The spatial distribution of discrete sample points from an image affect digital image manipulation. The geometries of the grid lattice and edge are described for digital images. Edge detecting digital filters are considered for segmenting an image. A comparison is developed between digital filters for two different digital image grid lattice geometries — 8-neighbor grid lattice (rectangular tesselation) and the 6-neighbor grid lattice (hexagonal tesselation). Digital filters for discrete images are developed that are best approximations to the Laplacian operator applied to continuous two- dimensional mathematical surfaces. Discrepancies between the calculated Laplacian and the digital filtering results are analyzed and a criterion is developed that compares grid lattice effects. The criterion shows that digital filtering in a 6-neighbor grid lattice is preferable to digital filtering in an 8-neighbor grid lattice. / Master of Science