Related papers: RDA-INR: Riemannian Diffeomorphic Autoencoding via…

We present Latent Diffeomorphic Dynamic Mode Decomposition (LDDMD), a new data reduction approach for the analysis of non-linear systems that combines the interpretability of Dynamic Mode Decomposition (DMD) with the predictive power of…

Euclidean representations distort data with intrinsic non-Euclidean structure. While Riemannian representation learning offers a solution by embedding data onto matching manifolds, it typically relies on an encoder to estimate densities on…

Diffeomorphic image registration is crucial for various medical imaging applications because it can preserve the topology of the transformation. This study introduces DCCNN-LSTM-Reg, a learning framework that evolves dynamically and learns…

This work proposes a multimodal diffeomorphic registration method using Neural Ordinary Differential Equations (Neural ODEs). Nonrigid registration algorithms exhibit tradeoffs between their accuracy, the computational complexity of their…

Manifold learning-based encoders have been playing important roles in nonlinear dimensionality reduction (NLDR) for data exploration. However, existing methods can often fail to preserve geometric, topological and/or distributional…

Graph diffusion models have made significant progress in learning structured graph data and have demonstrated strong potential for predictive tasks. Existing approaches typically embed node, edge, and graph-level features into a unified…

We present a method to predict image deformations based on patch-wise image appearance. Specifically, we design a patch-based deep encoder-decoder network which learns the pixel/voxel-wise mapping between image appearance and registration…

This study introduces a deep learning framework for the inferential exploration of latent representations in 3D brain MRI, leveraging a simple convolutional autoencoder with a hierarchical encoder and a compact latent space. Trained on…

Deep generative models have demonstrated successful applications in learning non-linear data distributions through a number of latent variables and these models use a nonlinear function (generator) to map latent samples into the data space.…

Recent studies have introduced a new class of generative models for synthesizing implicit neural representations (INRs) that capture arbitrary continuous signals in various domains. These models opened the door for domain-agnostic…

Diffeomorphic image registration, offering smooth transformation and topology preservation, is required in many medical image analysis tasks.Traditional methods impose certain modeling constraints on the space of admissible transformations…

In this paper, we propose a novel mathematical framework for piecewise diffeomorphic image registration that involves discontinuous sliding motion using a diffeomorphism groupoid and algebroid approach. The traditional Large Deformation…

The purpose of this work is to contribute to the state of the art of deep-learning methods for diffeomorphic registration. We propose an adversarial learning LDDMM method for pairs of 3D mono-modal images based on Generative Adversarial…

Manifold-valued data naturally arises in medical imaging. In cognitive neuroscience, for instance, brain connectomes base the analysis of coactivation patterns between different brain regions on the analysis of the correlations of their…

Generative adversarial networks (GANs) have emerged as a powerful unsupervised method to model the statistical patterns of real-world data sets, such as natural images. These networks are trained to map random inputs in their latent space…

Deep learning has a great potential for estimating biomarkers in diffusion weighted magnetic resonance imaging (dMRI). Atlases, on the other hand, are a unique tool for modeling the spatio-temporal variability of biomarkers. In this paper,…

This paper discusses the mathematical framework for designing methods of large deformation matching (LDM) for image registration in computational anatomy. After reviewing the geometrical framework of LDM image registration methods, a…

Given data, deep generative models, such as variational autoencoders (VAE) and generative adversarial networks (GAN), train a lower dimensional latent representation of the data space. The linear Euclidean geometry of data space pulls back…

Conventional deformable registration methods aim at solving an optimization model carefully designed on image pairs and their computational costs are exceptionally high. In contrast, recent deep learning based approaches can provide fast…

Linear discriminant analysis (LDA) is a widely used algorithm in machine learning to extract a low-dimensional representation of high-dimensional data, it features to find the orthogonal discriminant projection subspace by using the Fisher…