Dense Projection Tomography on the Triangular Tiling
What is it about?
Binary tomography is about reconstruction of images from sums of pixel values (e.g., in rows). On the triangular grid there are three natural directions, that are the directions of the sides of the triangle pixels (we call these directions lane directions). In this paper we use the dense projection approach. By the geometry of the triangular grid, by having two projection rays instead of only one, some extra information is gained about the image. There are two different orientations of the pixels in this grid. The number of pixels with value 1 can easily be determined for each type of pixels in a lane. This extra information gives better reconstruction results in our energy minimization approach than similar algorithm using only one projection ray by a lane.
Why is it important?
By geometry of the triangular grid we gain some extra information that can efficiently be used in reconstruction of binary images. This fact shows that, in some cases, applying a non traditional grid, the scenario is changing so that new ideas (that do not work on the traditional square grid) could lead to better solutions.