R: Data Sharpening of Point Pattern

sharpen {spatstat} | 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 `"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],..., 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_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`.

### Author(s)

Adrian Baddeley Adrian.Baddeley@curtin.edu.au, Rolf Turner r.turner@auckland.ac.nz 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

`density.ppp`, `Smooth.ppp`.

### Examples

       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)

[Package spatstat version 1.54-0 Index]