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Polygonal meshes have become the standard for discretely approximating 3D shapes, thanks to their efficiency and high flexibility in capturing non-uniform shapes. This non-uniformity, however, leads to irregularity in the mesh structure,…

In this work, we study the well-posedness of certain sparse regularized linear regression problems, i.e., the existence, uniqueness and continuity of the solution map with respect to the data. We focus on regularization functions that are…

In this paper, we develop and analyze a trilinear immersed finite element method for solving three-dimensional elliptic interface problems. The proposed method can be utilized on interface-unfitted meshes such as Cartesian grids consisting…

Implicit neural representations (INRs) are increasingly being used as tools to map coordinates to signals, encompassing applications from neural fields to texture compression, shape representations, and beyond. Most INR methods are based on…

Visual perception relies on inference of 3D scene properties such as shape, pose, and lighting. To understand how visual sensory neurons enable robust perception, it is crucial to characterize their selectivity to such physically…

This paper presents Polylidar, an efficient algorithm to extract non-convex polygons from 2D point sets, including interior holes. Plane segmented point clouds can be input into Polylidar to extract their polygonal counterpart, thereby…

Generalizing tensor-product splines to smooth functions whose control nets outline topological polyhedra, bi-cubic polyhedral splines form a piecewise polynomial, first-order differentiable space that associates one function with each…

Plane Wave imaging enables many applications that require high frame rates, including localisation microscopy, shear wave elastography, and ultra-sensitive Doppler. To alleviate the degradation of image quality with respect to conventional…

Segmenting curvilinear structures in medical images is essential for analyzing morphological patterns in clinical applications. Integrating topological properties, such as connectivity, improves segmentation accuracy and consistency.…

Multivariate functions emerge naturally in a wide variety of data-driven models. Popular choices are expressions in the form of basis expansions or neural networks. While highly effective, the resulting functions tend to be hard to…

Deep learning based methods have recently pushed the state-of-the-art on the problem of Single Image Super-Resolution (SISR). In this work, we revisit the more traditional interpolation-based methods, that were popular before, now with the…

Automated detection of curvilinear structures, e.g., blood vessels or nerve fibres, from medical and biomedical images is a crucial early step in automatic image interpretation associated to the management of many diseases. Precise…

Diffusion-weighted magnetic resonance imaging (DW-MRI) allows for non-invasive imaging of the local fiber architecture of the human brain at a millimetric scale. Multiple classical approaches have been proposed to detect both single (e.g.,…

This paper addresses the challenges of designing mesh convolution neural networks for 3D mesh dense prediction. While deep learning has achieved remarkable success in image dense prediction tasks, directly applying or extending these…

Superpixels are a useful representation to reduce the complexity of image data. However, to combine superpixels with convolutional neural networks (CNNs) in an end-to-end fashion, one requires extra models to generate superpixels and…

Ultrafast Plane-Wave (PW) imaging often produces artifacts and shadows that vary with insonification angles. We propose a novel approach using Implicit Neural Representations (INRs) to compactly encode multi-planar sequences while…

Many network architectures exist for learning on meshes, yet their constructions entail delicate trade-offs between difficulty learning high-frequency features, insufficient receptive field, sensitivity to discretization, and inefficient…

Geometric Deep Learning has recently made striking progress with the advent of continuous deep implicit fields. They allow for detailed modeling of watertight surfaces of arbitrary topology while not relying on a 3D Euclidean grid,…

Implicit neural representations have emerged as a powerful tool in learning 3D geometry, offering unparalleled advantages over conventional representations like mesh-based methods. A common type of INR implicitly encodes a shape's boundary…

Video interpolation aims to generate a non-existent intermediate frame given the past and future frames. Many state-of-the-art methods achieve promising results by estimating the optical flow between the known frames and then generating the…