Discrete Tomography on the Triangular Grid based on Ryser's Results

Abstract

In this paper, we consider a binary hexagonal shape image on a triangular grid, with three projections along the three natural directions of the considered coordinate system. We propose an algorithm based on Ryser's theory for reconstructing the original image. In a nutshell, the first step of the reconstruction provides an image that has errorless projection values for two directions applying Ryser's method for these two directions. Then the image and its projection values are turned to be better by using traditional switching pairs (for the rectangular case) without worsening the projection data for the original two directions, but increasing the quality by having better fit projection data for the third direction.