Mathematical Nonlinear Image Processing: A Special Issue of by Edward R. Dougherty, Jaakko Astola

By Edward R. Dougherty, Jaakko Astola

Mathematical Nonlinear photograph Processing bargains with a quick starting to be examine zone. the advance of the topic springs from elements: (1) the nice enlargement of nonlinear tools utilized to difficulties in imaging and imaginative and prescient, and (2) the measure to which nonlinear ways are either utilizing and fostering new advancements in various components of arithmetic. Mathematical Nonlinear picture Processing could be of curiosity to humans operating within the parts of utilized arithmetic in addition to researchers in computing device imaginative and prescient. Mathematical Nonlinear snapshot Processing is an edited quantity of unique learn. It has additionally been released as a distinct factor of the magazine of Mathematical Imaging and imaginative and prescient. (Volume 2, factor 2/3).

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Consider a random variable Y whose distribution function is u(F(t)), where F(t) is a strictly monotonous and piecewise differentiable distribution function and u : [0, 1] ---. [0, 1] is a differentiable function. Let the integrals J~ tF'(t)dt and J~oo tu'(F(t))F'(t)dt be finite, and let v( t) : [0, 1] ---. [0, 00) be a differentiable function that satisfies v(o) = 0, v(l) = 1 and vet) 2: u(t) for all < t < 1. Then for the expectation of Y Now, a manipulation similar to the one above leads to the equation (tv(F(t))) [co I: I: tv'(F(t))F'(t)dt.

27) In this case a k is well defined and is given by does not, then the step value is reduced by half until an appropriate step size that reduces the functional is found. , it stops when II akpk 112 < 10). The number of iterations needed to converge to the solution varies with the amount of smoothing required. For little smoothing (>'/20'2 large) the process will converge in two or three iterations, whereas for large amounts of smoothing the number of iterations will increase. Note that because the consistency measure consists of only local computations, it is possible to significantly reduce the total computation time through the use of a tightly coupled mesh of parallel-processing nodes [27].

This suggests that a Neyman-Pearson-type criterion should be used for choosing the decision threshold D, that Nonlinear Filtering Structure 143 is, choose D by D = arg max DE [o,R] E the application, either flexibility or extremely high computation speeds can be achieved. {D: Pr«m,n) ID I (m,n) E I) 2: o:}. 98 ensured that, for the most part, all of the most significant impulses were correctly identified. As was mentioned above, it is also desirable to have Pr«m, n) E ID I (m, n) (j. I) ~ 0; this provides a criterion by which to rank the various filters.

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