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The generalized Hough transform (GHT), introduced by Dana H. Ballard in 1981, is the modification of the Hough transform using the principle of template matching. [1] The Hough transform was initially developed to detect analytically defined shapes (e.g., line, circle, ellipse etc.).
The Hough transform as it is universally used today was invented by Richard Duda and Peter Hart in 1972, who called it a "generalized Hough transform" [3] after the related 1962 patent of Paul Hough. [ 4 ] [ 5 ] The transform was popularized in the computer vision community by Dana H. Ballard through a 1981 journal article titled " Generalizing ...
Dana Harry Ballard (1946–2022) was a professor of computer science at the University of Texas at Austin and formerly with the University of Rochester. [1] Ballard attended MIT and graduated in 1967 with his bachelor's degree in aeronautics and astronautics. He then attended the University of Michigan for his masters in information and control ...
The generalized logistic function or curve is an extension of the logistic or sigmoid functions. Originally developed for growth modelling, it allows for more flexible S-shaped curves. The function is sometimes named Richards's curve after F. J. Richards, who proposed the general form for the family of models in 1959.
Hough transform identifies clusters of features with a consistent interpretation by using each feature to vote for all object poses that are consistent with the feature. When clusters of features are found to vote for the same pose of an object, the probability of the interpretation being correct is much higher than for any single feature.
The intensive use of the Laplace transform in engineering led to the heuristic use of symbolic methods, called operational calculus. Since justifications were given that used divergent series, these methods were questionable from the point of view of pure mathematics. They are typical of later application of generalized function methods.
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In mathematics, the Stieltjes transformation S ρ (z) of a measure of density ρ on a real interval I is the function of the complex variable z defined outside I by the formula S ρ ( z ) = ∫ I ρ ( t ) d t t − z , z ∈ C ∖ I . {\displaystyle S_{\rho }(z)=\int _{I}{\frac {\rho (t)\,dt}{t-z}},\qquad z\in \mathbb {C} \setminus I.}