coxmap: Identify Dense and Sparse Regions in a Point Pattern

In spatstat.explore: Exploratory Data Analysis for the 'spatstat' Family

Identify Dense and Sparse Regions in a Point Pattern

Description

Given a point pattern, classify the spatial domain into regions where the pattern is dense, sparse, or neither.

Usage

coxmap(X, ...)

## S3 method for class 'ppp'
coxmap(X, n, alpha=0.05, ...)

Arguments

X	A point pattern (object of class "ppp").
n	Maximum number of neighbours to consider. An integer greater than 1.
alpha	Threshold for upper and lower quantiles. A number strictly between 0 and 1.
...	Additional arguments passed to as.mask to determine the pixel resolution.

Details

T. F. Cox (1979) proposed a method for identifying dense and sparse regions in a forest stand.

Each spatial location u is classified as belonging to the “clumped” region if T_n(u) < d_n, or belonging to the “sparse” region if T_n(u) > c_n, and otherwise belonging to neither the clumped nor the sparse regions. Here d_n,c_n are constants depending on n and alpha, and T_n(u) is the statistic

T_n(u) = b_2 + b_1 \overline\lambda \pi \sum_{k=1}^n R_k(u)^2

where b_1,b_2 are constants depending on n, \overline\lambda is the estimated intensity (number of points of X divided by area of the window of X), and R_k(u) is the distance from u to the k-th nearest point of X.

This function evaluates T_n(u) at each pixel location u in a grid, and classifies each pixel as belonging to the clumped, sparse or intermediate regions. The result is a pixel image with categorical values giving the classification.

Value

A pixel image (object of class "im") with factor values, with possible levels clumped, sparse and neither.

Author(s)

\adrian

.

References

Cox, T.F. (1979) A method for mapping the dense and sparse regions of a forest stand. Applied Statistics 28, 14–19.

See Also

nnclean, distmap, nnmap, quantess

Examples

   plot(coxmap(redwoodfull, 5))
   points(redwoodfull, col="white", cex=0.5)

spatstat.explore documentation built on March 22, 2026, 5:06 p.m.