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Array set addressing: making the world safe for hexagonal imaging

It has been shown through various research efforts over the past few decades that there are numerous advantages to sampling images hexagonally rather than rectangularly. Despite the advantages, hexagonal imaging has not been generally accepted as being advantageous due to the lack of sensors that sample hexagonally, lack of displays for hexagonal images, and lack of an elegant addressing scheme. The advantages gained by sampling hexagonally are offset by the additional processing required to deal with the problems that are inherent with the previously proposed addressing schemes. Hence, there is insufficient motivation to develop sensors and displays that operate in the hexagonal domain. This paper introduces an addressing scheme, array set addressing, that solves the problems exhibited by other approaches. This new approach represents the hexagonal grid with a pair of rectangular arrays, supporting efficient linear algebra and image processing manipulation. Early results have shown that image processing techniques such as convolution, downsampling, calculating Euclidean distances, and vector arithmetic can be done with no more complexity than is required for processing rectangularly sampled images.