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In this article we introduce a diffeomorphism-invariant Riemannian metric on the space of vector valued one-forms. The particular choice of metric is motivated by potential future applications in the field of functional data and shape…

Differential Geometry · Mathematics 2020-09-04 Martin Bauer , Eric Klassen , Stephen C. Preston , Zhe Su

We propose a new variational model for joint image reconstruction and motion estimation in spatiotemporal imaging, which is investigated along a general framework that we present with shape theory. This model consists of two components, one…

Numerical Analysis · Mathematics 2019-11-06 Chong Chen , Barbara Gris , Ozan Öktem

In computational anatomy, the statistical analysis of temporal deformations and inter-subject variability relies on shape registration. However, the numerical integration and optimization required in diffeomorphic registration often lead to…

Graphics · Computer Science 2019-06-17 N. Guigui , Shuman Jia , Maxime Sermesant , Xavier Pennec

We present a new approach for matching regular surfaces in a Riemannian setting. We use a Sobolev type metric on deformation vector fields which form the tangent bundle to the space of surfaces. In this article we compare our approach with…

Differential Geometry · Mathematics 2014-09-22 Martin Bauer , Martins Bruveris

Deformable image registration can obtain dynamic information about images, which is of great significance in medical image analysis. The unsupervised deep learning registration method can quickly achieve high registration accuracy without…

Computer Vision and Pattern Recognition · Computer Science 2022-07-19 Xiao Fan , Shuxin Zhuang , Zhemin Zhuang , Ye Yuan , Shunmin Qiu , Alex Noel Joseph Raj , Yibiao Rong

Advances in the development of largely automated microscopy methods such as MERFISH for imaging cellular structures in mouse brains are providing spatial detection of micron resolution gene expression. While there has been tremendous…

Numerical Analysis · Mathematics 2022-12-20 Michael I Miller , Alain Trouvé , Laurent Younes

Deep neural networks are increasingly used for pair-wise image registration. We propose to extend current learning-based image registration to allow simultaneous registration of multiple images. To achieve this, we build upon the pair-wise…

Image and Video Processing · Electrical Eng. & Systems 2020-10-02 Tycho F. A. van der Ouderaa , Ivana Išgum , Wouter B. Veldhuis , Bob D. de Vos

We introduce an end-to-end deep-learning framework for 3D medical image registration. In contrast to existing approaches, our framework combines two registration methods: an affine registration and a vector momentum-parameterized stationary…

Computer Vision and Pattern Recognition · Computer Science 2019-03-22 Zhengyang Shen , Xu Han , Zhenlin Xu , Marc Niethammer

These lecture notes explain the geometry and discuss some of the analytical questions underlying image registration within the framework of large deformation diffeomorphic metric mapping (LDDMM) used in computational anatomy.

Differential Geometry · Mathematics 2013-11-01 Martins Bruveris , Darryl D. Holm

For a wide range of clinical applications, such as adaptive treatment planning or intraoperative image update, feature-based deformable registration (FDR) approaches are widely employed because of their simplicity and low computational…

Computer Vision and Pattern Recognition · Computer Science 2020-01-17 Siming Bayer , Ute Spiske , Jie Luo , Tobias Geimer , William M. Wells , Martin Ostermeier , Rebecca Fahrig , Arya Nabavi , Christoph Bert , Ilker Eyupoglo , Andreas Maier

Deep Implicit Functions (DIFs) represent 3D geometry with continuous signed distance functions learned through deep neural nets. Recently DIFs-based methods have been proposed to handle shape reconstruction and dense point correspondences…

Computer Vision and Pattern Recognition · Computer Science 2022-03-23 Shanlin Sun , Kun Han , Deying Kong , Hao Tang , Xiangyi Yan , Xiaohui Xie

Non-rigid registration computes an alignment between a source surface with a target surface in a non-rigid manner. In the past decade, with the advances in 3D sensing technologies that can measure time-varying surfaces, non-rigid…

Computer Vision and Pattern Recognition · Computer Science 2022-03-18 Bailin Deng , Yuxin Yao , Roberto M. Dyke , Juyong Zhang

Objects that undergo non-rigid deformation are common in the real world. A typical and challenging example is the human faces. While various techniques have been developed for deformable shape registration and classification, benchmarks…

Computer Vision and Pattern Recognition · Computer Science 2018-07-11 Gareth Andrews , Sam Endean , Roberto Dyke , Yukun Lai , Gwenno Ffrancon , Gary KL Tam

Deformable image registration is a fundamental task in medical image analysis and plays a crucial role in a wide range of clinical applications. Recently, deep learning-based approaches have been widely studied for deformable medical image…

Image and Video Processing · Electrical Eng. & Systems 2023-07-03 Jing Zou , Noémie Debroux , Lihao Liu , Jing Qin , Carola-Bibiane Schönlieb , Angelica I Aviles-Rivero

Traditional methods for high-dimensional diffeomorphic mapping often struggle with the curse of dimensionality. We propose a mesh-free learning framework designed for $n$-dimensional mapping problems, seamlessly combining variational…

Machine Learning · Computer Science 2025-11-05 Zhiwen Li , Cheuk Hin Ho , Lok Ming Lui

We present a fast learning-based algorithm for deformable, pairwise 3D medical image registration. Current registration methods optimize an objective function independently for each pair of images, which can be time-consuming for large…

Computer Vision and Pattern Recognition · Computer Science 2019-03-14 Guha Balakrishnan , Amy Zhao , Mert R. Sabuncu , John Guttag , Adrian V. Dalca

Diffeomorphic image registration (DIR) is a fundamental task in 3D medical image analysis that seeks topology-preserving deformations between image pairs. To ensure diffeomorphism, a common approach is to model the deformation field as the…

Computer Vision and Pattern Recognition · Computer Science 2025-03-18 Mohammadjavad Matinkia , Nilanjan Ray

Image registration is a fundamental step in medical image analysis. Ideally, the transformation that registers one image to another should be a diffeomorphism that is both invertible and smooth. Traditional methods like geodesic shooting…

Computer Vision and Pattern Recognition · Computer Science 2019-07-02 Dongyang Kuang

Accurately registering breast MR images from different time points enables the alignment of anatomical structures and tracking of tumor progression, supporting more effective breast cancer detection, diagnosis, and treatment planning.…

Image and Video Processing · Electrical Eng. & Systems 2026-01-01 Yaqian Chen , Hanxue Gu , Haoyu Dong , Qihang Li , Yuwen Chen , Nicholas Konz , Lin Li , Maciej A. Mazurowski

Multimodal registration is a challenging problem in medical imaging due the high variability of tissue appearance under different imaging modalities. The crucial component here is the choice of the right similarity measure. We make a step…

Computer Vision and Pattern Recognition · Computer Science 2016-09-20 Martin Simonovsky , Benjamín Gutiérrez-Becker , Diana Mateus , Nassir Navab , Nikos Komodakis