Related papers: Direct Variational Perspective Shape from Shading …

In this paper, we address the problem of dense 3D reconstruction from multiple view images subject to strong lighting variations. In this regard, a new piecewise framework is proposed to explicitly take into account the change of…

Shape from shading is a classical inverse problem in computer vision. This shape reconstruction problem is inherently ill-defined; it depends on the assumed light source direction. We introduce a novel mathematical formulation for…

This work extends our previous study from S. Shrestha et al. (2024) by introducing a new abstract framework for Variational Multiscale (VMS) methods at the discrete level. We introduce the concept of what we define as the optimal projector…

An analogue of the total variation prior for the normal vector field along the boundary of piecewise flat shapes in 3D is introduced. A major class of examples are triangulated surfaces as they occur for instance in finite element…

We propose a variational regularization approach based on a multiscale representation called cylindrical shearlets aimed at dynamic imaging problems, especially dynamic tomography. The intuitive idea of our approach is to integrate a…

In this paper we develop adaptive numerical schemes for certain nonlinear variational problems. The discretization of the variational problems is done by representing the solution as a suitable frame decomposition, i.e., a complete, stable,…

The same type of objects in different images may vary in their shapes because of rigid and non-rigid shape deformations, occluding foreground as well as cluttered background. The problem concerned in this work is the shape extraction in…

Shape calculus concerns the calculation of directional derivatives of some quantity of interest, typically expressed as an integral. This article introduces a type of shape calculus based on localized dilation of boundary faces through…

Regularization is used in many different areas of optimization when solutions are sought which not only minimize a given function, but also possess a certain degree of regularity. Popular applications are image denoising, sparse regression…

In the past, optimization-based registration models have used spatially-varying regularization to account for deformation variations in different image regions. However, deep learning-based registration models have mostly relied on…

We consider discretized two-dimensional PDE-constrained shape optimization problems, in which shapes are represented by triangular meshes. Given the connectivity, the space of admissible vertex positions was recently identified to be a…

We establish a family of subspace-based learning method for multi-view learning using the least squares as the fundamental basis. Specifically, we investigate orthonormalized partial least squares (OPLS) and study its important properties…

This paper introduces a set of numerical methods for Riemannian shape analysis of 3D surfaces within the setting of invariant (elastic) second-order Sobolev metrics. More specifically, we address the computation of geodesics and geodesic…

3D shape completion is important to enable machines to perceive the complete geometry of objects from partial observations. To address this problem, view-based methods have been presented. These methods represent shapes as multiple depth…

This paper addresses the problem of inverse rendering from photometric images. Existing approaches for this problem suffer from the effects of self-shadows, inter-reflections, and lack of constraints on the surface reflectance, leading to…

PDE-constrained optimal control problems require regularisation to ensure well-posedness, introducing small perturbations that make the solutions challenging to approximate accurately. We propose a finite element approach that couples both…

The aim of this paper is to introduce and study a two-step debiasing method for variational regularization. After solving the standard variational problem, the key idea is to add a consecutive debiasing step minimizing the data fidelity on…

In image denoising problems, one widely-adopted approach is to minimize a regularized data-fit objective function, where the data-fit term is derived from a physical image acquisition model. Typically the regularizer is selected with two…

We propose a regularization scheme for image reconstruction that leverages the power of deep learning while hinging on classic sparsity-promoting models. Many deep-learning-based models are hard to interpret and cumbersome to analyze…

Regularization is a big issue for training deep neural networks. In this paper, we propose a new information-theory-based regularization scheme named SHADE for SHAnnon DEcay. The originality of the approach is to define a prior based on…