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Conflict-free communication in large networks of processors with particular application to image processing is discussed. A general network model and a general class of communication tasks are defined, and algorithms are given for carrying out such tasks on an arbitrary network. Specific types of communication tasks (e.g., one-to-many, many-to-one, and one-to-one) are then considered; these tasks are found to be sufficient for implementing the standard image processing operations. Next, various specific networks topologies are treated, including hypercubes, rings, arrays, and trees. Finally, these results are applied to defining algorithms for performing basic types of image processing operations on both general and specific types of networks.