Analysis of Variance in Statistical Image Processing by Ludwik Kurz

By Ludwik Kurz

A key challenge in functional picture processing is the detection of particular positive aspects in a loud photo. research of variance (ANOVA) thoughts might be very powerful in such occasions, and this ebook provides a close account of using ANOVA in statistical photograph processing. The publication starts by way of describing the statistical illustration of pictures within the quite a few ANOVA versions. The authors current a few computationally effective algorithms and methods to house such difficulties as line, side, and item detection, in addition to photograph recovery and enhancement. by way of describing the fundamental rules of those suggestions, and exhibiting their use in particular occasions, the booklet will facilitate the layout of recent algorithms for specific purposes. will probably be of serious curiosity to graduate scholars and engineers within the box of snapshot processing and trend acceptance.

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99) 7= 1 {J For the SBIB design, X = 0lf. Hence from Eq. 100) j=l By replacing c^ and /x in either Eq. 90) or Eq. =l The error sum of squares under the alternative can now be evaluated by replacing the estimates given in Eqs. 101) in Eq. 82). 102) The sum of squares under Ha is obtained by deriving the estimates of fi and the block effects fij given that all the treatment effects a,- are not present. Note that the least squares estimates under the hypotheses are different from the estimates under the alternatives.

It is then essential to derive the sum of squares SSa (y, (3) and SSb (y, (3) under Ha and Hb, respectively. First, when we consider Ha, all the a,- are equal to zero, which implies that we need to retain Eqs. 37) as the estimates of/x and Pj. Thus, SSa (y, (3) is given by ssa (y, /3) = E 5 > y " *y)2 (239) Similarly, we have Eqs. )2 (2-42) i= l 7= 1 Note that there are m + n + 1 parameters in the design with two side conditions; therefore, the number of degrees of freedom associated with Eq. 38) is mn — m — n + 1, which can be written as (m — \){n — 1).

I^m}, r = {n, t2, . . , 8m}. The F-statistics for testing Ha, Ht,, Hc, and Hd are given in Eqs. 78). A major advantage of the present model is that the detection of a line of a given orientation can be done independently of the existence or nonexistence of a line in any other direction. In this case, we say that the F-statistics are independent of each other or mutually decoupled. 11. 5x5 window for multidirectional detection of line elements. One possible structure for the detector is comprised of the maximum F-statistic among those for which the central treatment effect estimate is greater than the overall average.

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