Related papers: Certifying the Existence of Epipolar Matrices

Correspondences between k-tuples of points are key in multiple view geometry and motion analysis. Regular transformations are posed by homographies between two projective planes that serves as structural models for images. Such…

We revisit certain problems of pose estimation based on 3D--2D correspondences between features which may be points or lines. Specifically, we address the two previously-studied minimal problems of estimating camera extrinsics from $p \in…

Two matrices are said to be principal minor equivalent if they have equal corresponding principal minors of all orders. We give a characterization of principal minor equivalence and a deterministic polynomial time algorithm to check if two…

Computing the epipolar geometry between cameras with very different viewpoints is often very difficult. The appearance of objects can vary greatly, and it is difficult to find corresponding feature points. Prior methods searched for…

This article proposes a bivariate polynomial problem for finite-order real matrices that endows a \textit{`sufficient condition'} for a map from the standard vector spaces of finite-order real matrices to the same dimensional bivariate…

The problem of determining whether a diagonally dominant matrix is singular or nonsingular is a classical topic in matrix theory. This paper develops necessary and sufficient conditions for the singularity or nonsingularity of diagonally…

Matching two images while estimating their relative geometry is a key step in many computer vision applications. For decades, a well-established pipeline, consisting of SIFT, RANSAC, and 8-point algorithm, has been used for this task.…

We present subquadratic algorithms, in the algebraic decision-tree model of computation, for detecting whether there exists a triple of points, belonging to three respective sets $A$, $B$, and $C$ of points in the plane, that satisfy a…

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…

The rational camera model recently introduced in [19] provides a general methodology for studying abstract nonlinear imaging systems and their multi-view geometry. This paper builds on this framework to study "physical realizations" of…

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…

Camera pose estimation for two-view geometry traditionally relies on RANSAC. Normally, a multitude of image correspondences leads to a pool of proposed hypotheses, which are then scored to find a winning model. The inlier count is generally…

This paper is a theoretical study of the following Non-Rigid Structure from Motion problem. What can be computed from a monocular view of a parametrically deforming set of points? We treat various variations of this problem for affine and…

To what extent are two images picturing the same 3D surfaces? Even when this is a known scene, the answer typically requires an expensive search across scale space, with matching and geometric verification of large sets of local features.…

In this paper a deterministic preprocessing algorithm is presented, whose output can be given as input to most state-of-the-art epipolar geometry estimation algorithms, improving their results considerably. They are now able to succeed on…

The vast majority of modern consumer-grade cameras employ a rolling shutter mechanism. In dynamic geometric computer vision applications such as visual SLAM, the so-called rolling shutter effect therefore needs to be properly taken into…

The problem of self-calibration of two cameras from a given fundamental matrix is one of the basic problems in geometric computer vision. Under the assumption of known principal points and square pixels, the well-known Bougnoux formula…

The concepts of differentiation and integration for matrices are known. As far as each matrix is differentiable, it is not clear a priori whether a given matrix is integrable or not. Recently some progress was obtained for diagonalizable…

We present efficient algorithms for detecting central and mirror symmetry for the case of algebraic curves defined by means of polynomial parametrizations. The algorithms are based on the existence of a linear relationship between two…

We provide a necessary and sufficient condition for existence of Gaussian cubature formulas. It consists of checking whether some overdetermined linear system has a solution and so complements Mysovskikh's theorem which requires computing…