# integral.im

0th

Percentile

##### Integral of a Pixel Image

Computes the integral of a pixel image.

Keywords
spatial, math
##### Usage
integral(f, domain=NULL, …)# S3 method for 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).

eval.im, [.im

• integral
• integral.im
##### Examples
# NOT RUN {
# 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)

D <- density(cells)
integral.im(D)
# should be approximately equal to number of points = 42

# 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(D, W)
# }

Documentation reproduced from package spatstat, version 1.62-2, License: GPL (>= 2)

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