# rotmean

##### Rotational Average of a Pixel Image

Compute the average pixel value over all rotations of the image about the origin, as a function of distance from the origin.

##### Usage

`rotmean(X, ..., origin, padzero=TRUE, Xname, result=c("fv", "im"))`

##### Arguments

- X
- A pixel image.
- ...
- Ignored.
- origin
- Optional. Origin about which the rotations should be performed.
Either a numeric vector or a character string as described
in the help for
`shift.owin`

. - padzero
- Logical. If
`TRUE`

(the default), the value of`X`

is assumed to be zero outside the window of`X`

. If`FALSE`

, the value of`X`

is taken to be undefined outside the window of`X`

- Xname
- Optional name for
`X`

to be used in the function labels. - result
- Character string specifying the kind of result required: either a function object or a pixel image.

##### Details

This command computes, for each possible distance $r$, the average pixel value of the pixels lying at distance $r$ from the origin. Kernel smoothing is used to obtain a smooth function of $r$.

If `result="fv"`

(the default) the result is a function
object of class `"fv"`

giving the mean pixel value of `X`

as a function of distance from the origin.

If `result="im"`

the result is a pixel image, with the same
dimensions as `X`

, giving the mean value of `X`

over all pixels lying at the same distance from the origin
as the current pixel.

If `padzero=TRUE`

(the default), the value of `X`

is assumed to be zero outside the window of `X`

. The rotational
mean at a given distance $r$ is the average value of the image
`X`

over the *entire* circle of radius $r$,
including zero values outside the window if the circle
lies partly outside the window.
If `padzero=FALSE`

, the value of `X`

is taken to be
undefined outside the window of `X`

. The rotational mean
is the average of the `X`

values over the *subset* of the circle
of radius $r$ that lies entirely inside the window.

##### Value

- An object of class
`"fv"`

or`"im"`

.

##### Examples

```
if(interactive()) {
Z <- setcov(square(1))
plot(rotmean(Z))
plot(rotmean(Z, result="im"))
} else {
Z <- setcov(square(1), dimyx=32)
f <- rotmean(Z)
}
```

*Documentation reproduced from package spatstat, version 1.42-2, License: GPL (>= 2)*