R: Quadrature Scheme Based on Pixel Grid

pixelquad {spatstat.geom} | R Documentation

## Quadrature Scheme Based on Pixel Grid

### Description

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

### 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"`.

### Author(s)

Adrian Baddeley Adrian.Baddeley@curtin.edu.au

and Rolf Turner r.turner@auckland.ac.nz

### See Also

`quadscheme`, `quad.object`, `ppm`

### Examples

      W <- owin(c(0,1),c(0,1))
      X <- runifrect(42, W)
      W <- as.mask(W,dimyx=128)
      pixelquad(X,W)

[Package spatstat.geom version 2.2-0 Index]