分水平集图像分割算法

A Variational Level Set Method for Image Segmentation Based on Improved Signed Distance Function

为保证水平集图像分割算法的稳定性,传统水平集方法常采用重新初始化的方法或引入符号距离函数,但这两种方法存在计算量大或计算不稳定的问题.因此,提出一种基于改进符号距离函数的变分水平集图像分割算法.首先,改进已有的Double-Well型符号距离函数约束项,改进后的约束项可避免重新初始化、提高计算效率,同时也能更好地保证水平集函数演化过程的稳定.然后,利用基于全局灰度信息和局部灰度信息的活动轮廓模型构造能量泛函,该能量函数继承了全局模型和局部模型的优点,可驱动水平集函数准确演化至目标边界,且可动态调整组合权重.最后,引入高斯卷积运算,加快演化速度同时也对水平集函数起到平滑的作用.对人工合成和自然图像的数值实验及与同类模型的对比实验证明,提出的模型具有较高的分割准确度及对噪声和初始轮廓的鲁棒性.

In order to maintain the stability of traditional level set methods, the re-initialization method or a signed distance function is often used. However, those two methods are either time-consuming or instable. Thus, a signed distance function based level set method is proposed for overcoming those disadvantages. Firstly, the existing Double-Well constraint term is improved, which avoids re-initialization, increases the computational efficiency and makes the evolution more stable. Secondly, the active contour model based on the global grey information and local grey information is used to construct the energy function, thus it inherits the advantages of global and local models and drives the level set function accurately to real objective boundaries. Besides, the weigh of combination can be adjusted dynamically. At last, Gaussian convolution is presented to accelerate the speed of evolution and smooth the level set function. The experiments on both synthesis images and real images show that the proposed method has high computational efficiency and accuracy, and it is robust to noia~ nnd ;n;,;~l