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Graph representation learning is a fast-growing field where one of the main objectives is to generate meaningful representations of graphs in lower-dimensional spaces. The learned embeddings have been successfully applied to perform various…

An increasingly common viewpoint is that protein dynamics data sets reside in a non-linear subspace of low conformational energy. Ideal data analysis tools for such data sets should therefore account for such non-linear geometry. The…

Statistical shape modeling (SSM) is a powerful computational framework for quantifying and analyzing the geometric variability of anatomical structures, facilitating advancements in medical research, diagnostics, and treatment planning.…

Manifold learning offers nonlinear dimensionality reduction of high-dimensional datasets. In this paper, we bring geometry processing to bear on manifold learning by introducing a new approach based on metric connection for generating a…

This article introduces a new data-driven approach that leverages a manifold embedding generated by the invertible neural network to improve the robustness, efficiency, and accuracy of the constitutive-law-free simulations with limited…

We introduce a new regression framework designed to deal with large-scale, complex data that lies around a low-dimensional manifold with noises. Our approach first constructs a graph representation, referred to as the skeleton, to capture…

Meshes are ubiquitous in visual computing and simulation, yet most existing machine learning techniques represent meshes only indirectly, e.g. as the level set of a scalar field or deformation of a template, or as a disordered triangle soup…

This paper presents a novel method for unsupervised segmentation of pathology images. Staging of lung cancer is a major factor of prognosis. Measuring the maximum dimensions of the invasive component in a pathology images is an essential…

Many current neural networks for medical imaging generalise poorly to data unseen during training. Such behaviour can be caused by networks overfitting easy-to-learn, or statistically dominant, features while disregarding other potentially…

Uniform Manifold Approximation and Projection (UMAP) is a widely used manifold learning technique for dimensionality reduction. This paper studies UMAP, supervised UMAP, and several competing dimensionality reduction methods, including…

Motor Imagery (MI) is an emerging Brain-Computer Interface (BCI) paradigm where a person imagines body movements without physical action. By decoding scalp-recorded electroencephalography (EEG) signals, BCIs establish direct communication…

Optimization over the Stiefel manifold is a fundamental computational problem in many scientific and engineering applications. Despite considerable research effort, high-dimensional optimization problems over the Stiefel manifold remain…

Learning-based single image super-resolution (SISR) methods are continuously showing superior effectiveness and efficiency over traditional model-based methods, largely due to the end-to-end training. However, different from model-based…

Accurate surface geometry representation is crucial in 3D visual computing. Explicit representations, such as polygonal meshes, and implicit representations, like signed distance functions, each have distinct advantages, making efficient…

Deep neural networks (DNNs) on Riemannian manifolds have garnered increasing interest in various applied areas. For instance, DNNs on spherical and hyperbolic manifolds have been designed to solve a wide range of computer vision and nature…

Perceptual manifolds arise when a neural population responds to an ensemble of sensory signals associated with different physical features (e.g., orientation, pose, scale, location, and intensity) of the same perceptual object. Object…

Reliably modeling normality and differentiating abnormal appearances from normal cases is a very appealing approach for detecting pathologies in medical images. A plethora of such unsupervised anomaly detection approaches has been made in…

When analyzing parametric statistical models, a useful approach consists in modeling geometrically the parameter space. However, even for very simple and commonly used hierarchical models like statistical mixtures or stochastic deep neural…

Skull stripping magnetic resonance images (MRI) of the human brain is an important process in many image processing techniques, such as automatic segmentation of brain structures. Numerous methods have been developed to perform this task,…

In this paper, we study the problem of facial expression recognition using a novel space-time geometric representation. We describe the temporal evolution of facial landmarks as parametrized trajectories on the Riemannian manifold of…