# integral.im

From spatstat v1.21-0
by Adrian Baddeley

##### Integral of a Pixel Image

Computes the integral of a pixel image.

##### Usage

`integral.im(x, ...)`

##### Arguments

- x
- A pixel image (object of class
`"im"`

) with pixel values that can be treated as numeric or complex values. - ...
- Ignored.

##### Details

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 `eval.im`

to
construct an integrand or `[.im`

to extract a subset of
the image.

##### Value

- A single numeric or complex value.

##### See Also

##### 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
data(cells)
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))
DW <- D[W, drop=FALSE]
integral.im(DW)
```

*Documentation reproduced from package spatstat, version 1.21-0, License: GPL (>= 2)*

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