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The processing of compressed imagery can exhibit advantages of (1) reduced space requirement for image storage, due to fewer data; (2) computational speedup resulting from fewer operations on reduced data; and (3) increased data security due to an obscure encoding format. We call this technique compressive processing, which we have shown can simulate an image-domain operation using an analogous operation over a given compressed image format. The output of the analogous operation, when decompressed, equals or approximates the output of the corresponding image operation. In Part 1 of this three-part series, we show that compressive processing can lead to sequential computational efficiencies that approach the compression ratio. Additionally, we present unifying theory that portrays the derivation of compressive operations at a high level for image operations such as pointwise, global reduce (e.g., image summation or maximum), and image-template (e.g., linear convolution) operations. Further discussion and analysis concerned formulations of block truncation coding (BTC) and visual pattern image coding (VPIC) compressive transforms. In this paper, we analyze high-level formulations of the vector quantization (VQ) and JPEG compression transforms. Additionally, we illustrate the utility of our high-level derivational methods by demonstrating the derivation and operation of several pixel-level operations over VPIC- and BTC-compressed imagery. Such operations are extended to include VQ- and JPEG-compressed imagery. In Part 3, we consider the pixel- level operations of edge detection and smoothing, as well as higher-level operations such as target classification and connected component labeling. Analyses emphasize computational efficiency, as well as effects of information loss and computational error. Our algorithms are expressed in terms of image algebra, a rigorous, concise notation that unifies linear and nonlinear mathematics in the image domain. Since image algebra has been implemented on numerous sequential and parallel computers, our algorithms are feasible and widely portable.
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