Performs Choi-Hall data sharpening of a spatial point pattern.

```
sharpen(X, …)
# S3 method for ppp
sharpen(X, sigma=NULL, …,
varcov=NULL, edgecorrect=FALSE)
```

X

A marked point pattern (object of class `"ppp"`

).

sigma

Standard deviation of isotropic Gaussian smoothing kernel.

varcov

Variance-covariance matrix of anisotropic Gaussian kernel.
Incompatible with `sigma`

.

edgecorrect

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) # }