## DESCRIPTION

v.kernel generates a raster density map from vector points data using a moving kernel. Available kernel density functions are uniform, triangular, epanechnikov, quartic, triweight, gaussian, cosine, default is gaussian.

The module can also generate a vector density map on a vector network. Conventional kernel functions produce biased estimates by overestimating the densities around network nodes, whereas the equal split method of Okabe et al. (2009) produces unbiased density estimates. The equal split method uses the kernel function selected with the kernel option and can be enabled with node=split.

## NOTES

The multiplier option is needed to overcome the limitation that the resulting density in case of a vector map output is stored as category (integer). The density result stored as category may be multiplied by this number.

For the gaussian kernel, standard deviation for the gaussian function is set to 1/4 of the radius.

With the -o flag (experimental) the command tries to calculate an optimal radius. The value of radius is taken as maximum value. The radius is calculated based on the gaussian function, using ALL points, not just those in the current region.

## EXAMPLES

Compute density of points (using vector map of schools from North Carolina sample dataset):

    g.region region=wake_30m
    v.kernel input=schools_wake output=schools_density radius=5000 multiplier=1000000
    r.colors map=schools_density color=bcyr

School density

## KNOWN ISSUES

The module only considers the presence of points, but not (yet) any attribute values.

## REFERENCES

- Okabe, A., Satoh, T., Sugihara, K. (2009). A kernel density estimation method for networks, its computational method and a GIS-based tool. International Journal of Geographical Information Science, Vol 23(1), pp. 7-32.
  DOI: 10.1080/13658810802475491

## SEE ALSO

v.surf.rst

Overview: Interpolation and Resampling in GRASS GIS

## AUTHORS

Stefano Menegon, ITC-irst, Trento, Italy
Radim Blazek (additional kernel density functions and network part)

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