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In mathematics, computer science and especially graph theory, a distance matrix is a square matrix (two-dimensional array) containing the distances, taken pairwise, between the elements of a set. [1] Depending upon the application involved, the distance being used to define this matrix may or may not be a metric .
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 x 1 , x 2 , … , x n {\displaystyle x_{1},x_{2},\ldots ,x_{n}} in k -dimensional space ℝ k , the elements of their Euclidean distance matrix A are given by squares of distances between them.
In mathematics, the Euclidean distance between two points in Euclidean space is the length of the line segment between them. It can be calculated from the Cartesian coordinates of the points using the Pythagorean theorem , and therefore is occasionally called the Pythagorean distance .
The closest pair of points problem or closest pair problem is a problem of computational geometry: given points in metric space, find a pair of points with the smallest distance between them. The closest pair problem for points in the Euclidean plane [ 1 ] was among the first geometric problems that were treated at the origins of the systematic ...
Lloyd's algorithm is usually used in a Euclidean space. The Euclidean distance plays two roles in the algorithm: it is used to define the Voronoi cells, but it also corresponds to the choice of the centroid as the representative point of each cell, since the centroid is the point that minimizes the average squared Euclidean distance to the ...
SIFT keypoints of objects are first extracted from a set of reference images [1] and stored in a database. An object is recognized in a new image by individually comparing each feature from the new image to this database and finding candidate matching features based on Euclidean distance of their feature vectors. From the full set of matches ...
A simple way to parallelize single-color line rasterization is to let multiple line-drawing algorithms draw offset pixels of a certain distance from each other. [2] Another method involves dividing the line into multiple sections of approximately equal length, which are then assigned to different processors for rasterization. The main problem ...
The basic algorithm – greedy search – works as follows: search starts from an enter-point vertex by computing the distances from the query q to each vertex of its neighborhood {: (,)}, and then finds a vertex with the minimal distance value. If the distance value between the query and the selected vertex is smaller than the one between the ...