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Shape matching has been a long-studied problem for the computer graphics and vision community. The objective is to predict a dense correspondence between meshes that have a certain degree of deformation. Existing methods either consider the…
Shape correspondence is a fundamental problem in computer graphics and vision, with applications in various problems including animation, texture mapping, robotic vision, medical imaging, archaeology and many more. In settings where the…
Edge detection, as a core component in a wide range of visionoriented tasks, is to identify object boundaries and prominent edges in natural images. An edge detector is desired to be both efficient and accurate for practical use. To achieve…
Image inpainting, the task of reconstructing missing segments in corrupted images using available data, faces challenges in ensuring consistency and fidelity, especially under information-scarce conditions. Traditional evaluation methods,…
Classifying fine-grained lesions is challenging due to minor and subtle differences in medical images. This is because learning features of fine-grained lesions with highly minor differences is very difficult in training deep neural…
Generative adversarial networks (GANs) are a novel approach to generative modelling, a task whose goal it is to learn a distribution of real data points. They have often proved difficult to train: GANs are unlike many techniques in machine…
Machine learning problems have an intrinsic geometric structure as central objects including a neural network's weight space and the loss function associated with a particular task can be viewed as encoding the intrinsic geometry of a given…
We resolve the complexity of the point-boundary variant of the art gallery problem, showing that it is $\exists\mathbb{R}$-complete, meaning that it is equivalent under polynomial time reductions to deciding whether a system of polynomial…
Free boundary problems are those described by PDEs that exhibit a priori unknown (free) interfaces or boundaries. These problems appear in Physics, Probability, Biology, Finance, or Industry, and the study of solutions and free boundaries…
Drawings of non-planar graphs always result in edge crossings. When there are many edges crossing at small angles, it is often difficult to follow these edges, because of the multiple visual paths resulted from the crossings that slow down…
The design of numerical boundary conditions is a challenging problem that has been tackled in different ways depending on the nature of the problem and the numerical scheme used to solve it. In this paper we present a new weighted…
Imaging is critical to the characterisation of materials. However, even with careful sample preparation and microscope calibration, imaging techniques are often prone to defects and unwanted artefacts. This is particularly problematic for…
Presenting a 3D scene from multiview images remains a core and long-standing challenge in computer vision and computer graphics. Two main requirements lie in rendering and reconstruction. Notably, SOTA rendering quality is usually achieved…
We study elliptic and parabolic boundary value problems in spaces of mixed scales with mixed smoothness on the half space. The aim is to solve boundary value problems with boundary data of negative regularity and to describe the…
Area of image inpainting over relatively large missing regions recently advanced substantially through adaptation of dedicated deep neural networks. However, current network solutions still introduce undesired artifacts and noise to the…
Geometry problem solving (GPS) represents a critical frontier in artificial intelligence, with profound applications in education, computer-aided design, and computational graphics. Despite its significance, automating GPS remains…
We introduce a simple semi-supervised learning approach for images based on in-painting using an adversarial loss. Images with random patches removed are presented to a generator whose task is to fill in the hole, based on the surrounding…
Efficiently solving Poisson equations on complex, irregular domains remains a fundamental challenge in scientific computing, as classical iterative solvers often suffer from prohibitive runtime due to ill-conditioned systems. While neural…
The goal of ordinal embedding is to represent items as points in a low-dimensional Euclidean space given a set of constraints in the form of distance comparisons like "item $i$ is closer to item $j$ than item $k$". Ordinal constraints like…
Despite high-dimensionality of images, the sets of images of 3D objects have long been hypothesized to form low-dimensional manifolds. What is the nature of such manifolds? How do they differ across objects and object classes? Answering…