Analysis of Incomplete Multivariate Data

Chapter 5 moves the focus to object detection. Here, the model is developed using transformed space-based techniques. The authors mention the use of moment-invariant techniques and provide a few references. There is also some illustration of cases in which these techniques would work well. The book does not even mention what these techniques are, however. It is difficult, therefore, to appreciate what the supposed merits or drawbacks are. For the transformed space-based techniques, it is not clear how one should choose the transformation. The methodology is illustrated on some test examples. It is not clear what advantage these methods would have over other methodology in use [such as the use of object processes; see Baddeley and van Lieshout (1993)] in the statistics and imaging literature, especially because the objects are very easy to detect in each of the supplied examples. Once again, there is no mention of these other methods. Chapter 6 develops image segmentation using a nested design algorithm. The authors advocate a top-down splitting and merging strategy to segmentation, starting from the top left corner of the image. The methodology is illustrated on the “Lena” image, but though the segmented image seems to look similar to the original, we wonder whether the results are really any good. For example, we could detect at least five segments in the face of “Lena” (Fig. 6.12) and six on her hat, but should not a good algorithm detect these in the same (and only one) segment for each? Once again, there is no discussion at all on an interpretation of these results and the drawbacks and no comparison with other procedures (e.g., see Chen, Lin, and Chen 1991). Chapter 9 addresses the aspect of image restoration. Two restoration procedures based on a two-stage approach are presented. In this, edge detectors based on generalized least squares and Youden square masks are presented. The examples here work well, though once again, it is not readily apparent how the different 5 x 5 masks are merged. Other approaches for image restoration (see Amit, Grenander, and Piccioni 1991) are not even mentioned. The authors are also quite sloppy with the notations and definitions. Here are just a few examples. On page 14 [e.g., in Eq. (2.28)], the degrees of freedom for the denominator should be m(n l), not m2 m. In Equation (2.58), +y.k should be -y,,k. For the Tukey method on page 30, the confidence interval is & i Ts( &), not just Ts( &). In Equation (3.26) on page 49, s2 cannot be equal to 0’; s2 is only an estimator of c2. In Equation (3.42) on page 53, the error sum of squares cannot depend on ,! ; it should involve only the estimator of p. On the bottom of page 69, it is mentioned, “Based on numerous simulations on test images, $2 is selected as the additional test statistic. ” What does this mean? $2 cannot be a test statistic, being an unknown parameter; see (4.5). In Equation (6.3) on page 134, -13~~~1 should be +03c2). What is A, in Equation (6.7)? Below Equation (A.l) on page 145, it is mentioned that A, = c, q3. It is not clear if this is the right quantity in Equation (6.7). In Equation (6.8) +yZ. , should be -yi. On page 148, below Equation (7.8) Qa should not involve /3. We find the discussion in Section 8.1, on Bayes and maximum likelihood estimation, very vague. The authors talk of p(a), p(r/a), and E(r/a), without explaining what these quantities are. In short, the book should not be consulted for learning anything about ANOVA or image analysis. In writing this book, the authors were hoping that “this book will stimulate a wider acceptance of the methodology of image processing suggested here” (see Preface, p. xii). We have serious doubts about the book achieving this goal.