Binary tomography on the isometric tessellation involving pixel shape orientation

Abstract

In this study, a tomography reconstruction problem of binary images is considered on the isometric grid. On this grid, the triangle pixels have two types of orientations, accordingly, the authors call them delta or nabla shape pixels. The proposed reconstruction method uses data of projections of three natural directions. They are the lane directions of the triangular tessellation (these directions are somewhat analogous to row/column directions on the rectangular grids). The projection ray, penetrating through a grid lane, now not passing through the middle of pixels (i.e. through the middle line of triangle shape pixels), as usually taken, but little bit shifted from the middle parallel to the lane. This method provides the exact information about the number of nabla and delta shape triangle pixels in each lane of the image. This additional information is included in the reconstruction process to improve the quality of reconstruction. They formulate the suggested model into an energy-minimisation problem and apply a gradient-based approach for its minimisation. They show and analyse various experimental results on test images. The presented approach shows both better quality reconstructions and shorter running time than the earlier approaches.