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In computational geometry, the largest empty rectangle problem, [2] maximal empty rectangle problem [3] or maximum empty rectangle problem, [4] is the problem of finding a rectangle of maximal size to be placed among obstacles in the plane. There are a number of variants of the problem, depending on the particularities of this generic ...
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An example of histogram matching. In image processing, histogram matching or histogram specification is the transformation of an image so that its histogram matches a specified histogram. [1] The well-known histogram equalization method is a special case in which the specified histogram is uniformly distributed. [2]
Scott's rule is a method to select the number of bins in a histogram. [1] Scott's rule is widely employed in data analysis software including R , [ 2 ] Python [ 3 ] and Microsoft Excel where it is the default bin selection method.
The Hammersley sofa has area 2.2074 but is not the largest solution Gerver's sofa of area 2.2195 with 18 curve sections A telephone handset, a closer match than a sofa to Gerver's shape. A lower bound on the sofa constant can be proven by finding a specific shape of a high area and a path for moving it through the corner.
A v-optimal histogram is based on the concept of minimizing a quantity which is called the weighted variance in this context. [1] This is defined as = =, where the histogram consists of J bins or buckets, n j is the number of items contained in the jth bin and where V j is the variance between the values associated with the items in the jth bin.
Series of umbrella sampling simulations can be analyzed using the weighted histogram analysis method (WHAM) [2] or its generalization. [3] WHAM can be derived using the maximum likelihood method. Subtleties exist in deciding the most computationally efficient way to apply the umbrella sampling method, as described in Frenkel and Smit's book ...
Here, a d-dimensional rectangular range is defined to be a Cartesian product of d intervals of real numbers, which is a subset of R d. The problem is named after Victor Klee , who gave an algorithm for computing the length of a union of intervals (the case d = 1) which was later shown to be optimally efficient in the sense of computational ...