Acta Stereologica



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Jan Rataj

Estimation of oriented normal direction distribution via mixed areas

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An indirect method for the estimation of the area measure of a planar set X from the convex ring is proposed. At first, the mixed area A(X,ﬠ,K) of X with sufficiently enough rotations ﬠ of a chosen convex test set K is estimated by means of the dilation area. Then, the area measure estimate is obtained by solving an integral equation. The estimation bias is discussed and several particular examples are presented.

Keywords : direction distribution, unit outer normal, convex ring, dilation area, mixed area, area measure, estimation variance

To cite this article

Jan Rataj, «Estimation of oriented normal direction distribution via mixed areas», Acta Stereologica [En ligne], Volume 15 (1996), Number 1 - Mathematical foundations of stereology - Feb. 1996, 77-82 URL :

About: Jan Rataj

Mathematical Institute of the Charles University, Sokolovská 83, 186 00 Praha 8, Czech Republic