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_i
X[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) # }