Convex-set perimeter estimation from its two projections

Authors:
Étienne Baudrier;Mohamed Tajine;Alain Daurat
Affiliations:
Laboratoire des Sciences de l'Image, de l'Informatique et de la Télédétection, University of Strasbourg, Strasbourg, France;Laboratoire des Sciences de l'Image, de l'Informatique et de la Télédétection, University of Strasbourg, Strasbourg, France;Laboratoire des Sciences de l'Image, de l'Informatique et de la Télédétection, University of Strasbourg, Strasbourg, France
Venue:
IWCIA'11 Proceedings of the 14th international conference on Combinatorial image analysis
Year:
2011

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Abstract

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 vertice number increases is established for such polygons. In the case of a multiple reconstruction, lower and upper bounds for the perimeter are exhibited.