Description Usage Arguments Details Value Author(s) See Also Examples

Unfolding the (joint) distribution of planar parameters

1 2 |

`sp` |
section profiles, see |

`nclass` |
number of classes, see details |

`maxIt` |
maximum number of EM iterations |

`nCores` |
number of cpu cores |

`...` |
optional arguments passed to |

This is a S3 method for either trivariate stereological unfolding or estimation of the 3D diameter distribution
of spheres which is better known as the *Wicksell's corpuscle problem*. The function aggregates all intermediate
computations required for the unfolding procedure given the data in the prescribed format, see reference of functions below,
and returning the characteristics as count data in form of a *trivariate* histogram. The section profile objects `sp`

,
see `sectionProfiles`

, are either of class `prolate`

or `oblate`

for the reconstruction of the corresponding
spheroids or, respectively, spheres. The result of the latter is simply a numeric vector of circle diameters. The number of bin
classes for discretization of the underlying integral equations which must be solved is set by the argument `nclass`

.
In case of Wicksell's corpuscle problem (spheres as grains) this is simply a scalar value denoting the number of bins for the diameter.
For spheroids it refers to a vector of length three defined in the order of the number of size, angle and shape class limits which are used.
If `sp`

is a numeric vector (such as for the estimation of the 3D diameter distribution from a 2D section of spheres) the function calls
the EM algorithm as described in [3].
The return value of the function is an object of class "`unfold`

" with elements as follows

N_A (trivariate) histogram of section profile parameters

N_V (trivariate) histogram of reconstructed parameters

P array of coefficients

breaks list of class limits for binning the parameter values

object of class "`unfold`

", see details

M. Baaske

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 | ```
lam <- 100
# parameter rlnorm distribution (radii)
theta <- list("size"=list("meanlog"=-2.5,"sdlog"=0.5))
# simulation bounding box
box <- list("xrange"=c(0,5),"yrange"=c(0,5),"zrange"=c(0,5))
# simulate only 3D system
S <- simPoissonSystem(theta,lam,size="rlnorm",box=box,type="spheres",
perfect=TRUE, pl=1)
# intersect
sp <- planarSection(S,d=2.5,intern=TRUE,pl=1)
# unfolding
ret <- unfold(sp,nclass=25)
cat("Intensities: ", sum(ret$N_V)/25, "vs.",lam,"\n")
``` |

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