Polygonal estimation of planar convex-set perimeter from its two projections |
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Authors: | Étienne Baudrier Mohamed Tajine Alain Daurat |
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Institution: | 1. Laboratoire des Sciences de l’Image, de l’Informatique et de la Télédétection, Illkirch, France;2. University of Strasbourg, Strasbourg, France;3. Centre National de la Recherche Scientifique, UMR 7005, Illkirch, France |
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Abstract: | This paper deals with the problem of extracting qualitative and quantitative information from few tomographic projections of an object without reconstructing this object. 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 multiple reconstruction, lower and upper bounds for the perimeter are established. 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 is included in another one. The convergence of the polygon perimeter, when the number of vertices increases, is established for such polygons. |
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Keywords: | Perimeter estimation Convex set Tomography Two projections Polygonal reconstruction |
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