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.
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Christopher G. Small (1991) studied this question.
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