This paper introduces Fourier-approximated Lie algebras for shooting (FLASH), a fast geodesic shooting algorithm for diffeomorphic image registration. We approximate the infinite-dimensional Lie algebra of smooth vector fields, i.e., the tangent space at the identity of the diffeomorphism group, with a low-dimensional, bandlimited space. We show that most of the computations for geodesic shooting can be carried out entirely in this low-dimensional space. Our algorithm results in dramatic savings in time and memory over traditional large-deformation diffeomorphic metric mapping algorithms, which require dense spatial discretizations of vector fields. To validate the effectiveness of FLASH, we run pairwise image registration on both 2D synthetic data and real 3D brain images and compare with the state-of-the-art geodesic shooting methods. Experimental results show that our algorithm dramatically reduces the computational cost and memory footprint of diffemorphic image registration with little or no loss of accuracy.

中文翻译：

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基于傅里叶近似李代数的快速微分纯图像配准

本文介绍了傅立叶近似李代数拍摄（FLASH），一种用于微分纯射图像配准的快速测地线拍摄算法。我们用一个低维的带限空间来近似平滑向量场的无限维李代数，即微分同胚群标识处的切空间。我们表明，测地线拍摄的大部分计算都可以完全在这个低维空间中进行。与需要矢量场密集空间离散化的传统大变形微分形度量映射算法相比，我们的算法显着节省了时间和内存。为了验证 FLASH 的有效性，我们在 2D 合成数据和真实 3D 大脑图像上运行成对图像配准，并与最先进的测地线拍摄方法进行比较。