Obtaining Centroids Of Digitized Regions Using Square And Hexagonal Tilings For Photosensitive Elements
Samir R. Chettri, Michael Keefe, John R. Zimmerman · Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE · 1990
In computer vision and graphics, the square or rectangular tessellation is most commonly used. The hexagonal lattice has not been studied as frequently. In this paper we project squares and circles on each of these grids, digitize these figures and obtain the error in locating the centroid. We adopt a Monte Carlo approach, with the centroid of the actual figures being chosen randomly. In the case of the circle, we project various sizes onto the respective grids and study the error in obtaining the centroid. In the case of the square we combine different sizes with angles of rotation that vary from 0 to 90 degrees. Theoretical formulae are developed for the circle on square tile case. These symbolic representations are compared to the results from the Monte Carlo simulation and they are found to be quite close. Finally, comparisons are drawn between the two grids. In the case of the circle, there is a definite advantage in using the hexagonal grid. For the square there is no inherent advantage to either. These results are of use if it is decided to build a camera with hexagonal picture elements.