R: Integral of a Pixel Image

integral.im {spatstat.geom} | R Documentation

## Integral of a Pixel Image

### Description

Computes the integral of a pixel image.

### Usage

    integral(f, domain=NULL, ...)

    ## S3 method for class 'im'
    integral(f, domain=NULL, ...)

### Arguments

`f` | A pixel image (object of class `"im"`) with pixel values that can be treated as numeric or complex values.
`domain` | Optional. Window specifying the domain of integration. Alternatively a tessellation.
`...` | Ignored.

### Details

The function `integral` is generic, with methods for `"im"`, `"msr"`, `"linim"` and `"linfun"`.

The method `integral.im` treats the pixel image `f` as a function of the spatial coordinates, and computes its integral. The integral is calculated by summing the pixel values and multiplying by the area of one pixel.

The pixel values of `f` may be numeric, integer, logical or complex. They cannot be factor or character values.

The logical values `TRUE` and `FALSE` are converted to `1` and `0` respectively, so that the integral of a logical image is the total area of the `TRUE` pixels, in the same units as `unitname(x)`.

If `domain` is a window (class `"owin"`) then the integration will be restricted to this window. If `domain` is a tessellation (class `"tess"`) then the integral of `f` in each tile of `domain` will be computed.

### Value

A single numeric or complex value (or a vector of such values if `domain` is a tessellation).

### Author(s)

Adrian Baddeley Adrian.Baddeley@curtin.edu.au, Rolf Turner r.turner@auckland.ac.nz and Ege Rubak rubak@math.aau.dk.

### See Also

`eval.im`, `[.im`

### Examples

       # approximate integral of f(x,y) dx dy
       f <- function(x,y){3*x^2 + 2*y}
       Z <- as.im(f, square(1))
       integral.im(Z)
       # correct answer is 2

       # integrate over the subset [0.1,0.9] x [0.2,0.8]
       W <- owin(c(0.1,0.9), c(0.2,0.8))
       integral.im(Z, W)

[Package spatstat.geom version 2.3-2 Index]