Related papers: Closed-Form Optimal Two-View Triangulation Based o…
Multiple-view triangulation by $\ell_{\infty}$ minimisation has become established in computer vision. State-of-the-art $\ell_{\infty}$ triangulation algorithms exploit the quasiconvexity of the cost function to derive iterative update…
This paper proposes a method to compute camera 6Dof poses to achieve a user defined coverage. The camera placement problem is modeled as a combinatorial optimization where given the maximum number of cameras, a camera set is selected from a…
Exposure correction is one of the fundamental tasks in image processing and computational photography. While various methods have been proposed, they either fail to produce visually pleasing results, or only work well for limited types of…
We present an approach to solving hard geometric optimization problems in the RANSAC framework. The hard minimal problems arise from relaxing the original geometric optimization problem into a minimal problem with many spurious solutions.…
We propose a new framework for deriving screening rules for convex optimization problems. Our approach covers a large class of constrained and penalized optimization formulations, and works in two steps. First, given any approximate point,…
In this work, we address the problem of refining the geometry of local image features from multiple views without known scene or camera geometry. Current approaches to local feature detection are inherently limited in their keypoint…
Error bound analysis, which estimates the distance of a point to the solution set of an optimization problem using the optimality residual, is a powerful tool for the analysis of first-order optimization algorithms. In this paper, we use…
The vast majority of mesh-based modelling applications iteratively transform the mesh vertices under prescribed geometric conditions. This occurs in particular in methods cycling through the constraint set such as Position-Based Dynamics…
Despite the increasing prevalence of rotating-style capture (e.g., surveillance cameras), conventional stereo rectification techniques frequently fail due to the rotation-dominant motion and small baseline between views. In this paper, we…
Determining the position and orientation of a calibrated camera from a single image with respect to a 3D model is an essential task for many applications. When 2D-3D correspondences can be obtained reliably, perspective-n-point solvers can…
Line features are valid complements for point features in man-made environments. 3D-2D constraints provided by line features have been widely used in Visual Odometry (VO) and Structure-from-Motion (SfM) systems. However, how to accurately…
The aim of this paper is twofold: first, to extend the area of applications of tropical optimization by solving new constrained location problems, and second, to offer new closed-form solutions to general problems that are of interest to…
Imaging systems are inherently prone to aberrations. We present an optimization method to design two-dimensional freeform reflectors that minimize aberrations for various parallel ray beams incident on the optical system. We iteratively…
We propose two new alternating direction methods to solve "fully" nonsmooth constrained convex problems. Our algorithms have the best known worst-case iteration-complexity guarantee under mild assumptions for both the objective residual and…
The recent development of calibration algorithms has been driven into two major directions: (1) an increasing accuracy of mathematical approaches and (2) an increasing flexibility in usage by reducing the dependency on calibration objects.…
Meshes composed of well-centered simplices have nice orthogonal dual meshes (the dual Voronoi diagram). This is useful for certain numerical algorithms that prefer such primal-dual mesh pairs. We prove that well-centered meshes also have…
We propose a minimal solution for pose estimation using both points and lines for a multi-perspective camera. In this paper, we treat the multi-perspective camera as a collection of rigidly attached perspective cameras. These type of…
Most of the optimal guidance problems can be formulated as nonconvex optimization problems, which can be solved indirectly by relaxation, convexification, or linearization. Although these methods are guaranteed to converge to the global…
Vision-based motion estimation and 3D reconstruction, which have numerous applications (e.g., autonomous driving, navigation systems for airborne devices and augmented reality) are receiving significant research attention. To increase the…
In this letter, we present a closed-form initialization method that recovers the full visual-inertial state without nonlinear optimization. Unlike previous approaches that rely on iterative solvers, our formulation yields analytical,…