Related papers: Certifying the Existence of Epipolar Matrices
This paper considers the foundational question of the existence of a fundamental (resp. essential) matrix given $m$ point correspondences in two views. We present a complete answer for the existence of fundamental matrices for any value of…
This paper studies the problem of recovering cameras from a set of fundamental matrices. A set of fundamental matrices is said to be compatible if a set of cameras exists for which they are the fundamental matrices. We focus on the complete…
The essential matrix incorporates relative rotation and translation parameters of two calibrated cameras. The well-known algebraic characterization of essential matrices, i.e. necessary and sufficient conditions under which an arbitrary…
In recent work, algebraic computational software was used to provide the exact algebraic conditions under which a sixtuple $\{F^{ij}\}$ of fundamental matrices, corresponding to $4$ images, will be compatible, i.e. there will exist cameras…
In two-view geometry, the essential matrix describes the relative position and orientation of two calibrated images. In three views, a similar role is assigned to the calibrated trifocal tensor. It is a particular case of the (uncalibrated)…
We present a novel approach for RANSAC-based computation of the fundamental matrix based on epipolar homography decomposition. We analyze the geometrical meaning of the decomposition-based representation and show that it directly induces a…
In general it requires at least 7 point correspondences to compute the fundamental matrix between views. We use the cross ratio invariance between corresponding epipolar lines, stemming from epipolar line homography, to derive a simple…
Essential matrix averaging, i.e., the task of recovering camera locations and orientations in calibrated, multiview settings, is a first step in global approaches to Euclidean structure from motion. A common approach to essential matrix…
Robust estimation of the essential matrix, which encodes the relative position and orientation of two cameras, is a fundamental step in structure from motion pipelines. Recent deep-based methods achieved accurate estimation by using complex…
Extracting point correspondences from two or more views of a scene is a fundamental computer vision problem with particular importance for relative camera pose estimation and structure-from-motion. Existing local feature matching…
We address the problem of epipolar geometry using the motion of silhouettes. Such methods match epipolar lines or frontier points across views, which are then used as the set of putative correspondences. We introduce an approach that…
We aim at estimating the fundamental matrix in two views from five correspondences of rotation invariant features obtained by e.g.\ the SIFT detector. The proposed minimal solver first estimates a homography from three correspondences…
Estimating fundamental matrices is a classic problem in computer vision. Traditional methods rely heavily on the correctness of estimated key-point correspondences, which can be noisy and unreliable. As a result, it is difficult for these…
In this note we study the connection between the existence of a projective reconstruction and the existence of a fundamental matrix satisfying the epipolar constraints.
A frame is an overcomplete set that can represent vectors(signals) faithfully and stably. Two frames are equivalent if signals can be essentially represented in the same way, which means two frames differ by a permutation, sign change or…
A minimal solution using two affine correspondences is presented to estimate the common focal length and the fundamental matrix between two semi-calibrated cameras - known intrinsic parameters except a common focal length. To the best of…
Keypoint matching can be slow and unreliable in challenging conditions such as repetitive textures or wide-baseline views. In such cases, known geometric relations (e.g., the fundamental matrix) can be used to restrict potential…
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…
A set of fundamental matrices relating pairs of cameras in some configuration can be represented as edges of a "viewing graph". Whether or not these fundamental matrices are generically sufficient to recover the global camera configuration…
The criteria for determining graph isomorphism are crucial for solving graph isomorphism problems. The necessary condition is that two isomorphic graphs possess invariants, but their function can only be used to filtrate and subdivide…