# integral.im

##### Integral of a Pixel Image

Computes the integral of a pixel image.

##### Usage

`integral(f, domain=NULL, ...)`## S3 method for class 'im':
integral(f, domain=NULL, \dots)

##### 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).

##### 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
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 1.42-2, License: GPL (>= 2)*