Data Sharpening of Point Pattern
Performs Choi-Hall data sharpening of a spatial point pattern.
sharpen(X, ...)
## S3 method for class 'ppp'
sharpen(X, sigma=NULL, ...,
varcov=NULL, edgecorrect=FALSE)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 |
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],..., X[n] then the sharpened points are
X^[i] = (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 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.
A point pattern (object of class "ppp") in the same window
as the original pattern X, and with the same marks as X.
Adrian Baddeley Adrian.Baddeley@curtin.edu.au, Rolf Turner r.turner@auckland.ac.nz and Ege Rubak rubak@math.aau.dk
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.
data(shapley)
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)Please choose more modern alternatives, such as Google Chrome or Mozilla Firefox.