By Ludwik Kurz

ISBN-10: 0511530161

ISBN-13: 9780511530166

ISBN-10: 0521031966

ISBN-13: 9780521031967

ISBN-10: 0521581826

ISBN-13: 9780521581820

A key challenge in sensible photo processing is the detection of particular positive factors in a loud photo. research of variance (ANOVA) recommendations will be very potent in such occasions, and this e-book provides an in depth account of using ANOVA in statistical photo processing. The publication starts by way of describing the statistical illustration of pictures within the numerous ANOVA types. The authors current a couple of computationally effective algorithms and methods to accommodate such difficulties as line, facet, and item detection, in addition to photo recovery and enhancement. by way of describing the fundamental rules of those recommendations, and displaying their use in particular events, the e-book 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 picture processing and trend reputation.

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Extra info for Analysis of Variance in Statistical Image Processing

Example text

K. — y.... k = l, 2 , . . , m Si = y i — y I = 1, 2, . . , m and the minimum of 5 5 . k. 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...

F (2-64) UJ,k)eS and finally, ssc(j,0)-sse(j,0)= The total number of observations in the design is m2. Under the Q assumptions there are 3m + 1 parameters with three side conditions. Thus, the degree of freedom ne corresponding to Eq. 58) is equal to (m — l)(m — 2). Since the numbers of levels for each effect are all equal, then na = n\, = nc = (m - 1). As a result, the test statistics for testing the hypotheses Ha : all a,- = 0,Hb • all fij = 0 and Hc : all Xk = 0 are given by y^ Fa = ^ : ty. y \2 - yu - yj.

For the multicomparison model, an essential parameter is the noise variance estimate, which is equal to SSe(y, (3)/(n—r). Therefore, it is necessary to determine the sum of squares under the alternative. Note that the degree of freedom n — r is equal to (m — l)(m — 3) for the GLS design. Recalling Eq. 72), we have s2 = a2 = - yt... *. 26) 50 Line detection Because we consider the one-contrast case {q = 1) for the four directional contrast, Eq. 27) where a is the vector of coefficients from Eq. 115).

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