Computes the integral of a pixel image.
integral(f, domain=NULL, ...)# S3 method for im
integral(f, domain=NULL, weight=NULL, ...)
A single numeric or complex value (or a vector of such values
if domain is a tessellation).
A pixel image (object of class "im") with pixel values
that can be treated as numeric or complex values.
Optional. Window specifying the domain of integration. Alternatively a tessellation.
Ignored.
Optional. A pixel image (object of class "im")
or a function(x,y) giving a numerical weight
to be applied to the integration.
Adrian Baddeley Adrian.Baddeley@curtin.edu.au, Rolf Turner r.turner@auckland.ac.nz and Ege Rubak rubak@math.aau.dk.
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.
If weight is given, it should be a pixel image or a function of
coordinates f
will be multiplied by the corresponding value of weight.
Effectively, the result is the integral of weight * f.
eval.im,
[.im
# 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})
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