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This paper presents an enhanced adaptive random Fourier features (ARFF) training algorithm for shallow neural networks, building upon the work introduced in "Adaptive Random Fourier Features with Metropolis Sampling", Kammonen et al.,…
We prove that, if u is a function satisfying all Euler conditions for the Mumford-Shah functional and the discontinuity set of u is given by three line segments meeting at the origin with equal angles, then there exists a neighbourhood U of…
We consider a family of critical points of the Ambrosio-Tortorelli energy with an obstacle condition on the phase field variable. This problem can be interpreted as a time discretization of a quasistatic evolution problem where the obstacle…
The proximal gradient method is a generic technique introduced to tackle the non-smoothness in optimization problems, wherein the objective function is expressed as the sum of a differentiable convex part and a non-differentiable…
One-dimensional function approximation is a fundamental problem in scientific computing and engineering applications. While neural networks possess powerful universal approximation capabilities, their optimization process is often hindered…
Purpose: The segmentation of brain tumors is one of the most active areas of medical image analysis. While current methods perform superhuman on benchmark data sets, their applicability in daily clinical practice has not been evaluated. In…
Linear approximation approaches suffer from Gibbs oscillations when approximating functions with singularities. ENO-SR resolution is a local approach avoiding oscillations and with a full order of accuracy, but a loss of regularity of the…
Minimizing the Mumford-Shah functional is frequently used for smoothing signals or time series with discontinuities. A significant limitation of the standard Mumford-Shah model is that linear trends -- and in general polynomial trends -- in…
We present a novel segmentation algorithm based on a hierarchical representation of images. The main contribution of this work is to explore the capabilities of the A Contrario reasoning when applied to the segmentation problem, and to…
An adaptive refinement strategy, based on an equilibrated flux a posteriori error estimator, is proposed in the context of defeaturing problems. Defeaturing consists of removing features from complex domains to simplify mesh generation and…
Image segmentation is the process of partitioning an image into meaningful segments. The meaning of the segments is subjective due to the definition of homogeneity is varied based on the users perspective hence the automation of the…
Topological accuracy in medical image segmentation is a highly important property for downstream applications such as network analysis and flow modeling in vessels or cell counting. Recently, significant methodological advancements have…
The Douglas Rachford algorithm is an algorithm that converges to a minimizer of a sum of two convex functions. The algorithm consists in fixed point iterations involving computations of the proximity operators of the two functions…
The subject of the present study is the Monte Carlo path-integral evaluation of the moments of spectral functions. Such moments can be computed by formal differentiation of certain estimating functionals that are infinitely-differentiable…
Convex optimization has become ubiquitous in most quantitative disciplines of science, including variational image processing. Proximal splitting algorithms are becoming popular to solve such structured convex optimization problems. Within…
Morphological reconstruction (MR) is often employed by seeded image segmentation algorithms such as watershed transform and power watershed as it is able to filter seeds (regional minima) to reduce over-segmentation. However, MR might…
Umbral theory, formulated in its modern version by S. Roman and G.~C. Rota, has been reconsidered in more recent times by G. Dattoli and collaborators with the aim of devising a working computational tool in the framework of special…
Foreground segmentation is an essential task in the field of image understanding. Under unsupervised conditions, different images and instances always have variable expressions, which make it difficult to achieve stable segmentation…
Chemical accuracy serves as an important metric for assessing the effectiveness of the numerical method in Kohn--Sham density functional theory. It is found that to achieve chemical accuracy, not only the Kohn--Sham wavefunctions but also…
We are interested in restoring images having values in a symmetric Hadamard manifold by minimizing a functional with a quadratic data term and a total variation like regularizing term. To solve the convex minimization problem, we extend the…