具有萎缩约束的LDDMM表面配准

Weight metamorphosis of varifolds and the LDDMM-Fisher-Rao metric

This paper introduces and studies a metamorphosis framework for geometric measures known as varifolds, which extends the diffeomorphic registration model for objects such as curves, surfaces and measures by complementing diffeomorphic deformations with a transformation process on the varifold weights. We consider two classes of cost functionals to penalize those combined transformations, in particular the LDDMM-Fisher-Rao energy which, as we show, leads to a well-defined Riemannian metric on the space of varifolds with existence of corresponding geodesics. We further introduce relaxed formulat…

Efficient Gauss-Newton-Krylov momentum conservation constrained PDE-LDDMM using the band-limited vector field parameterization

The class of non-rigid registration methods proposed in the framework of PDE-constrained Large Deformation Diffeomorphic Metric Mapping is a particularly interesting family of physically meaningful diffeomorphic registration methods. PDE-constrained LDDMM methods are formulated as constrained variational problems, where the different physical models are imposed using the associated partial differential equations as hard constraints. Inexact Newton-Krylov optimization has shown an excellent numerical accuracy and an extraordinarily fast convergence rate in this framework. However, the Galerkin …

Sliding at first order: Higher-order momentum distributions for discontinuous image registration

In this paper, we propose a new approach to deformable image registration that captures sliding motions. The large deformation diffeomorphic metric mapping (LDDMM) registration method faces challenges in representing sliding motion since it per construction generates smooth warps. To address this issue, we extend LDDMM by incorporating both zeroth- and first-order momenta with a non-differentiable kernel. This allows to represent both discontinuous deformation at switching boundaries and diffeomorphic deformation in homogeneous regions. We provide a mathematical analysis of the proposed deform…

基于约束最优控制的多形状配准

Multiple Shape Registration using Constrained Optimal Control

拉格朗日粒子制剂的大变形几何度量映射算法（LDDMM）只允许研究一个单一的形状。在本文中，我们介绍并讨论了同时研究多个形状的理论和实践设置，这些形状要么彼此缝合，要么沿着子流形滑动。该方法描述内的最优控制形式主义，并给出了最优性条件，连同方程，需要实施增广拉格朗日方法。缝合和滑动表面的实验结果。

Diffeomorphic registration of discrete geometric distributions

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 corre…

最优传输用于变形匹配

Optimal Transport for Diffeomorphic Registration

本文提出基于不平衡最优传输的快速全局相似性度量，用于影像数据的变形匹配，提升匹配精度。