Binary Tomography on Triangular Grid Involving Hexagonal Grid Approach

Abstract

© 2018, Springer Nature Switzerland AG. In this paper, we consider the binary tomography reconstruction problem of images on the triangular grid. The reconstruction process is based on three natural directions of projections, defined by the lane directions of the triangular grid (they are analogous to row and column directions on the square grid). The recently proposed shifted projection approach is applied, which allows that the number of delta and nabla shape triangular pixels in each lane to be exactly determined. The structure of the set of the same type pixels coincides with the structure of the hexagonal grid. The proposed new reconstruction process solve separately the task for the delta and nabla shape pixels on two hexagonal grids. Experimental results on a number of test images is presented and analyzed. The new method shows advantage in both aspects, quality of the reconstructions and running times.