Nonuniform region processing on SIMD arrays using the coterie network

Computation on and among data sets mapped to irregular, nonuniform, aggregates of processing elements (PEs) is an important problem in parallel vision processing, arising in segmentation and in support operations for intermediate-level grouping tasks. The difficulty is that the SIMD processors which map so effectively to pixel-based processing are restricted here in data-dependent computations by their limited control mechanisms. Associative processing is an effective means of applying parallel processing to nonuniform computations (Weems 1984), but often results in operating on one data set at a time. We address this problem by introducing an additional level of parallelism we call multiassociativity which provides a framework for performing associative computation on these data sets simultaneously. In this article we present algorithms developed for the coterie network (Weems et al. 1989) to simulate efficiently within nonuniform aggregates of PEs simultaneously the associative algorithms typically supported in hardware at the array level. One result is that algorithms requiring a number of operations proportional to the diameters of the regions in a mesh-connected topology can be executed in constant or logarithmic time using the coterie network. Other results are: the efficient application of existing associative algorithms (e.g., Falkoff 1962; Foster 1976) to arbitrary aggregates of PEs in parallel, and the development of efficient new multiassociative algorithms, among them parallel prefix and convex hull. The multiassociative framework also extends the associative paradigm by allowing operations on and among aggregates of PEs themselves, operations not defined when the entity in question is always an entire array. Two consequences are the support of divide-and-conquer algorithms within aggregates, and communication among aggregates. Numerous multiassociative low-level vision algorithms are presented.