Comparison of three hexagonal tessellations through extraction of blood cell geometric features

Although image data are almost universally acquired on rectangular sampling lattices, the regular hexagonal lattice offers important theoretical advantages for tessellation of images, particularly when subsequent processing involves operations on local image neighborhoods. The few systems capable of processing hexagonally tessellated images have approximated this tessellation by using image data acquired on a rectangular sampling lattice, from which six of the eight image samples were selected from each local neighborhood. This paper describes a simple method of directly acquiring image data in hexagonal image tessellations; the method is used to compare at constant sampling density the most common of these approximating image tessellations with both a nonregular and a regular hexagonal image tessellation. The test objects were human blood cells, from which features describing cellular geometry were extracted for each image tessellation. Compared to the approximating tessellation, the nonregular tessellation tended to decrease feature means and increase feature variances. In contrast, the regular tessellation tended to increase feature means and decrease feature variances. Consequently, the extracted features showed subtle but consistent differences, with decreasing anisotropic effects and data dispersion for the regular tessellation. In addition, cells contacting others near the 45 degree diagonals were more readily segmented when the image was tessellated on the regular lattice. Expected to be general, these trends recommend use of the regular tessellation, especially when classification accuracy may depend on small differences in several similar geometric features.