无约束图像分割模型的快速数值算法

Fast Numerical Algorithm for Unconstrained Image Segmentation Model

针对无约束图像分割模型的实现问题,提出一种基于分块协调下降方法的快速数值算法.该算法将模型的对偶问题转化为一组约束一元或二元二次极值问题,不仅避免了原问题求解时局部不可微性和高非线性性等难点,使得求解过程简单并易于实现;而且与现有的基于梯度下降的算法相比,具有无条件全局收敛性并显著地提高了收敛速度.仿真实验结果表明了所提出算法的有效性和在分割效率上的优越性.

This paper proposes a fast numerical algorithm for unconstrained image segmentation model based on block coordinate de- scent method. The algorithm makes the dual formulation of primal model is equal to a set of constrained quadratic minimization prob- lems with at most two unknowns. It is not only easy to implement for avoiding the local non-differentiability and highly nonlinearity when minimizing primal model, but also global convergent and more efficient compared with those algorithms based on gradient descend method. The numerical examples illustrates its validity and advantage of efficiency.