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Thismonographisconcernedwithdescriptionanddesignfortwo-dimensional and three-dimensional images; it will be of special interest to researchers and graduate students who specialized in image processing and system theory. From the data in digital images, mathematical models will be constructed. Then new systems which describe faithfully any two-dimensional or thr- dimensional digital images will be proposed. Using the systems thus allows description to be treated as realization problem and design. By virtue of this approach, this monograph provides new results and their extensions which are designing of two-dimensional and three-dimensional images. Some actual design examples will be also shown. In usual image processing today, two-dimensional images are transformed into one-dimensional signals, then which are analyzed by means of various established methods in signal processing theory. Likewise, three-dimensional images are transformed into two-dimensional signals and these signals are analyzedbyestablishedmethodsintwo-dimensionalsignalprocessingtheory. Another common processing procedure employs tree structures such as qu- trees for two-dimensional images and oct-trees for three-dimensional ones.