RECONSTRUCTING CONVEX-BODIES FROM RANDOM PROJECTED IMAGES

被引：1

作者：

SMALL, CG ^{[1
]}

机构：

[1] UNIV WATERLOO,DEPT STAT & ACTUARIAL SCI,WATERLOO N2L 3G1,ONTARIO,CANADA

来源：

CANADIAN JOURNAL OF STATISTICS-REVUE CANADIENNE DE STATISTIQUE | 1991年 / 19卷 / 04期

关键词：

PROJECTION; STEREOMETRY; STEREOLOGY; CONVEX SET; ESTIMATOR; CAUCHY FORMULA; GEOMETRIC PROBABILITY; INTEGRAL GEOMETRY; VOLUME; SURFACE AREA; IMAGE;

D O I：

10.2307/3315425

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

摘要：

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.

引用

页码：341 / 347

页数：7

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