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Micro-pipelines are linear (1D) structures for asynchronous communications. In retinotopic VLSI vision chips, communicating over 2D image regions is a key to efficient mid-level vision computations. However, micro-pipelines are limited to 1D communications only. In this paper, we introduce an extension of the micro-pipeline, called the convergent micro-pipeline, for implementing mixed asynchronous-synchronous regional computations over arbitrary shaped regions. This operator is exploited in programmable artificial retinas (PAR), that is, image sensors with a digital processor in each pixel, for low power vision applications. To illustrate the behavior and versatility, several regional computations are described.