On set covariance and three-point test sets

Rataj, Jan. "On set covariance and three-point test sets." Czechoslovak Mathematical Journal 54.1 (2004): 205-214. <http://eudml.org/doc/30850>.

@article{Rataj2004,
abstract = {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.},
author = {Rataj, Jan},
journal = {Czechoslovak Mathematical Journal},
keywords = {convex body; set with positive reach; normal measure; set covariance; convex body; set with positive reach; normal measure; set covariance},
language = {eng},
number = {1},
pages = {205-214},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {On set covariance and three-point test sets},
url = {http://eudml.org/doc/30850},
volume = {54},
year = {2004},
}

TY - JOUR
AU - Rataj, Jan
TI - On set covariance and three-point test sets
JO - Czechoslovak Mathematical Journal
PY - 2004
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 54
IS - 1
SP - 205
EP - 214
AB - 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.
LA - eng
KW - convex body; set with positive reach; normal measure; set covariance; convex body; set with positive reach; normal measure; set covariance
UR - http://eudml.org/doc/30850
ER -