Integral of a Pixel Image

Computes the integral of a pixel image.

spatial, math
Usage, ...)
A pixel image (object of class "im") with pixel values that can be treated as numeric or complex values.

This function treats the pixel image x 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 x 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).

For more complicated integration tasks such as computing the integral of an image over a specified subset, use to construct an integrand or [.im to extract a subset of the image.


  • A single numeric or complex value.

See Also, [.im

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

   D <- density(cells)
   # 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))
   DW <- D[W, drop=FALSE]
Documentation reproduced from package spatstat, version 1.19-2, License: GPL (>= 2)

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