An Algorithm for the Reconstruction of hv-convex Planar Bodies by Finitely Many and Noisy Measurements of their Coordinate X-rays

作者：Vincze Csaba^*; Nagy Abris

来源：Fundamenta Informaticae, 2015, 141(2-3): 169-189.

DOI：10.3233/FI-2015-1270

Parallel X-rays are functions that measure the intersection of a given set with lines parallel to a fixed direction in R-2. The reconstruction problem concerning parallel X-rays is to reconstruct the set if the parallel X-rays into some directions are given. There are several algorithms to give an approximate solution of this problem. In general we need some additional knowledge on the object to obtain a unique solution. By assuming convexity a suitable finite number of directions is enough for all convex planar bodies to be uniquely determined by their X-rays in these directions [13]. Gardner and Kiderlen [12] presented an algorithm for reconstructing convex planar bodies from noisy X-ray measurements belonging to four directions. For a reconstruction algorithm assuming convexity we can also refer to [17]. An algorithm for the reconstruction of hv-convex planar sets by their coordinate X-rays (two directions) can be found in [18]: given the coordinate X-rays of a compact connected hv-convex planar set K the algorithm gives a sequence of polyominoes L-n all of whose accumulation points (with respect to the Hausdorff metric) have the given coordinate X-rays almost everywhere. If the set is uniquely determined by the coordinate X-rays then L-n tends to the solution of the problem. This algorithm is based on generalized conic functions measuring the average taxicab distance by integration [21]. Now we would like to give an extension of this algorithm that works in the case when only some measurements of the coordinate X-rays are given. Following the idea in [12] we extend the algorithm for noisy X-ray measurements too.

• 出版日期2015