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Intrinsic Delaunay triangulation (IDT) is a fundamental data structure in computational geometry and computer graphics. However, except for some theoretical results, such as existence and uniqueness, little progress has been made towards…
Training deep networks for semantic segmentation requires large amounts of labeled training data, which presents a major challenge in practice, as labeling segmentation masks is a highly labor-intensive process. To address this issue, we…
Urban reconstruction from a video captured by a surveying vehicle constitutes a core module of automated mapping. When computational power represents a limited resource and, a detailed map is not the primary goal, the reconstruction can be…
Unfitted (also known as embedded or immersed) finite element approximations of partial differential equations are very attractive because they have much lower geometrical requirements than standard body-fitted formulations. These schemes do…
In industrial inspection and component alignment tasks, template matching requires efficient estimation of a target's position and geometric state (rotation and scaling) under complex backgrounds to support precise downstream operations.…
Deep learning-based medical image segmentation and surface mesh generation typically involve a sequential pipeline from image to segmentation to meshes, often requiring large training datasets while making limited use of prior geometric…
This article introduces a general purpose framework and software to approximate partial differential equations (PDEs). The sparsity patterns of finite element discretized operators is identified automatically using the tools from…
Developing efficient numerical algorithms for the solution of high dimensional random Partial Differential Equations (PDEs) has been a challenging task due to the well-known curse of dimensionality. We present a new solution framework for…
Medical image segmentation is essential for computer-assisted diagnosis and treatment planning, yet substantial anatomical variability and boundary ambiguity hinder reliable delineation of fine structures. We propose RDTE-UNet, a…
We develop a new optimisation technique that combines multiresolution subdivision surfaces for boundary description with immersed finite elements for the discretisation of the primal and adjoint problems of optimisation. Similar to wavelets…
The construction of anisotropic triangulations is desirable for various applications, such as the numerical solving of partial differential equations and the representation of surfaces in graphics. To solve this notoriously difficult…
Template matching is a fundamental task in computer vision and has been studied for decades. It plays an essential role in manufacturing industry for estimating the poses of different parts, facilitating downstream tasks such as robotic…
Dimensionality reduction algorithms map high-dimensional data into visualizable 2D or 3D spaces, but traditionally rely on a discrete point-cloud paradigm. This discrete abstraction is susceptible to visual occlusion and artificial…
We present a volume rendering-based neural surface reconstruction method that takes as few as three disparate RGB images as input. Our key idea is to regularize the reconstruction, which is severely ill-posed and leaving significant gaps…
Dense geometric matching determines the dense pixel-wise correspondence between a source and support image corresponding to the same 3D structure. Prior works employ an encoder of transformer blocks to correlate the two-frame features.…
In spite of achieving revolutionary successes in machine learning, deep convolutional neural networks have been recently found to be vulnerable to adversarial attacks and difficult to generalize to novel test images with reasonably large…
Numerical solutions of partial differential equations (PDEs) require expensive simulations, limiting their application in design optimization, model-based control, and large-scale inverse problems. Surrogate modeling techniques seek to…
Restoring images affected by various types of degradation, such as noise, blur, or improper exposure, remains a significant challenge in computer vision. While recent trends favor complex monolithic all-in-one architectures, these models…
Segmentation of microscopy images constitutes an ill-posed inverse problem due to measurement noise, weak object boundaries, and limited labeled data. Although deep neural networks provide flexible nonparametric estimators, unconstrained…
We consider discretized two-dimensional PDE-constrained shape optimization problems, in which shapes are represented by triangular meshes. Given the connectivity, the space of admissible vertex positions was recently identified to be a…