Compute a MSE approximation for volume predictors. The structure of
interest is an isotropic 3D random compact set. The sampling device is a
uniform random lattice of figures (point patterns, line segments,
sections...). The approximation depends only on sampling parameters
and on the mean surface (to be provided) of the structure.
Usage
vol.mse(x, S = 1, L = 3)
Arguments
x
a lattice of figures, object of class FigLat-class.
S
the mean surface. Default: 1.
L
an integer, the criterion for stopping summation of the
Epstein zeta function. Argument of the function Ezeta. Default: 3.
Value
The MSE approximation as a numeric.
References
Kieu, K. and Mora, M. (2005). Stereological estimation of mean
volume: precision of three sampling designs. Technical report 2005-1,
Unite de Mathematiques et informatique appliquees,
INRA. http://www.inra.fr/bia/J/nosdoc/rapport_miaj_2005_1.pdf.
See Also
area.mse, dvol.mse.
Examples
# Sampling by a unit cubic point lattice
vol.mse(FigLat(3,VecLat(diag(3)),PointPattern(rep(0,3))))
# Sampling by serial sections
vol.mse(FigLat(3,VecLat(c(0,0,1)),PointPattern(rep(0,3)),lmat=rbind(diag(2),rep(0,2))))