Distance Regularized Level Set Evolution and Its Application to Image Segmentation
Distance Regularized Level Set Evolution and Its Application to Image Segmentation
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DOI：
10.1109/tip.2010.2069690
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发表时间：
2010-12-01
影响因子：
10.6
通讯作者：
Fox, Martin D.
中科院分区：
文献类型：
--
作者：
Li, Chunming;Xu, Chenyang;Fox, Martin D.
水平集方法在图像处理和计算机视觉中得到了广泛的应用。在传统的水平集公式中，水平集函数在其演化过程中通常会出现不规则性，这可能会导致数值误差，最终破坏演化的稳定性。因此，通常应用称为重新初始化的数值补救方法来周期性地将退化的水平集函数替换为带符号距离函数。然而，重新初始化的做法不仅带来了应该在何时以及如何执行的严重问题，而且还以一种不受欢迎的方式影响了数值精度。本文提出了一种新的变分水平集公式，该公式在水平集演化过程中本质上保持了水平集函数的正则性。水平集演化被导出为梯度流，其最小化具有距离正则项的能量泛函和驱动零水平集向期望位置移动的外部能量。利用势函数定义距离正则化项，使得导出的水平集演化具有唯一的向前和向后(FAB)扩散效应，其能够保持水平集函数的期望形状，特别是零水平集附近的带符号距离轮廓。这产生了一种新的水平集进化，称为距离正则化水平集进化(DRLSE)。距离正则化效应消除了重新初始化的需要，从而避免了其引起的数值误差。与传统水平集公式的复杂实现相比，可以使用更简单和更有效的有限差分格式来实现DRLSE公式。DRLSE还允许使用更通用和更有效的水平集函数初始化。在数值实现中，有限差分格式可以使用较大的时间步长来减少迭代次数，同时保证足够的数值精度。为了验证DRLSE公式的有效性，我们将其应用于基于边缘的活动轮廓模型的图像分割，并提供了一种简单的窄带实现，大大降低了计算量。
Level set methods have been widely used in image processing and computer vision. In conventional level set formulations, the level set function typically develops irregularities during its evolution, which may cause numerical errors and eventually destroy the stability of the evolution. Therefore, a numerical remedy, called reinitialization, is typically applied to periodically replace the degraded level set function with a signed distance function. However, the practice of reinitialization not only raises serious problems as when and how it should be performed, but also affects numerical accuracy in an undesirable way. This paper proposes a new variational level set formulation in which the regularity of the level set function is intrinsically maintained during the level set evolution. The level set evolution is derived as the gradient flow that minimizes an energy functional with a distance regularization term and an external energy that drives the motion of the zero level set toward desired locations. The distance regularization term is defined with a potential function such that the derived level set evolution has a unique forward-and-backward (FAB) diffusion effect, which is able to maintain a desired shape of the level set function, particularly a signed distance profile near the zero level set. This yields a new type of level set evolution called distance regularized level set evolution (DRLSE). The distance regularization effect eliminates the need for reinitialization and thereby avoids its induced numerical errors. In contrast to complicated implementations of conventional level set formulations, a simpler and more efficient finite difference scheme can be used to implement the DRLSE formulation. DRLSE also allows the use of more general and efficient initialization of the level set function. In its numerical implementation, relatively large time steps can be used in the finite difference scheme to reduce the number of iterations, while ensuring sufficient numerical accuracy. To demonstrate the effectiveness of the DRLSE formulation, we apply it to an edge-based active contour model for image segmentation, and provide a simple narrowband implementation to greatly reduce computational cost.