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In computer-aided design (CAD), the ability to "reverse engineer" the modeling steps used to create 3D shapes is a long-sought-after goal. This process can be decomposed into two sub-problems: converting an input mesh or point cloud into a…

We present a method of CutFEM type for the Poisson problem with either Dirichlet or Neumann boundary conditions. The computational mesh is obtained from a background (typically uniform Cartesian) mesh by retaining only the elements…

Pseudoline arrangements are fundamental objects in discrete and computational geometry, and different works have tackled the problem of improving the known bounds on the number of simple arrangements of $n$ pseudolines over the past…

This paper investigates d-dimensional CFTs in the presence of a codimension-one boundary and CFTs defined on real projective space RP^d. Our analysis expands on the alpha space method recently proposed for one-dimensional CFTs in…

Surface reconstruction is a fundamental problem in 3D graphics. In this paper, we propose a learning-based approach for implicit surface reconstruction from raw point clouds without normals. Our method is inspired by Gauss Lemma in…

Consider an information source generating a symbol at the root of a tree network whose links correspond to noisy communication channels, and broadcasting it through the network. We study the problem of reconstructing the transmitted symbol…

Gradient reconstruction is a key process for the spatial accuracy and robustness of finite volume method, especially in industrial aerodynamic applications in which grid quality affects reconstruction methods significantly. A novel gradient…

A second-order face-centred finite volume strategy on general meshes is proposed. The method uses a mixed formulation in which a constant approximation of the unknown is computed on the faces of the mesh. Such information is then used to…

We propose a mechanism enabling the appearance of border cells -- neurons firing at the boundaries of the navigated enclosures. The approach is based on the recent discovery of discrete complex analysis on a triangular lattice, which allows…

For the past several decades, it has been popular to reconstruct Fourier imaging data using model-based approaches that can easily incorporate physical constraints and advanced regularization/machine learning priors. The most common…

Recent works on implicit neural representations have made significant strides. Learning implicit neural surfaces using volume rendering has gained popularity in multi-view reconstruction without 3D supervision. However, accurately…

Modeling scene geometry using implicit neural representation has revealed its advantages in accuracy, flexibility, and low memory usage. Previous approaches have demonstrated impressive results using color or depth images but still have…

A modified Weighted Essentially Non-Oscillatory (WENO) reconstruction technique preventing accuracy loss near critical points (regardless of their order) of the underlying data is presented. This approach only uses local data from the…

Annotating lots of 3D medical images for training segmentation models is time-consuming. The goal of weakly supervised semantic segmentation is to train segmentation models without using any ground truth segmentation masks. Our work…

The goal of this thesis is to improve our understanding of the internal mechanisms by which deep artificial neural networks create meaningful representations and are able to generalize. We focus on the challenge of characterizing the…

Low dose CT is of great interest in these days. Dose reduction raises noise level in projections and decrease image quality in reconstructions. Model based image reconstruction can combine statistical noise model together with prior…

Neural implicit functions have recently shown promising results on surface reconstructions from multiple views. However, current methods still suffer from excessive time complexity and poor robustness when reconstructing unbounded or…

Traditionally, 3D indoor scene reconstruction from posed images happens in two phases: per-image depth estimation, followed by depth merging and surface reconstruction. Recently, a family of methods have emerged that perform reconstruction…

Anomaly detection has a wide range of applications and is especially important in industrial quality inspection. Currently, many top-performing anomaly-detection models rely on feature-embedding methods. However, these methods do not…

In the previous studies, the high-order gas-kinetic schemes (HGKS) have achieved successes for unsteady flows on three-dimensional unstructured meshes. In this paper, to accelerate the rate of convergence for steady flows, the implicit…