Image registration by minimization of Mapping Complexity

A. Myronenko, Xubo B. Song
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引用次数: 2

Abstract

The criterion for the correct spatial alignment is a key component in image registration. We formulate the registration problem as one that finds the spatial and intensity mappings of minimal complexity that make images exactly equal. We do not assume any parametric forms of these functions, and estimate them within variational calculus. We analytically solve for non-stationary intensity mapping, eliminate it from the objective function and arrive with a new similarity measure. We name it the mapping complexity (MC) similarity measure, because it achieves the optimum when intensity and spatial mappings are of minimal complexity. Due to its general formulation, the similarity measure works both for complex intensity relationships (e.g. multimodal registration) and for spatially-varying intensity distortions. Our similarity measure can be interpreted as the one that favors one image to lie mostly within a span of the leading eigenvectors of the kernel matrix, where the kernel matrix is constructed from the second image. We introduce a fast algorithm to compute the similarity measure. In particular, we introduce a fast kernel vector product (FKVP) algorithm, which is of general interest in computer vision. We demonstrate the accuracy of the new similarity measure on several mono- and multi-modal examples with complex intensity non-uniformities.
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最小化映射复杂度的图像配准
正确的空间对齐准则是图像配准的关键。我们将配准问题表述为找到最小复杂度的空间和强度映射,使图像完全相等。我们不假设这些函数的任何参数形式,并在变分演算中估计它们。对非平稳强度映射进行解析求解,将其从目标函数中剔除,得到新的相似性测度。我们将其命名为映射复杂性(MC)相似度度量,因为当强度和空间映射的复杂性最小时,它能达到最优。由于其一般公式,相似性度量既适用于复杂的强度关系(如多模态注册),也适用于空间变化的强度扭曲。我们的相似性度量可以被解释为倾向于一个图像大部分位于核矩阵的主要特征向量的跨度内,其中核矩阵是由第二张图像构造的。我们引入了一种快速的相似度计算算法。特别地,我们介绍了一种快速核向量积(FKVP)算法,这是计算机视觉中普遍感兴趣的算法。我们在几个具有复杂强度非均匀性的单模态和多模态例子上证明了新的相似性度量的准确性。
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