Fast global minimization of the active Contour/Snake model
Fast global minimization of the active Contour/Snake model
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DOI：
10.1007/s10851-007-0002-0
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发表时间：
2007-06-01
影响因子：
2
通讯作者：
Osher, Stanley
中科院分区：
文献类型：
--
作者：
Bresson, Xavier;Esedoglu, Selim;Osher, Stanley
活动轮廓/Snake模型是图像分割中最成功的变分模型之一。它包括使图像中的轮廓朝着对象的边界演变。它的成功是基于强大的数学性质和基于Level Set方法的高效数值格式。该模型唯一的缺点是活动轮廓能量局部极小值的存在，这使得初始猜测对于获得满意的结果是至关重要的。在本文中，我们提出通过确定活动轮廓模型的全局最小值来解决这一问题。我们的方法基于将图像分割和图像去噪任务统一到一个全局最小化框架中。更准确地说，我们建议统一三个著名的图像变分模型，即Snake模型、Rudin-Osher-Fatei去噪模型和Mumford-Shah分割模型。我们将建立带有证明的定理来确定活动轮廓模型的全局最小值的存在性。从数值角度出发，通过最小化问题的对偶表示，提出了一种新的实用方法来解决活动轮廓向目标边界的传播问题。对偶公式，易于实现，允许我们快速地全局最小化蛇的能量。它避免了水平集方法中通常的缺点，即在距离函数中初始化活动轮廓，并在进化过程中周期性地重新初始化它，这是耗时的。我们将我们的分割算法应用于合成图像和真实世界的图像，例如纹理图像和医学图像，以强调我们的模型与其他分割模型相比的性能。
The active contour/snake model is one of the most successful variational models in image segmentation. It consists of evolving a contour in images toward the boundaries of objects. Its success is based on strong mathematical properties and efficient numerical schemes based on the level set method. The only drawback of this model is the existence of local minima in the active contour energy, which makes the initial guess critical to get satisfactory results. In this paper, we propose to solve this problem by determining a global minimum of the active contour model. Our approach is based on the unification of image segmentation and image denoising tasks into a global minimization framework. More precisely, we propose to unify three well-known image variational models, namely the snake model, the Rudin-Osher-Fatemi denoising model and the Mumford-Shah segmentation model. We will establish theorems with proofs to determine the existence of a global minimum of the active contour model. From a numerical point of view, we propose a new practical way to solve the active contour propagation problem toward object boundaries through a dual formulation of the minimization problem. The dual formulation, easy to implement, allows us a fast global minimization of the snake energy. It avoids the usual drawback in the level set approach that consists of initializing the active contour in a distance function and re-initializing it periodically during the evolution, which is time-consuming. We apply our segmentation algorithms on synthetic and real-world images, such as texture images and medical images, to emphasize the performances of our model compared with other segmentation models.