具有bregman散度的变分非刚性配准

Daniela Portes L. Ferreira, Eraldo Ribeiro, C. Barcelos
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引用次数: 0

摘要

本文提出了一种新的能量泛函,推广了非刚性图像配准的变分方法。我们的新函数使用Bregman散度作为相似性度量。Fisher和Modersitzki在[5]中提出的配准方法是我们方法中的一个特例。我们证明了变分配准方法可以应用于任意Bregman散度。这个结果是相关的,因为这些散度包括大量有用的相似函数,如欧几里得距离的平方,散度KL, Logistic损失,Mahalanobis距离,Itakura-Saito散度和广义i散度。推导了该泛函的欧拉-拉格朗日方程和流动方程,并对其进行了最小化。实验表明,该函数可以确定不同扫描或模态图像配准的变形场。布雷格曼散度下的图像配准效果优于欧氏距离下的配准。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Variational non rigid registration with bregman divergences
In this paper, we propose a new energy functional that generalizes the variational method for non-rigid image registration. Our new functional uses the Bregman divergence as a similarity measure. The registration method presented by Fisher and Modersitzki in [5] is an special case in our approach. We show that the variational registration method can be applied to arbitrary Bregman divergences. This result is relevant because these divergences include a large number of useful similarity functions, such as the square of the Euclidean distance, the divergence KL, Logistic loss, the Mahalanobis distance, Itakura-Saito divergence and the Generalized I-divergence. The Euler-Lagrange and the flow equations for the proposed functional were deduced and used to minimize it. Our experiments show that the new functional can determine the deformation field for the images registration obtained from different scans or modalities. The image registration under the Bregman divergences performed better than when using the Euclidean distance as the similarity measure.
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