Related papers: A clever elimination strategy for efficient minima…
The affine rank minimization problem consists of finding a matrix of minimum rank that satisfies a given system of linear equality constraints. Such problems have appeared in the literature of a diverse set of fields including system…
We tackle the problem of estimating a Manhattan frame, i.e. three orthogonal vanishing points, and the unknown focal length of the camera, leveraging a prior vertical direction. The direction can come from an Inertial Measurement Unit that…
Natural image matting, which separates foreground from background, is a very important intermediate step in recent computer vision algorithms. However, it is severely underconstrained and difficult to solve. State-of-the-art approaches…
We have recently presented a method to solve an overdetermined linear system of equations with multiple right hand side vectors, where the unknown matrix is to be symmetric and positive definite. The coefficient and the right hand side…
A new technique for approximating the entire solution set for a nonlinear system of relations (nonlinear equations, inequalities, etc. involving algebraic, smooth, or even continuous functions) is presented. The technique is to first plot…
We introduce and compare new compression approaches to obtain regularized solutions of large linear systems which are commonly encountered in large scale inverse problems. We first describe how to approximate matrix vector operations with a…
We propose an approach for estimating the relative pose between calibrated image pairs by jointly exploiting points, lines, and their coincidences in a hybrid manner. We investigate all possible configurations where these data modalities…
We derive a numerically stable method to compute an image representation of an unknown linear system only from data, leveraging a continuous-time version of Willems et al.'s fundamental lemma. To this end, we use derivatives approximated by…
We introduce a new, integrated approach to uncalibrated photometric stereo. We perform 3D reconstruction of Lambertian objects using multiple images produced by unknown, directional light sources. We show how to formulate a single…
We give a non-iterative solution to a particular case of the four-point three-views pose problem when three camera centers are collinear. Using the well-known Cayley representation of orthogonal matrices, we derive from the epipolar…
Ill-posed linear inverse problems (ILIP), such as restoration and reconstruction, are a core topic of signal/image processing. A standard approach to deal with ILIP uses a constrained optimization problem, where a regularization function is…
Coordinate-wise minimization is a simple popular method for large-scale optimization. Unfortunately, for general (non-differentiable) convex problems it may not find global minima. We present a class of linear programs that coordinate-wise…
We introduce a randomized algorithm for computing the minimal-norm solution to an underdetermined system of linear equations. Given an arbitrary full-rank m x n matrix A with m<n, any m x 1 vector b, and any positive real number epsilon…
A non-iterative auto-calibration algorithm is presented. It deals with a minimal set of six scene points in three views taken by a camera with fixed but unknown intrinsic parameters. Calibration is based on the image correspondences only.…
We present a novel solution to the camera pose estimation problem, where rotation and translation of a camera between two views are estimated from matched feature points in the images. The camera pose estimation problem is traditionally…
The internal geometry of most modern consumer cameras is not adequately described by the perspective projection. Almost all cameras exhibit some radial lens distortion and are equipped with an electronic rolling shutter that induces…
Calibrations are a possible tool to validate the minimality of a certain candidate. They have been introduced in the context of minimal surfaces and adapted to the case of Steiner problem in several variants. Our goal is to compare the…
Modelling real world systems frequently requires the solution of systems of nonlinear equations. A number of approaches have been suggested and developed for this computational problem. However, it is also possible to attempt solutions…
Image Segmentation is one of the core tasks in Computer Vision and solving it often depends on modeling the image appearance data via the color distributions of each it its constituent regions. Whereas many segmentation algorithms handle…
We consider the problem of solving mixed random linear equations with $k$ components. This is the noiseless setting of mixed linear regression. The goal is to estimate multiple linear models from mixed samples in the case where the labels…