本文对曲面上分段常值和分段光滑的两相图像分割的变分水平集模型及其对偶方法进行了研究.图像所在的曲面用静态的符号距离函数的零水平集表达,曲面上图像分割轮廓线用另一动态符号距离函数的零水平集与上述静态的零水平集的交线表达,借助内蕴梯度、内蕴散度的概念平面两相图像分割的变分水平集模型已被推广到隐式曲面上图像分割的变分模型.本文借助二值标记函数和凸松弛的概念,将该模型转化为全局凸优化的极值问题,避免了轮廓线初始化对分割结果的影响.针对隐式曲面上两相图像分割的凸优化模型,设计了相应的对偶方法.最后通过数值实验验证了本文所提方法的计算效率优于传统方法.

The variational level set model for piecewise constant/smooth image segmentation on surfaces and the related dual methods are investigated in this paper.The implicit surface on which the image is defined is represented by zero level set of a static signed distance function,the spatial contour used to divide regions of image on the implicit surface is expressed by the intersection of another dynamic zero level set and implicit surface.The variational level set model for planar image segmentation has been extended to the one on implicit surface by means of intrinsic gradient and intrinsic divergence,which is transformed to a global convex minimization problem in this paper using a new binary label function and the concept of convex relaxation to void the effect of initialization of active contour on the result of segmentation.Finally,the dual methods for solving the global convex minimization problem is designed in this paper and some numerical experiments demonstrate the proposed method is superior to traditional method in computation efficiency.