**Hexagonal Pixel Arrays**

One of our current image sensor chips, the Hawksbill, supports a 136×136 resolution in a hexagonal array.

The vast majority of image sensor chips available use a square array geometry, in which pixels are arranged in an X-Y square grid, with each pixel belonging to a “row” and a “column”. This standard came about partially because such image sensor chips are easier to design, and partially because the image output can be expressed as a 2D matrix of pixel values, a format convenient for signal processing and linear algebra.

However hexagonal pixel arrays have several advantages over square arrays. First, and most important, hexagonal arrays allow a tighter packing of pixels, for a given pixel pitch, than square arrays. This correlates with the observation that the tightest method of packing spheres (or oranges at a grocer’s stand) is to use a hexagonal array. As a result of this, hexagonal pixel arrays sample the Fourier image space more efficiently than square arrays.

A second advantage of hexagonal pixel arrays is that they have three dominant axes 60 degrees apart, whereas square arrays have only two axes 90 degrees apart. Hexagonal arrays thus have the potential to handle severe warping more elegantly than square arrays. The additional dominant axis can also assist with directional and motion analysis in image processing.

The third benefit will surprise people- for many standard image processing operations, hexagonal arrays are as computationally efficient, and in many cases even more efficient, than square arrays. Much of this was made possible by recent mathematical advances in the representation of hexagonal arrays, in particular Array Set Addressing (ASA) which makes processing of hexagonal array images almost as conceptually easy as processing square array images. Indeed, operations such as computing a fast Fourier transform (FFT) and edge detection are in fact faster per pixel over hexagonal arrays than square ones.

For those interested in exploring hexagonal image acquisition and processing, we encourage using the Hawksbill chip for your research activities.