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The problem of reconstructing a binary image (usually rations containing edges and corners. Each Gibbs distribution an image in the plane and not necessarily on a Cartesian grid) from produces a class of images: Randomly selected members of the a few projections translates into the problem of solving a system of class will have certain similarities to each other (e.g., they will equations which is very underdetermined and leads in general to a contain a similar number of objects, which are of similar size large class of solutions. It is desirable to limit the class of possible and convexity) . A sample image from a given Gibbs distribution solutions, by using appropriate prior information, to only those which can be generated using the Metropolis algorithm [4,6] . are reasonably typical of the class of images which contains the unFor images defined on the hexagonal grid, the description of known image that we wish to reconstruct. One may indeed pose the a Gibbs distribution can be done in a straightforward way. In the following hypothesis: If the image is a typical member of a class of hexagonal grid, an image is composed of picture elements of images having a certain distribution, then by using this information hexagonal shape (hexels) . Every hexel has six neighbors and we can limit the class of possible solutions to only those which are close to the given unknown image. This hypothesis is experimentally shares with each of them one side; thus, the abovementioned validated for the specific case of a class of binary images defined configurations consist of the various possible arrangements of the on the hexagonal grid, where the probability of the occurrence of a six black and white neighbors of a black or white hexel. particular image of the class is determined by a Gibbs distribution In our work, the image is defined to be spatially limited to a and reconstruction is to be done from the three natural projections. large hexagonal support, but in principle the image support can q 1998 John Wiley & Sons, Inc. Int J Imaging Syst Technol, 9, 126–131, 1998 be of any shape. The hexagonal grid has three natural projections which are at 607 to each other. A projection is defined as a data set, which for every line (in a set of parallel lines, each of which

Binary tomography on the hexagonal grid using Gibbs priors