Orientation analysis in second-order stereology
Dept. of Statistics, Charles University, Sokolovská 83, 18600 Prague 8, Czech Republic
Dept. of Mathematics FSI, Czech Technical University, Karlovo nám. 13, 12135 Prague 2, Czech Republic
Abstract
Probability distributions on orientation spaces appear frequently in anisotropic stereology (Philofsky and Hilliard, 1967, Kanatani, 1984). In the present paper special cases of integral transformations where two such distributions appear are studied. One corresponds to the rose of directions of a stationary random process of geometrical objects in R3; the other corresponds to the orientations of probes. In comparison with earlier results (Beneš, 1995; Beneš et al., I995) spherical harmonics are tried to be used for the evaluation. As an application a new formula for the variance of intensity estimator of a Boolean surface process is obtained, based on projections.