Dense Projection Tomography on the Triangular Tiling

Abstract

In this paper, we consider the binary tomography reconstruction problem. A new approach is proposed what exploits a possibility provided by the natural structure of the triangular grid, which is not available in the case of the classical square grid. In contrast to the square grid, in the case of the triangular grid information need for the reconstruction of the unknown image is increasing when not only one, but two projections are used by lanes. In this way, the number of Δ and ∇ shaped pixels per lane can be determined. We propose this type of projection approach and call it dense projections. The reconstruction is based on three projection directions by the lane directions of the grid (they are analogous to row and column directions on the square grid). Our algorithm is deterministic and uses energy minimization technique to find (near) optimal solution in a reasonable time. The experimental evaluation of the new method, using regular hexagon shaped test images, is given. Comparison with reconstructions based on the square grid is also considered.