By Ludwik Kurz
A key challenge in useful photograph processing is the detection of particular gains in a loud photograph. research of variance (ANOVA) options will be very powerful in such occasions, and this e-book supplies a close account of using ANOVA in statistical photograph processing. The ebook starts off via 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, area, and item detection, in addition to photograph recovery and enhancement. by way of describing the fundamental rules of those thoughts, and exhibiting their use in particular events, the ebook will facilitate the layout of recent algorithms for specific purposes. it is going to be of serious curiosity to graduate scholars and engineers within the box of photo processing and development popularity.
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Extra info for Analysis of Variance in Statistical Image Processing
Now, by using Eq. 104) The error sum of squares under Ha is SSa (y, (3) = J2 E (vij ~ ir) nU i= l 7= 1 V K J ( 2 - 105 ) Using a similar argument in the case of hypothesis H^, we obtain SSb (y, P) = J2b ( ) There are bt observations in the design with b and t block and treatment effects. With the side conditions, the degree of freedom associated with SSe (y, /3) is ne = bt — b — t + 1 while na = t — 1 and rib = b — 1, respectively. 6 Contrast functions The test of the hypothesis, let us say Ha, in the one-way design, is based mainly on the comparison of the test statistic (Eq.
74) Finally, the numerator of the F-test is 55. (y, 13) - SSe (y, (3) = £) (y,-... 75) and the number of degree of freedom associated with 55 a (y, (3) is m — 1. Hence, the F-statistic for testing Ha is obtained by forming the ratio of Eqs. 72) with the proper degree of freedom assigned to each quadratic. Thus, we have ij - w... j.. k. )2 A similar approach may be used for the determination of the statistics under Hc, and Hd> In which case we obtain ij - yt... j.. k. k. - yJ Fc = u - yt... j.. k.
Thus, we can write i= l 7= 1 7= 1 Finally, substituting Eqs. 87) in Eq. 85), we obtain t b t n b a k E E yij u = nji + pY, i + Y,Pj i= l 7= 1 i= l 7= 1 where use has been made of the hat notation to denote the estimate of the effect instead of the actual value. 5 Incomplete designs 27 By expanding the summation and using the same argument involving the indicator j , Eq. 92) = Ei=i Using the side conditions for the treatment and block effects, we obtain from Eq. 93) n Combining Eqs. 94) which can be written as b b n t b kT[ = kpjl + kpoti + 2_^ Bj ij ~ kfi T^ ij ~ Yl Yl ®inijnU 7= 1 n 7= 1 (2-95) 1=1 7 = 1 The last term in Eq.