DK1212_C001

DK1212_C001 - Part I Images as Multidimensional Signals...

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Part I Images as Multidimensional Signals Part I provides the theoretical background for the rest of the book. It introduces the concept of still images interpreted as two-dimen- sional signals, as well as the generalization to multidimensional interpretation of moving images and three-dimensional (spatial) image information. Once this general notion is introduced, the sig- nal theoretical concepts, after generalization to the two-dimensional or multidimensional case, can be utilized for image processing and analysis. This concept proved very successful in enabling the for- malization (and consequently optimization) of many approaches to image acquisition, processing, and analysis that were originally designed as heuristic or even not feasible. A characteristic example comes from the area of medical tomo- graphic imaging: the intuitively suggested heuristic algorithm of image reconstruction from projections by back-projection turned out to be very unsatisfactory, giving only a crude approximation of the proper image, with very disturbing artifacts. Later, relatively com- plex theory (see Chapter 9) was developed that led to a formally derived algorithm of filtered back-projection, widely used nowadays, that is theoretically correct and provides very good images, even © 2006 by Taylor & Francis Group, LLC
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under practical limitations. Both algorithms are quite similar, with the only difference being the filtering of each individual projection added to the original procedure in the later method — seemingly an elementary step, but probably impossible to discover without the involved theory. The alternative methods of image reconstruction from projections rely heavily on other aspects of the multidimen- sional signal theory as well. Part I introduces the basic image processing concepts and ter- minology needed to understand further sections of the book. Broader and deeper treatment of the theory can be found in the numerous literature that is partly listed in the references to this section, e.g., in [4], [5], [6], [18], [22], [23], [25], [26]. Other sources used but not cited elsewhere are [1], [2], [8], [12], [14]–[17], [19], [21], [24]. In context of the theoretical principles, we shall introduce the concepts of two-dimensional systems and operators, two-dimensional transforms, and two-dimensional stochastic fields. The text is con- ceived to be self-contained: the necessary concepts of the one-dimen- sional signal theory will be briefly included, however, without detailed derivations. A prior knowledge of the signal theory elements, though definitely advantageous, is thus not necessary. With respect to the purpose of the book, we shall mostly limit ourselves to the two-dimen- sional case; the generalization to three- and four-dimensional cases is rather straightforward and will be mentioned where necessary.
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This note was uploaded on 02/27/2008 for the course BME 525 taught by Professor Singh during the Fall '07 term at USC.

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DK1212_C001 - Part I Images as Multidimensional Signals...

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