# sharpen

##### Data Sharpening of Point Pattern

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

- Keywords
- spatial, nonparametric

##### 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
`"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.

##### 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
$X_1, \ldots, X_n$
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.

##### Value

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

) in the same window as the original pattern`X`

, and with the same marks as`X`

.

##### 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

```
data(shapley)
X <- unmark(shapley)
if(!(interactive())) X <- rthin(X, 0.05)
Y <- sharpen(X, sigma=0.5)
```

*Documentation reproduced from package spatstat, version 1.21-0, License: GPL (>= 2)*