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##### Quadrature Scheme Based on Pixel Grid

Makes a quadrature scheme with a dummy point at every pixel of a pixel image.

Keywords
spatial, datagen
##### Usage
pixelquad(X, W = as.owin(X))
##### Arguments
X

Point pattern (object of class "ppp") containing the data points for the quadrature scheme.

W

Specifies the pixel grid. 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.

##### Details

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.

##### Value

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".

quadscheme, quad.object, ppm

##### Aliases
# NOT RUN {