Geodesic
On set covariance and three-point test sets
Czechoslovak Mathematical Journal, Tome 54 (2004) no. 1, pp. 205-214 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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The information contained in the measure of all shifts of two or three given points contained in an observed compact subset of $\mathbb{R}^d $ is studied. In particular, the connection of the first order directional derivatives of the described characteristic with the oriented and the unoriented normal measure of a set representable as a finite union of sets with positive reach is established. For smooth convex bodies with positive curvatures, the second and the third order directional derivatives of the characteristic is computed.
The information contained in the measure of all shifts of two or three given points contained in an observed compact subset of $\mathbb{R}^d $ is studied. In particular, the connection of the first order directional derivatives of the described characteristic with the oriented and the unoriented normal measure of a set representable as a finite union of sets with positive reach is established. For smooth convex bodies with positive curvatures, the second and the third order directional derivatives of the characteristic is computed.
Classification : 52A22, 60D05
Keywords: convex body; set with positive reach; normal measure; set covariance 
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Rataj, J. On set covariance and three-point test sets. Czechoslovak Mathematical Journal, Tome 54 (2004) no. 1, pp. 205-214. http://geodesic.mathdoc.fr/item/CMJ_2004_54_1_a17/

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