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The eight-point algorithm is an algorithm used in computer vision to estimate the essential matrix or the fundamental matrix related to a stereo camera pair from a set of corresponding image points. It was introduced by Christopher Longuet-Higgins in 1981 for the case of the essential matrix. In theory, this algorithm can be used also for the ...
Coplanarity. In geometry, a set of points in space are coplanar if there exists a geometric plane that contains them all. For example, three points are always coplanar, and if the points are distinct and non-collinear, the plane they determine is unique. However, a set of four or more distinct points will, in general, not lie in a single plane.
In computer vision, the fundamental matrix is a 3×3 matrix which relates corresponding points in stereo images. In epipolar geometry, with homogeneous image coordinates, x and x ′, of corresponding points in a stereo image pair, Fx describes a line (an epipolar line) on which the corresponding point x ′ on the other image must lie. That ...
Let P and Q be two sets, each containing N points in .We want to find the transformation from Q to P.For simplicity, we will consider the three-dimensional case (=).The sets P and Q can each be represented by N × 3 matrices with the first row containing the coordinates of the first point, the second row containing the coordinates of the second point, and so on, as shown in this matrix:
Collinearity equation. Light beams passing through the pinhole of a pinhole camera. The collinearity equations are a set of two equations, used in photogrammetry and computer stereo vision, to relate coordinates in a sensor plane (in two dimensions) to object coordinates (in three dimensions). The equations originate from the central projection ...
Formally, a parity check matrix H of a linear code C is a generator matrix of the dual code, C ⊥. This means that a codeword c is in C if and only if the matrix-vector product Hc ⊤ = 0 (some authors [1] would write this in an equivalent form, cH ⊤ = 0.) The rows of a parity check matrix are the coefficients of the parity check equations. [2]
A generator matrix for a linear [,,]-code has format , where n is the length of a codeword, k is the number of information bits (the dimension of C as a vector subspace), d is the minimum distance of the code, and q is size of the finite field, that is, the number of symbols in the alphabet (thus, q = 2 indicates a binary code, etc.).
Euclidean distance matrix. In mathematics, a Euclidean distance matrix is an n×n matrix representing the spacing of a set of n points in Euclidean space. For points in k -dimensional space ℝk, the elements of their Euclidean distance matrix A are given by squares of distances between them. That is. where denotes the Euclidean norm on ℝk.