Abstract: The existing Region Scalable Fitting（RSF） energy model is based on the approximation of the gray value inside and outside the initial contour, which better deals with the problem of image gray unevenness existing in image segmentation. However, when choosing an inappropriate initial contour, it is easy to fall into the local minimum due to the non-convexity of the energy functional of the RSF model. In order to ensure the robustness of initialization, a RSF model with fitting function optimization is proposed. In the process of curve evolution, a function is added in the opposite direction of the evolution direction to exchange the internal and external fitting values of the curve, so that the whole curve evolves along the ipsilateral boundary of the object. Spectral theory is introduced into the model to enable it to cluster large data samples and quickly converge to global optimal solutions. The improved model is applied to medical image segmentation. The experimental results show that the model obtains more robust segmentation results and higher segmentation efficiency than RSF model.

Key words: level set method, spectral clustering, nystrom method, cosine similarity, [k]-means

摘要： 现有的可变区域拟合能量（RSF）模型基于初始轮廓内外灰度值的近似，较好地处理了图像分割中存在的图像灰度不均匀的问题。但当选择不恰当的初始轮廓时，由于RSF模型能量函数的非凸性质，极易陷入局部最小值。为了保证初始化的鲁棒性，提出了一种拟合函数优化的RSF模型。在曲线演化过程中，在演化方向相反的区域增加一个函数来交换曲线内外拟合值，使整条曲线沿物体的同侧边界演化。又将谱图理论引入该模型，使其能对大数据样本聚类且快速收敛至全局最优解。将改进模型应用于医学图像分割，实验结果表明该模型较RSF模型获得了更鲁棒的分割结果和较高的分割效率。

关键词: 水平集, 谱聚类, nystrom方法, 余弦相似度, [k]-means