Related papers: Closed-Form Optimal Two-View Triangulation Based o…
This paper introduces a new computational methodology for determining a-posteriori multi-objective error estimates for finite-element approximations, and for constructing corresponding (quasi-)optimal adaptive refinements of finite-element…
Motivated by problems in contact mechanics, we propose a duality approach for computing approximations and associated a posteriori error bounds to solutions of variational inequalities of the first kind. The proposed approach improves upon…
In recent years, semidefinite relaxations of common optimization problems in robotics have attracted growing attention due to their ability to provide globally optimal solutions. In many cases, it was shown that specific handcrafted…
This work proposes a novel convex-non-convex formulation of the image segmentation and the image completion problems. The proposed approach is based on the minimization of a functional involving two distinct regularization terms: one…
The rotation averaging problem is a fundamental task in computer vision applications. It is generally very difficult to solve due to the nonconvex rotation constraints. While a sufficient optimality condition is available in the literature,…
An efficient and accurate computational approach is proposed for optimal attitude control of a rigid body. The problem is formulated directly as a discrete time optimization problem using a Lie group variational integrator. Discrete…
The problem of finding a next best viewpoint for 3D modeling or scene mapping has been explored in computer vision over the last decade. This paper tackles a similar problem, but with different characteristics. It proposes a method for…
This paper introduces a novel double regularization scheme for bilevel optimization problems whose lower-level problem is composite and convex, but not necessarily strongly convex, in the lower-level variable. The analysis focuses on the…
Why is it that semidefinite relaxations have been so successful in numerous applications in computer vision and robotics for solving non-convex optimization problems involving rotations? In studying the empirical performance we note that…
We propose a new fast algorithm for solving one of the standard formulations of frame-based image deconvolution: an unconstrained optimization problem, involving an $\ell_2$ data-fidelity term and a non-smooth regularizer. Our approach is…
Compressed sensing with sparse frame representations is seen to have much greater range of practical applications than that with orthonormal bases. In such settings, one approach to recover the signal is known as $\ell_1$-analysis. We…
Near isometric orthogonal embeddings to lower dimensions are a fundamental tool in data science and machine learning. In this paper, we present the construction of such embeddings that minimizes the maximum distortion for a given set of…
This article discusses nonconforming finite element methods for convex minimization problems and systematically derives dual mixed formulations. Duality relations lead to simple error estimates that avoid an explicit treatment of…
A simple, yet general, formalism for the optimized linear combination of astrophysical images is constructed and demonstrated. The formalism allows the user to combine multiple undersampled images to provide oversampled output at high…
We propose an alternating direction method of multipliers (ADMM) to solve an optimization problem stemming from inverse lithography. The objective functional of the optimization problem includes three terms: the misfit between the imaging…
We introduce a primal-dual framework for solving linearly constrained nonconvex composite optimization problems. Our approach is based on a newly developed Lagrangian, which incorporates \emph{false penalty} and dual smoothing terms. This…
This study presents a theoretical structure for the monocular pose estimation problem using the total least squares. The unit-vector line-of-sight observations of the features are extracted from the monocular camera images. First, the…
Given 2D point correspondences between an image pair, inferring the camera motion is a fundamental issue in the computer vision community. The existing works generally set out from the epipolar constraint and estimate the essential matrix,…
The integration of multi-view imaging and pose estimation represents a significant advance in computer vision applications, offering new possibilities for understanding human movement and interactions. This work presents a new algorithm…
We present a primal-dual algorithmic framework to obtain approximate solutions to a prototypical constrained convex optimization problem, and rigorously characterize how common structural assumptions affect the numerical efficiency. Our…