Convex-Set Perimeter Estimation from Its Two Projections

摘要

This paper addresses the problem of extracting qualitative and quantitative information from few tomographic projections without object reconstruction. It focuses on the extraction of quantitative information, precisely the border perimeter estimation for a convex set from horizontal and vertical projections. In the case of a unique reconstruction, we give conditions and a method for constructing an inscribed polygon in a convex set only from the convex-set projections. An inequality on border perimeter is proved when a convex set in included in another one. The convergence of the polygon perimeter when the ver-tice number increases is established for such polygons. In the case of a multiple reconstruction, lower and upper bounds for the perimeter are exhibited.