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In mathematical morphology and digital image processing, a top-hat transform is an operation that extracts small elements and details from given images.There exist two types of top-hat transform: the white top-hat transform is defined as the difference between the input image and its opening by some structuring element, while the black top-hat transform is defined dually as the difference ...
Mathematical Morphology was developed in 1964 by the collaborative work of Georges Matheron and Jean Serra, at the École des Mines de Paris, France.Matheron supervised the PhD thesis of Serra, devoted to the quantification of mineral characteristics from thin cross sections, and this work resulted in a novel practical approach, as well as theoretical advancements in integral geometry and ...
In N dimensions, the projection-slice theorem states that the Fourier transform of the projection of an N-dimensional function f(r) onto an m-dimensional linear submanifold is equal to an m-dimensional slice of the N-dimensional Fourier transform of that function consisting of an m-dimensional linear submanifold through the origin in the Fourier space which is parallel to the projection ...
In cryptography, a one-way compression function is a function that transforms two fixed-length inputs into a fixed-length output. [1] The transformation is "one-way", meaning that it is difficult given a particular output to compute inputs which compress to that output.
The top hat function can be generated by differentiating a linear ramp function of width . The limit of ϵ {\displaystyle \epsilon } then becomes the Dirac delta function . Its real-space form is the same as the moving average , with the exception of not introducing a shift in the output function.
Computer-generated holography (CGH) is a technique that uses computer algorithms to generate holograms.It involves generating holographic interference patterns.A computer-generated hologram can be displayed on a dynamic holographic display, or it can be printed onto a mask or film using lithography. [1]
Triangular functions are useful in signal processing and communication systems engineering as representations of idealized signals, and the triangular function specifically as an integral transform kernel function from which more realistic signals can be derived, for example in kernel density estimation.
Plot of normalized function (i.e. ()) with its spectral frequency components.. The unitary Fourier transforms of the rectangular function are [2] = = (), using ordinary frequency f, where is the normalized form [10] of the sinc function and = (/) / = (/), using angular frequency , where is the unnormalized form of the sinc function.