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Reconstructing convex bodies from random projected images
Author(s) -
Small Christopher G.
Publication year - 1991
Publication title -
canadian journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.804
H-Index - 51
eISSN - 1708-945X
pISSN - 0319-5724
DOI - 10.2307/3315425
Subject(s) - convex body , mathematics , combinatorics , regular polygon , convex set , cauchy distribution , convergence (economics) , convex optimization , geometry , mathematical analysis , economics , economic growth
We consider the problem of reconstructing a convex body from samples of lower‐dimensional projections, or shadows. Such problems have been studied using mean cross‐sectional measures of convex sets. We develop new methods based upon inner and outer estimates of the convex body, for which rates of convergence are obtained. These asymptotic results for the inner and outer estimates are compared with each other as well as those based upon Cauchy's formula.