Related papers: A gradient system based on anisotropic monochrome …
In this paper, we investigate a system of parabolic partial differential equations with unknown-dependent coefficients that integrates two models: an anisotropic orientation-adaptive denoising process in image processing and a phase-field…
This paper develops a general mathematical framework for pseudo-parabolic gradient systems with state-dependent dynamics. The state dependence is induced by variable coefficient fields in the governing energy functional. Such coefficients…
In this paper, we consider a coupled system of nonlinear elliptic and pseudo-parabolic PDEs arising in anisotropic monochrome image denoising with orientation-adaptation. The system is derived from the minimization process of a nonconvex…
In this paper we extend the adaptive gradient descent (AdaGrad) algorithm to the optimal distributed control of parabolic partial differential equations with uncertain parameters. This stochastic optimization method achieves an improved…
Multivariate problems are typically governed by anisotropic features such as edges in images. A common bracket of most of the various directional representation systems which have been proposed to deliver sparse approximations of such…
It is well known that for gradient systems in Euclidean space or on a Riemannian manifold, the energy decreases monotonically along solutions. In this letter we derive and analyse functionally fitted energy-diminishing methods to preserve…
We suggest and implement an approach for the bottom-up description of systems undergoing large-scale structural changes and chemical transformations from dynamic atomically resolved imaging data, where only partial or uncertain data on…
We propose a novel PDE-based anisotropic filter for noise reduction in multicolor images. It is a generalization of Nitzberg & Shiota's (1992) model being a hyperbolic relaxation of the well-known parabolic Perona & Malik's filter (1990).…
Semi-supervised (SS) semantic segmentation exploits both labeled and unlabeled images to overcome tedious and costly pixel-level annotation problems. Pseudolabel supervision is one of the core approaches of training networks with both…
We introduce Soft Anisotropic Diagrams (SAD), an explicit and differentiable image representation parameterized by a set of adaptive sites in the image plane. In SAD, each site specifies an anisotropic metric and an additively weighted…
We review the theory of, and develop algorithms for transforming a finite point set in ${\bf R}^d$ into a set in \emph{radial isotropic position} by a nonsingular linear transformation followed by rescaling each image point to the unit…
Computing the gradient of an image is a common step in computer vision pipelines. The image gradient quantifies the magnitude and direction of edges in an image and is used in creating features for downstream machine learning tasks.…
Autoencoder reconstructions are widely used for the task of unsupervised anomaly localization. Indeed, an autoencoder trained on normal data is expected to only be able to reconstruct normal features of the data, allowing the segmentation…
We present a practical algorithm for partially relaxing multiwell energy densities such as pertain to materials undergoing martensitic phase transitions. The algorithm is based on sequential lamination, but the evolution of the…
This paper proposes a gradient descent based optimization method that relies on automatic differentiation for the computation of gradients. The method uses tools and techniques originally developed in the field of artificial neural networks…
As the resolution of digital images increase significantly, the processing of images becomes more challenging in terms of accuracy and efficiency. In this paper, we consider image segmentation by solving a partial differentiation equation…
The intrinsic energy minimization in dynamical systems offers a valuable tool for minimizing the objective functions of computationally challenging problems in combinatorial optimization. However, most prior works have focused on mapping…
Trajectory optimization of a controlled dynamical system is an essential part of autonomy, however many trajectory optimization techniques are limited by the fidelity of the underlying parametric model. In the field of robotics, a lack of…
Semi-supervised clustering problems focus on clustering data with labels. In this paper,we consider the semi-supervised hypergraph problems. We use the hypergraph related tensor to construct an orthogonal constrained optimization model. The…
We consider a variational model for single-image super-resolution based on the assumption that the gradient of the target image is sparse. We enforce this assumption by considering both an isotropic and an anisotropic $\ell^0$…