Kernel Smoothed Intensity of Point Pattern

Compute a kernel smoothed intensity function from a point pattern.

methods, smooth, spatial
## S3 method for class 'ppp':
density(x, sigma, \dots, weights, edge=TRUE, varcov=NULL)
Point pattern (object of class "ppp") to be smoothed.
Standard deviation of isotropic Gaussian smoothing kernel.
Optional vector of weights to be attached to the points. May include negative values.
Arguments passed to as.mask to determine the pixel resolution.
Logical flag: if TRUE, apply edge correction.
Variance-covariance matrix of anisotropic Gaussian kernel. Incompatible with sigma.

This is a method for the generic function density. A kernel estimate of the intensity function of the point pattern is computed (Diggle, 1985). The result is the convolution of the isotropic Gaussian kernel of standard deviation sigma with point masses at each of the data points. The default is to assign a unit weight to each point. If weights is present, the point masses have these weights (which may be signed real numbers).

If edge=TRUE, the intensity estimate is corrected for edge effect bias by dividing it by the convolution of the Gaussian kernel with the window of observation.

Instead of the isotropic Gaussian kernel with standard deviation sigma, the smoothing kernel may be chosen to be any Gaussian kernel, by giving the variance-covariance matrix varcov. The arguments sigma and varcov are incompatible. Also sigma may be a vector of length 2 giving the standard deviations of two independent Gaussian coordinates, thus equivalent to varcov = diag(sigma^2). Computation is performed using the Fast Fourier Transform. Accuracy depends on the pixel resolution, controlled by the arguments ... passed to as.mask.

To perform spatial interpolation of values that were observed at the points of a point pattern, use smooth.ppp.


  • A pixel image (object of class "im").


The result of density.ppp is not a probability density! It is an estimate of the intensity function of the underlying point process. The integral of this function over the window is not equal to 1; it equals the expected number of points falling in the window.


Diggle, P.J. (1985) A kernel method for smoothing point process data. Applied Statistics (Journal of the Royal Statistical Society, Series C) 34 (1985) 138--147.

Diggle, P.J. (2003) Statistical analysis of spatial point patterns, Second edition. Arnold.

See Also

smooth.ppp, ppp.object, im.object

  • density.ppp
  Z <- density.ppp(cells, 0.05)
Documentation reproduced from package spatstat, version 1.13-1, License: GPL (>= 2)

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