Diffeomorphic Registration of Discrete Geometric Distributions
Diffeomorphic Registration of Discrete Geometric Distributions
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DOI：
10.1142/9789811200137_0003
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发表时间：
2018-01
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通讯作者：
Hsi-Wei Hsieh;N. Charon
中科院分区：
文献类型：
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作者：
Hsi-Wei Hsieh;N. Charon
本文提出了一种新的框架和算法，以解决一般类的几何对象，可以被描述为离散分布的局部方向向量的同构配准问题。它建立在大变形几何度量映射（LDDMM）模型和以前的作品中引入的定向变倍概念（如[Kaltenmark 2017]）的基础上。不同于以往的方法，其中varifold表示仅用作代理定义和评估保真度条款，本文的特点是推导出直接的变形模型和相应的匹配算法离散varifolds。我们表明，它一方面提供了一个替代的数值设置曲线和曲面匹配，但它也可以有效地处理更一般的形状结构，包括多方向的对象或多模态图像表示为单位梯度向量的分布。
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.