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The histogram matching algorithm can be extended to find a monotonic mapping between two sets of histograms. Given two sets of histograms = {} = and = {} =, the optimal monotonic color mapping is calculated to minimize the distance between the two sets simultaneously, namely ((),) where (,) is a distance metric between two histograms.
Histogram. A histogram is a visual representation of the distribution of quantitative data. To construct a histogram, the first step is to "bin" (or "bucket") the range of values— divide the entire range of values into a series of intervals—and then count how many values fall into each interval. The bins are usually specified as consecutive ...
The overlap coefficient, [note 1] or Szymkiewicz–Simpson coefficient, [citation needed][3][4][5] is a similarity measure that measures the overlap between two finite sets. It is related to the Jaccard index and is defined as the size of the intersection divided by the size of the smaller of two sets: Note that .
Therefore, a naïve algorithm to calculate the estimated variance is given by the following: Let n ← 0, Sum ← 0, SumSq ← 0. For each datum x: n ← n + 1. Sum ← Sum + x. SumSq ← SumSq + x × x. Var = (SumSq − (Sum × Sum) / n) / (n − 1) This algorithm can easily be adapted to compute the variance of a finite population: simply ...
Dice-Sørensen coefficient. A statistic used for comparing the similarity of two samples. The Dice-Sørensen coefficient (see below for other names) is a statistic used to gauge the similarity of two samples. It was independently developed by the botanists Lee Raymond Dice [1] and Thorvald Sørensen, [2] who published in 1945 and 1948 respectively.
A stem-and-leaf display or stem-and-leaf plot is a device for presenting quantitative data in a graphical format, similar to a histogram, to assist in visualizing the shape of a distribution. They evolved from Arthur Bowley 's work in the early 1900s, and are useful tools in exploratory data analysis. Stemplots became more commonly used in the ...
A two-dimensional color histogram is a two-dimensional array. The size of each dimension is the number of colors that were used in the phase of color quantization. These arrays are treated as matrices, each element of which stores a normalized count of pixel pairs, with each color corresponding to the index of an element in each pixel neighborhood.
Definition. 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, nj is the number of items contained in the j th bin and where Vj is the variance between the values associated with the items in the ...