Optimal mass transport for registration and warping
Optimal mass transport for registration and warping
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DOI：
10.1023/b:visi.0000036836.66311.97
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发表时间：
2004-12-01
影响因子：
19.5
通讯作者：
Angenent, S
中科院分区：
文献类型：
--
作者：
Haker, S;Zhu, L;Angenent, S
图像配准是在可能在不同时间拍摄的两个或多个图像数据集之间建立公共几何参考系的过程。在本文中，我们提出了一种基于蒙日-坎托罗维奇最优质量传输理论计算弹性配准和扭曲图的方法。这种质量传输方法具有许多重要特征。首先，它是无参数的。此外，它利用了两幅图像中的所有灰度数据，将两幅图像放在平等的基础上并且是对称的：从图像A到图像B的最优映射是从B到A的最优映射的逆。该方法不需要指定地标，并且所涉及的距离函数的极小值是唯一的；没有其他局部最小化器。最后，最佳运输自然会考虑面积或体积变化引起的密度变化。尽管最优传输方法当然并不适合所有配准和翘曲问题，但这种质量保存特性使得 Monge-Kantorovich 方法对于一类有趣的翘曲问题非常有用，正如我们在本文中所示。我们寻找配准映射的方法基于偏微分方程方法，以在质量保存约束下最小化 L-2 Kantorovich-Wasserstein 或“地球移动器距离”。我们展示了这种方法如何产生实用的算法，并通过许多示例（包括来自医学领域的示例）展示了我们的方法。我们还扩展了这种方法以考虑强度的变化，并表明它非常适合图像变形等应用。
Image registration is the process of establishing a common geometric reference frame between two or more image data sets possibly taken at different times. In this paper we present a method for computing elastic registration and warping maps based on the Monge-Kantorovich theory of optimal mass transport. This mass transport method has a number of important characteristics. First, it is parameter free. Moreover, it utilizes all of the grayscale data in both images, places the two images on equal footing and is symmetrical: the optimal mapping from image A to image B being the inverse of the optimal mapping from B to A. The method does not require that landmarks be specified, and the minimizer of the distance functional involved is unique; there are no other local minimizers. Finally, optimal transport naturally takes into account changes in density that result from changes in area or volume. Although the optimal transport method is certainly not appropriate for all registration and warping problems, this mass preservation property makes the Monge-Kantorovich approach quite useful for an interesting class of warping problems, as we show in this paper. Our method for finding the registration mapping is based on a partial differential equation approach to the minimization of the L-2 Kantorovich-Wasserstein or "Earth Mover's Distance" under a mass preservation constraint. We show how this approach leads to practical algorithms, and demonstrate our method with a number of examples, including those from the medical field. We also extend this method to take into account changes in intensity, and show that it is well suited for applications such as image morphing.