Allard-Fraley Estimator of Cluster Feature
Detect high-density features in a spatial point pattern using the (unrestricted) Allard-Fraley estimator.
clusterset(X, result=c("marks", "domain"), ..., verbose=TRUE, fast=FALSE, exact=!fast && spatstat.options("gpclib"))
- A dimensional spatial point pattern (object of class
- Character string specifying the type of result. See Details.
- Logical value indicating whether to print progress reports.
- Logical. If
FALSE(the default), the Dirichlet tile areas will be computed exactly using polygonal geometry, so that the optimal choice of tiles will be computed exactly. If
TRUE, the Dirichlet tile areas will be
- Logical. If
TRUE, the Allard-Fraley estimator of the domain will be computed exactly using polygonal geometry. If
FALSE, the Allard-Fraley estimator of the domain will be approximated by a binary pixel mask. The d
- Optional arguments passed to
as.maskto control the pixel resolution if
Allard and Fraley (1997) developed a technique for recognising features of high density in a spatial point pattern in the presence of random clutter.
This algorithm computes the unrestricted Allard-Fraley estimator.
The Dirichlet (Voronoi) tessellation of the point pattern
computed. The smallest
m Dirichlet cells are selected,
where the number
m is determined by a maximum likelihood
fast=FALSE(the default), the areas of the tiles of the Dirichlet tessellation will be computed exactly using polygonal geometry. This ensures that the optimal selection of tiles is computed exactly.
fast=TRUE, the Dirichlet tile areas will be approximated by counting pixels. This is faster, and is usually correct (depending on the pixel resolution, which is controlled by the arguments
result="marks" the result is the point pattern
with a vector of marks labelling each point with a value
no depending on whether the corresponding Dirichlet cell is
selected by the Allard-Fraley estimator. In other words each point of
X is labelled as either a cluster point or a non-cluster point.
result="domain", the result is the Allard-Fraley estimator
of the cluster feature set, which is the union of all the
selected Dirichlet cells, represented as a window (object of class
exact=TRUE, the Allard-Fraley set estimator will be computed exactly using polygonal geometry. This requires the package
gpclibwhich has a restricted licence: see
licence.polygons. The result is a polygonal window.
exact=FALSE, the Allard-Fraley set estimator will be approximated by a binary pixel mask. This is much faster than the exact computation. The result is a binary mask.
result="marks", a multitype point pattern (object of class
result="domain", a window (object of class
Allard, D. and Fraley, C. (1997) Nonparametric maximum likelihood estimation of features in spatial point processes using Voronoi tessellation. Journal of the American Statistical Association 92, 1485--1493.
opa <- par(mfrow=c(1,2)) W <- grow.rectangle(as.rectangle(letterR), 1) X <- superimpose(runifpoint(300, letterR), runifpoint(50, W), W=W) plot(W, main="clusterset(X)") plot(clusterset(X, fast=TRUE), add=TRUE, chars=c("o", "+"), cols=1:2) plot(letterR, add=TRUE) plot(W, main="clusterset(X, 'd')") plot(clusterset(X, "d", exact=FALSE), add=TRUE) plot(letterR, add=TRUE) par(opa)