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

Deep generative models learn a mapping from a low dimensional latent space to a high-dimensional data space. Under certain regularity conditions, these models parameterize nonlinear manifolds in the data space. In this paper, we investigate…

Diffeomorphic deformable image registration is crucial in many medical image studies, as it offers unique, special properties including topology preservation and invertibility of the transformation. Recent deep learning-based deformable…

Recently deep neural networks have been widely and successfully applied in computer vision tasks and attracted growing interests in medical imaging. One barrier for the application of deep neural networks to medical imaging is the need of…

Latent space geometry provides a rigorous and empirically valuable framework for interacting with the latent variables of deep generative models. This approach reinterprets Euclidean latent spaces as Riemannian through a pull-back metric,…

Unsupervised discovery of latent representations, in addition to being useful for density modeling, visualisation and exploratory data analysis, is also increasingly important for learning features relevant to discriminative tasks.…

The paper adapts the large deformation diffeomorphic metric mapping framework for image registration to the indirect setting where a template is registered against a target that is given through indirect noisy observations. The registration…

Despite the popularity of the manifold hypothesis, current manifold-learning methods do not support machine learning directly on the latent $d$-dimensional data manifold, as they primarily aim to perform dimensionality reduction into…

Accurate tracking of an anatomical landmark over time has been of high interests for disease assessment such as minimally invasive surgery and tumor radiation therapy. Ultrasound imaging is a promising modality benefiting from low-cost and…

Designing generative models for 3D structural brain MRI that synthesize morphologically-plausible and attribute-specific (e.g., age, sex, disease state) samples is an active area of research. Existing approaches based on frameworks like…

In the era of generative AI, deep generative models (DGMs) with latent representations have gained tremendous popularity. Despite their impressive empirical performance, the statistical properties of these models remain underexplored. DGMs…

Conformal Autoencoders are a neural network architecture that imposes orthogonality conditions between the gradients of latent variables to obtain disentangled representations of data. In this work we show that orthogonality relations…

This paper introduces the Neural Differential Manifold (NDM), a novel neural network architecture that explicitly incorporates geometric structure into its fundamental design. Departing from conventional Euclidean parameter spaces, the NDM…

Registration is an essential tool in image analysis. Deep learning based alternatives have recently become popular, achieving competitive performance at a faster speed. However, many contemporary techniques are limited to volumetric…

Simultaneously odometry and mapping using LiDAR data is an important task for mobile systems to achieve full autonomy in large-scale environments. However, most existing LiDAR-based methods prioritize tracking quality over reconstruction…

We introduce a new algorithm to solve a regularized spatial-spectral image estimation problem. Our approach is based on the linearized alternating directions method of multipliers (LADMM), which is a variation of the popular ADMM algorithm.…

Recently, the theory of diffusion maps was extended to a large class of local kernels with exponential decay which were shown to represent various Riemannian geometries on a data set sampled from a manifold embedded in Euclidean space.…

Neural models learn representations of high-dimensional data on low-dimensional manifolds. Multiple factors, including stochasticities in the training process, model architectures, and additional inductive biases, may induce different…

The use of digitally reconstructed radiographs (DRRs) to solve inverse problems such as slice-to-volume registration and 3D reconstruction is well-studied in preoperative settings. In intraoperative imaging, the utility of DRRs is limited…

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…

When solving inverse problems in geophysical imaging, deep generative models (DGMs) may be used to enforce the solution to display highly structured spatial patterns which are supported by independent information (e.g. the geological…