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We consider planar networks of three curves that meet at two junctions with prescribed equal angles, minimizing a combination of the elastic energy and the length functional. We prove existence and regularity of minimizers, and we show some…
Dynamic networks represent the complex and evolving interrelationships between real-world entities. Given the scale and variability of these networks, finding an optimal slicing interval is essential for meaningful analysis. Nonuniform…
This study investigates the dynamics of alternating minimization applied to a bilinear regression task with normally distributed covariates, under the asymptotic system size limit where the number of parameters and observations diverge at…
In this paper, we explore how conventional image enhancement can improve model robustness in medical image analysis. By applying commonly used normalization methods to images from various vendors and studying their influence on model…
When considering the problem of unmixing hyperspectral images, most of the literature in the geoscience and image processing areas relies on the widely used linear mixing model (LMM). However, the LMM may be not valid and other nonlinear…
We investigate the properties of minimizers of one-dimensional variational problems when the Lagrangian has no higher smoothness than continuity. An elementary approximation result is proved, but it is shown that this cannot be in general…
Problems in differentiable rendering often involve optimizing scene parameters that cause motion in image space. The gradients for such parameters tend to be sparse, leading to poor convergence. While existing methods address this sparsity…
By generalizing the notion of linearization, a concept originally arising from microlocal analysis and symbolic calculus, to diffeological spaces, we make a first proposal setting for optimization problems in this category. We show how…
In this paper we consider minimizers for nonlocal energy functionals generalizing elastic energies that are connected with the theory of peridynamics \cite{Silling2000} or nonlocal diffusion models \cite{Rossi}. We derive nonlocal versions…
Image denoising is a classical signal processing problem that has received significant interest within the image processing community during the past two decades. Most of the algorithms for image denoising has focused on the paradigm of…
Image segmentation is one of the principal approaches of image processing. The choice of the most appropriate Binarization algorithm for each case proved to be a very interesting procedure itself. In this paper, we have done the comparison…
Training deep neural networks for classification often includes minimizing the training loss beyond the zero training error point. In this phase of training, a "neural collapse" behavior has been observed: the variability of features…
Numerical nonlinear algebra is applied to maximum likelihood estimation for Gaussian models defined by linear constraints on the covariance matrix. We examine the generic case as well as special models (e.g. Toeplitz, sparse, trees) that…
Visualisation is an effective way to facilitate the analysis and understanding of multivariate data. In the context of multi-objective optimisation, comparing to quantitative performance metrics, visualisation is, in principle, able to…
With the inexorable digitalisation of the modern world, every subset in the field of technology goes through major advancements constantly. One such subset is digital images which are ever so popular. Images can not always be as visually…
The aim of this paper is twofold: In the first part, we leverage recent results on scenario design to develop randomized algorithmsfor approximating the image set of a nonlinear mapping, that is, a (possibly noisy) mapping of a set via a…
The concept of natural pseudo-distance has proven to be a powerful tool for measuring the dissimilarity between topological spaces endowed with continuous real-valued functions. Roughly speaking, the natural pseudo-distance is defined as…
Due to the COVID-19 pandemic, there is an increasing demand for portable CT machines worldwide in order to diagnose patients in a variety of settings. This has led to a need for CT image reconstruction algorithms that can produce high…
This paper proposes several novel optimization algorithms for minimizing a nonlinear objective function. The algorithms are enlightened by the optimal state trajectory of an optimal control problem closely related to the minimized objective…
Images can vary according to changes in viewpoint, resolution, noise, and illumination. In this paper, we aim to learn representations for an image, which are robust to wide changes in such environmental conditions, using training pairs of…