It was a wonder to me when, back in the early 1980s while doing my graduate studies at Carnegie Mellon University, I learned about optical signal processing. Back then, when an FFT (fast Fourier transform) on a digital signal would take an interminable 10s of seconds, an optical lens could perform a 2-D Fourier transform at the speed of light! That may not be so surprising to any child who has produced a rainbow from a prism, but what truly surprised me was that one of the most useful and common operations in signal processing, correlation, could also be performed optically. It was Professors David Cassasent and Vijaya Kumar who taught that course, and now Professor Kumar with Abhijit Mahalanobis and Richard Juday have authored a book, Correlation Pattern Recognition, which describes theory and application of digital and optical correlation.

Correlation is a basic operation. If you know the signal you are trying to detect, this target signal can be correlated over a 1-D waveform or 2-D image to determine if and where the target exists. Furthermore, this operation can be performed with equivalent results in the time/spatial or 1-D/2-D frequency domain. So, what does a whole book on correlation offer beyond this? The answer is:  plenty. Just as we know that correlation is a straightforward operation, we also know the drawbacks—a low tolerance to noise, rotation, and size of the target and a high computational load to operate globally when only portions of a signal may be of interest. This book educates the reader on the richness of correlation and offers techniques to surmount these drawbacks.

As is stated in the Preface, the authors believe that one of the reasons correlation is not used more in pattern recognition is that the practitioner must know fundamentals of several fields. For this reason, the first three chapters (after the Introduction) provide this background. Chapter 2 provides mathematical background, mainly in matrix operations and probability. Chapter 3 discusses linear systems and filtering theory, including topics such as sampling theory and Fourier transforms, which are basics of a digital systems or digital signal processing course. Chapter 4 covers detection and estimation, basics of a first pattern recognition course.

Following this, the book digs into correlation. After acknowledging the matched filter, Chapter 5 explains more details, many of which will likely show the frustrated matched filter user how to deal with the subtleties that may have caused a switch to feature-based techniques. For instance, this chapter discusses noise, background, and the ability to optically detect the correlation peak. Chapter 6 covers advanced correlation filters. The synthetic discriminant function (SDF) addresses one of the problems of basic correlation, its intolerance to target distortions, such as occlusions, 3-D distortions, and illumination variations. The SDF entails the combination of training images containing expected distortions.

Chapters 7 and 8 cover optical correlation. My only disappointment is not with the book, but the fact as described here that optical correlation now takes a second place in popular use to digital correlation — despite optical’s speed-of-light processing time. One reason for this is increased digital computer speeds, but another is that the progress of input/output devices for optical processors, called spatial light modulators, has been slow. Another reason is that optical lenses and other optical hardware are adjusted, etc., with far less versatility than software alone. Chapter 7 describes basic optical concepts and Chapter 8 details optical correlation techniques.

Finally, Chapter 9 discusses two applications on which the authors have worked and published extensively: target recognition in synthetic aperture radar (SAR) images and face recognition. The inclusion of these two applications is complementary in the following ways. The SAR images contain mainly military vehicles that are objects of rigid shapes, but these are often occluded, camouflaged, and captured at various 3-D perspectives. The face images are often more constrained in pose (perspective angle) and background, but have the added difficulty that the shape of interest is non-rigid.

This book is well-written with many diagrams and gray-scale images to illustrate the concepts, although I felt that some of the images were rather small. I very much liked the bulleted summary points at the ends of each chapter. This book is intended for advanced undergraduate and graduate students, and would be especially useful for pattern recognition practitioners interested in expanding their tool chest beyond basic correlation.



Correlation Pattern Recognition



B. V. K. Vijaya Kumar, Abhijit Mahalanobis, Richard D. Juday

Cambridge University Press, 2005


Reviewed by:  Larry O’Gorman

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