Reconstructing h-convex binary images from its horizontal and vertical projections by simulated annealing

Abstract

The field of Discrete Tomography (DT) deals with the reconstruction of 2D discrete images from a few number of their projections. The ideal problem of DT is to reconstruct a binary image from its horizontal and vertical projections. It turns out that this problem of DT is highly underdetermined and therefore it is inevitable to impose additional constraints to this problem. This paper uses the convexity property of binary images and the problem of reconstruction of h-convex binary images from its horizontal and vertical projections is considered here. This problem is transformed into two different optimization problems by defining two appropriate objective functions. Then two simulated annealing (SA) algorithms to solve the two optimization problems are developed. The SA algorithms are tested on various randomly generated test images. The algorithms are also tested on noisy images. Finally numerical results have been reported showing good reconstruction fidelity.