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The Mandelbrot set ( / ˈmændəlbroʊt, - brɒt /) [1] [2] is a two-dimensional set with a relatively simple definition that exhibits great complexity, especially as it is magnified. It is popular for its aesthetic appeal and fractal structures. The set is defined in the complex plane as the complex numbers for which the function does not ...
The correspondence problem refers to the problem of ascertaining which parts of one image correspond to which parts of another image, [1] where differences are due to movement of the camera, the elapse of time, and/or movement of objects in the photos. Correspondence is a fundamental problem in computer vision — influential computer vision ...
In this process, the data is partitioned into v parts. Each of the parts is then set aside at turn as a test set, a clustering model computed on the other v − 1 training sets, and the value of the objective function (for example, the sum of the squared distances to the centroids for k-means) calculated for the
The root test is stronger than the ratio test: whenever the ratio test determines the convergence or divergence of an infinite series, the root test does too, but not conversely. Integral test. The series can be compared to an integral to establish convergence or divergence.
The top and bottom images produce a dent or projection depending on whether viewed with cross- () or wall- () eyed vergence. An autostereogram is a two-dimensional (2D) image that can create the optical illusion of a three-dimensional (3D) scene. Autostereograms use only one image to accomplish the effect while normal stereograms require two.
k-means clustering is a method of vector quantization, originally from signal processing, that aims to partition n observations into k clusters in which each observation belongs to the cluster with the nearest mean (cluster centers or cluster centroid ), serving as a prototype of the cluster. This results in a partitioning of the data space ...
An analogous statement for convergence of improper integrals is proven using integration by parts. If the integral of a function f is uniformly bounded over all intervals , and g is a non-negative monotonically decreasing function , then the integral of fg is a convergent improper integral.
Tightness and convergence. Tightness is often a necessary criterion for proving the weak convergence of a sequence of probability measures, especially when the measure space has infinite dimension. See. Finite-dimensional distribution. Prokhorov's theorem. Lévy–Prokhorov metric. Weak convergence of measures. Tightness in classical Wiener space.