integral.im: Integral of a Pixel Image

In spatstat.geom: Geometrical Functionality of the 'spatstat' Family

Integral of a Pixel Image

Description

Computes the integral of a pixel image.

Usage

## S3 method for class 'im'
integral(f, domain=NULL, weight=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.
weight	Optional. A pixel image (object of class "im") or a function(x,y) giving a numerical weight to be applied to the integration.

Details

The function integral is generic, with methods for spatial objects ("im", "msr", "linim", "linfun") and one-dimensional functions ("density", "fv").

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.

If weight is given, it should be a pixel image or a function of coordinates x and y returning numerical values. Then each pixel value of f will be multiplied by the corresponding value of weight. Effectively, the result is the integral of weight * f.

Value

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

Author(s)

\spatstatAuthors

.

See Also

integral, 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(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(Z, W)

   # weighted integral
   integral(Z, weight=function(x,y){x})

spatstat.geom documentation built on Nov. 5, 2025, 6:49 p.m.