Quantization error in spatial sampling: comparison between square and hexagonal pixels

Square and hexagonal spatial samplings, because of their processing ease, are used most widely in image and signal processing. The authors develop mathematical tools for estimating quantization error in hexagonal sensory configurations. These include analytic expressions for the average error and the error distribution of a function of an arbitrarily large number of hexagonally quantized variables. The two quantities (the average error and the error distribution) are essential in assessing the reliability of a given algorithm. The corresponding expressions for square spatial sampling are presented for comparison; they can be used to determine which sampling technique would result in less quantization error for a particular algorithm. Such a comparison is important due to the paramount role that quantization error plays in computational approaches to computer vision. Some general observations in regard to the relative accuracy of hexagonal vs. square quantization are also presented