By Ludwik Kurz
A key challenge in sensible photo processing is the detection of particular gains in a loud photo. research of variance (ANOVA) options may be very powerful in such occasions, and this publication offers an in depth account of using ANOVA in statistical photograph processing. The publication starts off via describing the statistical illustration of pictures within the a number of ANOVA types. The authors current a couple of computationally effective algorithms and strategies to accommodate such difficulties as line, part, and item detection, in addition to photograph recovery and enhancement. via describing the fundamental ideas of those ideas, and displaying their use in particular occasions, 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 development acceptance.
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Additional info for Analysis of Variance in Statistical Image Processing
M, whereas vertical lines are represented by the column effects Pj, j = 1, 2 , . . , n. Comparing Eqs. 1), we notice that the additional parameters Pj are used to formulate the hypothesis-alternative pair on the column effects. Thus, the two-way ANOVA model provides a framework for simultaneous detection of horizontal and vertical lines. C5-i (y i — y )2/(n H YlT=i Yl j=i(yij — l) ~ yi. 1 Using a square window (m = n), the detector structure is obtained by considering the maximum value of the pair (Fa, Fb) and comparing it to the threshold 7#, where TH = Fa>(m_i),(m_i)(H_i).
This is to be contrasted with previous designs such as the two-way design, where the analysis under the hypotheses is directly related to the analysis under the alternative. Eliminating the terms involving on in Eq. 82), we obtain t b SSa (y, /3) = E E ^ 7 -V>- Pjfntj ( 2 - 103 ) i= l 7= 1 which leads to the conclusion that as far as the estimate of /JL is concerned, it is the same as under Q. 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.
Throughout this book we will be interested in comparisons among effects, either vertical, horizontal, or diagonal, depending on the specific problem at hand. Therefore, it is necessary to provide some means to test the validity of the results of our comparisons; namely, providing confidence intervals on which to base our decisions.  Of interest to us are three tests that are commonly used in problems involving comparisons among effects. Before we embark on the definition of each comparison technique, we define some useful terms.