Performs Choi-Hall data sharpening of a spatial point pattern.
sharpen(X, …)
# S3 method for ppp
sharpen(X, sigma=NULL, …,
varcov=NULL, edgecorrect=FALSE)A marked point pattern (object of class "ppp").
Standard deviation of isotropic Gaussian smoothing kernel.
Variance-covariance matrix of anisotropic Gaussian kernel.
Incompatible with sigma.
Logical value indicating whether to apply edge effect bias correction.
Arguments passed to density.ppp
to control the pixel resolution of the result.
A point pattern (object of class "ppp") in the same window
as the original pattern X, and with the same marks as X.
Choi and Hall (2001) proposed a procedure for data sharpening of spatial point patterns. This procedure is appropriate for earthquake epicentres and other point patterns which are believed to exhibit strong concentrations of points along a curve. Data sharpening causes such points to concentrate more tightly along the curve.
If the original data points are \(X_1, \ldots, X_n\) then the sharpened points are $$ \hat X_i = \frac{\sum_j X_j k(X_j-X_i)}{\sum_j k(X_j - X_i)} $$ where \(k\) is a smoothing kernel in two dimensions. Thus, the new point \(\hat X_i\) is a vector average of the nearby points \(X[j]\).
The function sharpen is generic. It currently has only one
method, for two-dimensional point patterns (objects of class
"ppp").
If sigma is given, the smoothing kernel is the
isotropic two-dimensional Gaussian density with standard deviation
sigma in each axis. If varcov is given, the smoothing
kernel is the Gaussian density with variance-covariance matrix
varcov.
The data sharpening procedure tends to cause the point pattern
to contract away from the boundary of the window. That is,
points X_iX[i] that lie `quite close to the edge of the window
of the point pattern tend to be displaced inward.
If edgecorrect=TRUE then the algorithm is modified to
correct this vector bias.
Choi, E. and Hall, P. (2001) Nonparametric analysis of earthquake point-process data. In M. de Gunst, C. Klaassen and A. van der Vaart (eds.) State of the art in probability and statistics: Festschrift for Willem R. van Zwet, Institute of Mathematical Statistics, Beachwood, Ohio. Pages 324--344.
# NOT RUN {
data(shapley)
X <- unmark(shapley)
# }
# NOT RUN {
Y <- sharpen(X, sigma=0.5)
Z <- sharpen(X, sigma=0.5, edgecorrect=TRUE)
opa <- par(mar=rep(0.2, 4))
plot(solist(X, Y, Z), main= " ",
main.panel=c("data", "sharpen", "sharpen, correct"),
pch=".", equal.scales=TRUE, mar.panel=0.2)
par(opa)
# }