Three Dimensional Image Processing in Hexagonal Prism Lattice of Z3 Grid

Abstract

A 2D hexagonal image is an array of what are called pixels which are the coordinates of the hexagonal lattice points decided by the linear horizontal rows and the nonlinear vertical zig-zags. A 2D hexagonal image could also be informally called as image slice or a matrix of pixel values arranged in a hexagonal array. A 3D hexagonal image is viewed as an ordered sequence of 2D hexagonal image slices arranged in the z-direction and the 3D arrangement of voxel values is called as a prism of voxel values. Most of the 3D hexagonal image processing operations are similar to those of 2D hexagonal image processing. 3D hexagonal images are processed with the help of 3D hexagonal scanning windows, whereas 2D hexagonal images are processed with the help of 2D hexagonal scanning windows. For instance, a 3D hexagonal image processing operation like 3D surface detection is carried out using analogous 2D edge detection algorithm on every image slice and the processed slices assembled to visualize 3D surface detected image. In fact, 2D contours of an image slice are called superficial features and closed surfaces of a 3D image are called volumetric features. One can always obtain surface detected version of a 3D hexagonal image by processing the 2D hexagonal image slices using 2D edge detection operation, and consequently the 3D surface detection operation is termed as 2.5D hexagonal image processing. One could also process the 3D hexagonal image data using a 3D surface detection algorithm, in which case it is termed as 3D hexagonal image processing. This is not the case with the operation of skeltonization. One cannot make use of 2.5D skeletonization operation of 2D image slices in order to get skeltonized version of the corresponding 3D image. In fact, one would come across discrepancies and differences when 2.5D skeletonization of 2D hexagonal image slices of a 3D hexagonal image is carried out instead of the direct 3D skeletonization of the 3D hexagonal image. This paper highlights certain 3D algorithms for processing 3D hexagonal images.