unfold: Stereological unfolding
In unfoldr: Stereological Unfolding for Spheroidal Particles

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

Unfolding the (joint) distribution of planar parameters

1	unfold(sp, nclass, maxIt = 64, nCores = getOption("par.unfoldr", 2L), ...)

`sp`	section profiles, see `sectionProfiles`
`nclass`	number of classes, see details
`maxIt`	maximum number of EM iterations
`nCores`	number of cpu cores
`...`	optional arguments passed to `setbreaks`

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

setbreaks, binning3d

 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")