This paper proposes a new framework and algorithms to address the problem of diffeomorphic registration on a general class of geometric objects that can be described as discrete distributions of local direction vectors. It builds on both the large deformation diffeomorphic metric mapping (LDDMM) model and the concept of oriented varifolds introduced in previous works like [Kaltenmark 2017]. Unlike previous approaches in which varifold representations are only used as surrogates to define and evaluate fidelity terms, the specificity of this paper is to derive direct deformation models and corresponding matching algorithms for discrete varifolds. We show that it gives on the one hand an alternative numerical setting for curve and surface matching but that it can also handle efficiently more general shape structures, including multi-directional objects or multi-modal images represented as distributions of unit gradient vectors.
3D图像配准是医学图像分析中最基本和计算量最大的操作之一。在这里，我们提出了一个混合精度，高斯-牛顿-Krylov求解器的两个图像的双态配准。我们的工作将公开可用的CLAIRE库扩展到GPU架构。尽管图像配准很重要，但只有少数大变形同构配准软件包支持GPU。我们的贡献是新的算法，显着减少运行时间的两个主要计算内核CLAIRE：计算的衍生物和分散的数据插值。我们部署（i）高度优化的混合精度GPU内核用于评估分散数据插值，（ii）用优化的八阶有限差分替换基于快速傅立叶变换（FFT）的一阶导数，以及（iii）与最先进的CPU和GPU实现进行比较。作为一个亮点，我们证明了我们可以在不到6秒的时间内在一个NVIDIA Tesla V100上配准$256^3$临床图像。这相当于在当前版本的CLAIRE上加速超过20 $\times$，在现有GPU实现上加速超过30 $\times$。
VPREG: An Optimal Control Formulation for Diffeomorphic Image Registration Based on the Variational Principle Grid Generation Method
Department of Pharmacology and Neuroscience, University of North Texas Health Science Center（药理学与神经科学系，北德克萨斯健康科学中心大学）；Department of Mathematics, University of Texas at Arlington（数学系，德克萨斯大学阿灵顿分校）；Department of Mathematics, University of Houston（数学系，休斯顿大学）
Indirect Image Registration with Large Diffeomorphic Deformations
Department of Mathematics, KTH–Royal Institute of Technology（数学系，皇家理工学院）；LSEC, ICMSEC, Academy of Mathematics and Systems Science, Chinese Academy of Sciences（数学和系统科学研究所，中国科学院）
Multi-Node Multi-GPU Diffeomorphic Image Registration for Large-Scale Imaging Problems
本文提出了一种大变形双纯图像配准的Gauss-Newton-Krylov求解器。我们将公开可用的CLAIRE库扩展到多节点多图形处理单元（GPU）系统，并引入新的算法修改，显着提高性能。我们的贡献包括（$i$）一个新的预处理器减少空间高斯-牛顿海森系统，（$ii$）一个高度优化的多节点多GPU实现利用设备直接通信的主要计算内核（插值，高阶有限差分算子和快速傅立叶变换），和（$iii$）与国家的比较最先进的CPU和GPU实现。我们在单个NVIDIA Tesla V100上在5秒内解决了$256^3$分辨率图像配准问题，与最先进的技术相比，性能加速了70%。在我们最大的运行中，我们配准了$2048^3$分辨率图像（25 B未知数;大约152个$\times$，比最先进的GPU实现中解决的最大问题大），在TACC的Longhorn系统上具有256个GPU的64个节点上。
CLAIRE: A distributed-memory solver for constrained large deformation diffeomorphic image registration
University of Houston（休斯顿大学）；University of California, Berkeley（加州大学伯克利分校）；University of Pennsylvania（宾夕法尼亚大学）；University of Texas at Austin（德克萨斯大学奥斯汀分校）
A Semi-Lagrangian two-level preconditioned Newton-Krylov solver for constrained diffeomorphic image registration
The Institute for Computational Engineering and Sciences, The University of Texas at Austin（得克萨斯大学奥斯汀分校计算工程与科学研究所）；Department of Mathematics at the University of Houston（休斯顿大学数学系）
