论文标题
使用分裂的布雷格曼算法来解决自我依赖的蛇模型
Using the Split Bregman Algorithm to Solve the Self-repelling Snake Model
论文作者
论文摘要
在许多实际情况下，在图像分割过程中保留轮廓拓扑是有用的。通过保持轮廓同构，可以防止过度分割和分割不足，并遵守给定的拓扑结构。自我抑制蛇模型（SR）是一个变异模型，可通过将非本地排斥项与地球活性轮廓模型（GAC）相结合来保留轮廓拓扑。传统上，使用添加剂拆分（AOS）方案来解决SR。在我们的论文中，我们使用拆分布雷格曼方法为SR提出了替代解决方案。我们的算法将问题分解为更简单的子问题，以使用低阶进化方程和简单的投影方案，而不是重新定位。可以通过快速傅立叶变换（FFT）或近似软阈值公式来解决子问题，该公式可保持稳定性，缩短收敛时间并减少内存需求。在理论上和实验中比较了裂解的Bregman和AOS算法。
Preserving contour topology during image segmentation is useful in many practical scenarios. By keeping the contours isomorphic, it is possible to prevent over-segmentation and under-segmentation, as well as to adhere to given topologies. The Self-repelling Snake model (SR) is a variational model that preserves contour topology by combining a non-local repulsion term with the geodesic active contour model (GAC). The SR is traditionally solved using the additive operator splitting (AOS) scheme. In our paper, we propose an alternative solution to the SR using the Split Bregman method. Our algorithm breaks the problem down into simpler sub-problems to use lower-order evolution equations and a simple projection scheme rather than re-initialization. The sub-problems can be solved via fast Fourier transform (FFT) or an approximate soft thresholding formula which maintains stability, shortening the convergence time, and reduces the memory requirement. The Split Bregman and AOS algorithms are compared theoretically and experimentally.
