Comparison of square-pixel and hexagonal-pixel resolution in image processing

In most image processing applications, data is collected and displayed in square pixels. Hexagonal pixels offer the advantage of greater rotational symmetry, a close packed structure and a nearly circular pixel. We compared the quality of images using square pixels with that of images employing hexagonal pixels. The comparison was done using various images, each considering a different aspect of geometry (i.e., lines at different angles, curves, etc). The square pixel images were constructed using the average of a square area of smaller square pixels. Hexagonal pixel images were constructed using two techniques. The first one was called the "two-template approach", wherein two different templates were used to create a close packed hexagonal image from smaller square pixels. The second approach was called the "six-neighbor approach"; it creates a rectangular template using the six neighbors of a hexagonal pixel. A Euclidean distance measure was used to compare the square pixel and hexagonal pixel images. A brief explanation of the algorithm and the results are provided. Based on our results obtained using the Euclidean distance as a quality measure, we conclude that, contrary to our intuition and their widespread use in nature (retinas and ommatidia), hexagonal pixels do not offer any advantage over conventional square pixels.