Related papers: Diffeomorphic image matching with left-invariant m…
We introduce in this paper a learning paradigm in which the training data is transformed by a diffeomorphic transformation before prediction. The learning algorithm minimizes a cost function evaluating the prediction error on the training…
Cardiac deformation is a crucial biomarker for the evaluation of cardiac function. Current methods for estimating cardiac strain might underestimate local deformation due to through-plane motion and segmental averaging. Mesh-based mapping…
In image set classification, a considerable advance has been made by modeling the original image sets by second order statistics or linear subspace, which typically lie on the Riemannian manifold. Specifically, they are Symmetric Positive…
Deformable image registration poses a challenging problem where, unlike most deep learning tasks, a complex relationship between multiple coordinate systems has to be considered. Although data-driven methods have shown promising…
Many supervised learning problems involve high-dimensional data such as images, text, or graphs. In order to make efficient use of data, it is often useful to leverage certain geometric priors in the problem at hand, such as invariance to…
In this paper we consider simply connected Lie groups equipped with left invariant Randers metrics which arise from left invariant Riemannian metrics and left invariant vector fields. Then we study the intersection between automorphism and…
Brain cell structure and function reflect neurodevelopment, plasticity and ageing, and changes can help flag pathological processes such as neurodegeneration and neuroinflammation. Accurate and quantitative methods to non-invasively…
Metric and kernel learning are important in several machine learning applications. However, most existing metric learning algorithms are limited to learning metrics over low-dimensional data, while existing kernel learning algorithms are…
Living biological tissue is a complex system, constantly growing and changing in response to external and internal stimuli. These processes lead to remarkable and intricate changes in shape. Modeling and understanding both natural and…
In this article we study the field of Hilbertian metrics and positive definit (pd) kernels on probability measures, they have a real interest in kernel methods. Firstly we will make a study based on the Alpha-Beta-divergence to have a…
Diffusion-weighted magnetic resonance imaging (DW-MRI) is a non-invasive way of imaging white matter tracts in the human brain. DW-MRIs are usually acquired using echo-planar imaging (EPI) with high gradient fields, which could introduce…
Medical image segmentation has seen significant improvements with transformer models, which excel in grasping far-reaching contexts and global contextual information. However, the increasing computational demands of these models,…
Deformable part models (DPMs) and convolutional neural networks (CNNs) are two widely used tools for visual recognition. They are typically viewed as distinct approaches: DPMs are graphical models (Markov random fields), while CNNs are…
Fluorescence molecular tomography (FMT) is a sensitive optical imaging technology widely used in biomedical research. However, the ill-posedness of the inverse problem poses a huge challenge to FMT reconstruction. Although end-to-end deep…
This study proposes an end-to-end unsupervised diffeomorphic deformable registration framework based on moving mesh parameterization. Using this parameterization, a deformation field can be modeled with its transformation Jacobian…
Traditional deformable registration techniques achieve impressive results and offer a rigorous theoretical treatment, but are computationally intensive since they solve an optimization problem for each image pair. Recently, learning-based…
The problem of finding a time-dependent vector field which warps an initial set of points to a target set is common in shape analysis. It is an example of a problem in the diffeomorphic shape matching regime, and can be thought of as a…
Invariance to nuisance transformations is one of the desirable properties of effective representations. We consider transformations that form a \emph{group} and propose an approach based on kernel methods to derive local group invariant…
Area preserving diffeomorphisms of a 2-d compact Riemannian manifold with or without boundary are studied. We find two classes of decompositions of a Riemannian metric, namely, h- and g-decomposition, that help to formulate a gravitational…
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…