Quadrature Scheme Based on Pixel Grid
Makes a quadrature scheme with a dummy point at every pixel of a pixel image.
pixelquad(X, W = as.owin(X))
X |
Point pattern (object of class |
W |
Specifies the pixel grid.
A pixel image (object of class |
This is a method for producing a quadrature scheme
for use by ppm. It is an alternative to
quadscheme.
The function ppm fits a point process model to an
observed point pattern using
the Berman-Turner quadrature approximation (Berman and Turner, 1992;
Baddeley and Turner, 2000) to the pseudolikelihood of the model.
It requires a quadrature scheme consisting of
the original data point pattern, an additional pattern of dummy points,
and a vector of quadrature weights for all these points.
Such quadrature schemes are represented by objects of class
"quad". See quad.object for a description of this class.
Given a grid of pixels, this function creates a quadrature scheme in which there is one dummy point at the centre of each pixel. The counting weights are used (the weight attached to each quadrature point is 1 divided by the number of quadrature points falling in the same pixel).
The argument X specifies the locations of the data points
for the quadrature scheme. Typically this would be a point pattern
dataset.
The argument W specifies the grid of pixels for the dummy
points of the quadrature scheme. It should be a pixel image
(object of class "im"), a window (object of class
"owin"), or anything that can
be converted to a window by as.owin. If W is a
pixel image or a binary mask (a window of type "mask")
then the pixel grid of W will be used. If W is a
rectangular or polygonal window, then it will first be converted to a
binary mask using as.mask at the default pixel
resolution.
An object of class "quad" describing the quadrature scheme
(data points, dummy points, and quadrature weights)
suitable as the argument Q of the function ppm() for
fitting a point process model.
The quadrature scheme can be inspected using the
print and plot methods for objects
of class "quad".
Adrian Baddeley Adrian.Baddeley@curtin.edu.au
and Rolf Turner r.turner@auckland.ac.nz
W <- owin(c(0,1),c(0,1)) X <- runifrect(42, W) W <- as.mask(W,dimyx=128) pixelquad(X,W)
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