Related papers: Voronoi binning: Optimal adaptive tessellations of…
Neural Radiance Fields (NeRFs) learn to represent a 3D scene from just a set of registered images. Increasing sizes of a scene demands more complex functions, typically represented by neural networks, to capture all details. Training and…
Variational Data Assimilation (DA) has been broadly used in engineering problems for field reconstruction and prediction by performing a weighted combination of multiple sources of noisy data. In recent years, the integration of deep…
Cellular structures manifest their outstanding mechanical properties in many biological systems. One key challenge for designing and optimizing these geometrically complicated structures lies in devising an effective geometric…
Since the Voronoi diagram appears in many applications, the topic of improving its computational efficiency remains attractive. We propose a novel yet efficient method to compute Voronoi diagrams bounded by a given domain, i.e., the clipped…
In this paper, we investigate the optimization of Centroidal Voronoi Tessellations (CVT) under geometric constraints. For this purpose, we minimize a linear combination of the standard CVT energy functional with terms involving geometric…
Denoising is of utmost importance for the visualization and processing of images featuring low signal-to-noise ratio. Total variation methods are among the most popular techniques to perform this task improving the signal-to-noise ratio…
We propose a novel approach to model viscoelasticity materials using neural networks, which capture rate-dependent and nonlinear constitutive relations. However, inputs and outputs of the neural networks are not directly observable, and…
Determining the masses of new physics particles appearing in decay chains is an important and longstanding problem in high energy phenomenology. Recently it has been shown that these mass measurements can be improved by utilizing the…
This study presents the development of a spatially adaptive weighting strategy for Total Variation regularization, aimed at addressing under-determined linear inverse problems. The method leverages the rapid computation of an accurate…
Speed-of-sound has been shown as a potential biomarker for breast cancer imaging, successfully differentiating malignant tumors from benign ones. Speed-of-sound images can be reconstructed from time-of-flight measurements from ultrasound…
The use of data assimilation technique to identify optimal topography is discussed in frames of time-dependent motion governed by non-linear barotropic ocean model. Assimilation of artificially generated data allows to measure the influence…
We consider the Voronoi tessellation based on a homogeneous Poisson point process in $\mathbf{R}^{d}$. For a geometric characteristic of the cells (e.g. the inradius, the circumradius, the volume), we investigate the point process of the…
Pixel binning is a technique, widely used in optical image acquisition and spectroscopy, in which adjacent detector elements of an image sensor are combined into larger pixels. This reduces the amount of data to be processed as well as the…
We report significantly improved accuracy of grain boundary segmentation using Convolutional Neural Networks (CNN) trained on a combination of real and generated data. Manual segmentation is accurate but time-consuming, and existing…
We propose a data-driven interpolation method for approximating real-valued functions on smooth manifolds, based on the Laplace--Beltrami operator and Voronoi tessellations. Given pointwise evaluations, the method constructs a continuous…
Photometric redshift surveys map the distribution of matter in the Universe through the positions and shapes of galaxies with poorly resolved measurements of their radial coordinates. While a tomographic analysis can be used to recover some…
This paper presents an efficient Bayesian framework for solving nonlinear, high-dimensional model calibration problems. It is based on a Variational Bayesian formulation that aims at approximating the exact posterior by means of solving an…
We present a general framework for computing two-dimensional Voronoi diagrams of different classes of sites under various distance functions. The framework is sufficiently general to support diagrams embedded on a family of two-dimensional…
With our previous study, the Super-k algorithm, we have introduced a novel way of piecewise-linear classification. While working on the Super-k algorithm, we have found that there is a similar, and simpler way to explain for obtaining a…
Nowadays, big data of digital media (including images, videos and 3D graphical models) are frequently modeled as low-dimensional manifold meshes embedded in a high-dimensional feature space. In this paper, we summarized our recent work on…