sharpen {spatstat.explore} | R Documentation |
Data Sharpening of Point Pattern
Description
Performs Choi-Hall data sharpening of a spatial point pattern.
Usage
sharpen(X, ...)
## S3 method for class 'ppp'
sharpen(X, sigma=NULL, ...,
varcov=NULL, edgecorrect=FALSE)
Arguments
X |
A marked point pattern (object of class |
sigma |
Standard deviation of isotropic Gaussian smoothing kernel. |
varcov |
Variance-covariance matrix of anisotropic Gaussian kernel.
Incompatible with |
edgecorrect |
Logical value indicating whether to apply edge effect bias correction. |
... |
Arguments passed to |
Details
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
then the sharpened points are
where is a smoothing kernel in two dimensions.
Thus, the new point
is a
vector average of the nearby points
.
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 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.
Value
A point pattern (object of class "ppp"
) in the same window
as the original pattern X
, and with the same marks as X
.
Author(s)
Adrian Baddeley Adrian.Baddeley@curtin.edu.au, Rolf Turner rolfturner@posteo.net and Ege Rubak rubak@math.aau.dk
References
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.
See Also
Examples
X <- unmark(shapley)
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)