It has been known since the early 1960s that hexagonal sampling is the optimal sampling approach for isotropically band-limited images, providing a 13.4% improvement in sampling efficiency over rectangular sampling.

Two potential hexagonal RedGreenBlue (RGB) display geometries.

Despite the advantages of hexagonal sampling, rectangular sampling is still used for virtually all digital imaging applications. Part of the reason is that rectangular sampling leads to nice rectangular arrays that are easy to process and store on digital computers, whereas hexagonal sampling does not.

Several addressing approaches have been developed over the years to try to remedy this, but none have matched the efficiency and convenience of a rectangular array. Simply put, no prior efficient addressing method for hexagonal grids has been developed. For example, none of the prior art methods support efficient linear algebra and image processing manipulation. As a result, the processing overhead required to deal with addressing hexagonal sensor arrays or grids has thus far out-weighed the advantages gained by sampling hexagonally.

There is, therefore, a need for a new method for addressing hexagonally arranged image sensors that produces an output that can be efficiently computationally manipulated, particularly in digital systems.

Such a method has been developed. The patented invention, called array set addressing (ASA), solves the problems for any hexagonally arranged data sampling elements.

A primary concept behind ASA is that a hexagonal grid can be represented as a set of two rectangular arrays distinguished by a single binary coordinate. What's particularly new in the present invention is extending that concept and applying it to addressing captured information from a hexagonal grid of image sensor pixels. The hexagonal grid has greater angular resolution, equidistant spacing, and a higher degree of symmetry than rectangular grids. Also, since all neighboring pixels in a hexagonal grid share a side, there is no connectivity ambiguity as there is with rectangular grids, which leads to more efficient algorithms that deal with connectivity.

For more information, contact Dr. Brian Metzger, Senior Technology Manager, at This email address is being protected from spambots. You need JavaScript enabled to view it.; 406-994-7782.

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This article first appeared in the August, 2019 issue of Tech Briefs Magazine.

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