Related papers: Total Roto-Translational Variation
After characterizing the integrable discrete analogue of the Euler's elastica, we focus our attention on the problem of approximating a given discrete planar curve by an appropriate discrete Euler's elastica. We carry out the fairing…
We present a variational multi-label segmentation algorithm based on a robust Huber loss for both the data and the regularizer, minimized within a convex optimization framework. We introduce a novel constraint on the common areas, to bias…
For any unitary representation $\rho$ on a finite-dimensional Hilbert space \(V\) with differential \(d\rho : \mathfrak{g} \to \mathfrak{u}(V)\) for the Lie algebra $\mathfrak g$, we consider the Hamiltonian evolution \[ U_X(t) \coloneqq…
We study a nonlocal version of the total variation-based model with $L^1-$fidelity for image denoising, where the regularizing term is replaced with the fractional $s$-total variation. We discuss regularity of the level sets and uniqueness…
We propose an extension of the classical variational theory of evolution equations that accounts for dynamics also in possibly non-reflexive and non-separable spaces. The pivoting point is to establish a novel variational structure, based…
We propose an original method for vectorizing an image or zooming it at an arbitrary scale. The core of our method relies on the resolution of a geometric variational model and therefore offers theoretic guarantees. More precisely, it…
We introduce a technique for recovering a sufficiently smooth function from its ray transform over a wide class of curves in a general region of Euclidean space. The method is based on a complexification of the underlying vector fields…
Existence of strong solutions of an abstract Cauchy problem for a class of doubly nonlinear evolution inclusion of second order is established via a semi-implicit time discretization method. The principal parts of the operators acting on…
We consider the general class of time-homogeneous stochastic dynamical systems, both discrete and continuous, and study the problem of learning a representation of the state that faithfully captures its dynamics. This is instrumental to…
We study the problem of registering images. The framework we use is metamorphosis and we construct a variational Eulerian space-time setting and pose the registration problem as an infinite-dimensional optimisation problem. The geodesic…
The modeling of phenomenological structure is a crucial aspect in inverse imaging problems. One emerging modeling tool in computational imaging is the optimal transport framework. Its ability to model geometric displacements across an…
We establish a general principle which states that regularizing an inverse problem with a convex function yields solutions which are convex combinations of a small number of atoms. These atoms are identified with the extreme points and…
This article is the second work in our series of papers dedicated to image processing models based on the fractional order total variation $TV^r$. In our first work of this series, we studied key analytic properties of these semi-norms.…
We propose a novel model for decomposing grayscale images into three distinct components: the structural part, representing sharp boundaries and regions with strong light-to-dark transitions; the smooth part, capturing soft shadows and…
We define a class of "optimal" coordinate systems by requiring that the deviation from an exact Robertson-Walker metric is "as small as possible" within a given four dimensional volume. The optimization is performed by minimizing several…
A cornerstone of geometric reconstruction, rotation averaging seeks the set of absolute rotations that optimally explains a set of measured relative orientations between them. In spite of being an integral part of bundle adjustment and…
Graph-based variational methods have recently shown to be highly competitive for various classification problems of high-dimensional data, but are inherently difficult to handle from an optimization perspective. This paper proposes a convex…
Recently variational models with priors involving first and second order derivatives resp. differences were successfully applied for image restoration. There are several ways to incorporate the derivatives of first and second order into the…
We introduce a constrained optimization framework for training transformers that behave like optimization descent algorithms. Specifically, we enforce layerwise descent constraints on the objective function and replace standard empirical…
A common representation of a three dimensional object in computer applications, such as graphics and design, is in the form of a triangular mesh. In many instances, individual or groups of triangles in such representation need to satisfy…