# convolve.im

##### Convolution of Pixel Images

Computes the convolution of two pixel images.

##### Usage

`convolve.im(X, Y=X, …, reflectX=FALSE, reflectY=FALSE)`

##### Arguments

- X
A pixel image (object of class

`"im"`

.- Y
Optional. Another pixel image.

- …
Ignored.

- reflectX,reflectY
Logical values specifying whether the images

`X`

and`Y`

(respectively) should be reflected in the origin before computing the convolution.

##### Details

The *convolution* of two pixel images \(X\) and \(Y\) in the plane
is the function \(C(v)\) defined for each vector \(v\) as
$$
C(v) = \int X(u)Y(v-u)\, {\rm d}u
$$
where the integral is
over all spatial locations \(u\), and where \(X(u)\) and
\(Y(u)\) denote the pixel values of \(X\) and \(Y\) respectively
at location \(u\).

This command computes a discretised approximation to
the convolution, using the Fast Fourier Transform.
The return value is
another pixel image (object of class `"im"`

) whose greyscale values
are values of the convolution.

If `reflectX = TRUE`

then the pixel image `X`

is reflected
in the origin (see `reflect`

)
before the convolution is computed, so that
`convolve.im(X,Y,reflectX=TRUE)`

is mathematically
equivalent to `convolve.im(reflect(X), Y)`

. (These two commands
are not exactly equivalent, because the reflection is performed
in the Fourier domain in the first command, and reflection is
performed in the spatial domain in the second command).

Similarly if `reflectY = TRUE`

then the pixel image `Y`

is reflected
in the origin before the convolution is computed, so that
`convolve.im(X,Y,reflectY=TRUE)`

is mathematically
equivalent to `convolve.im(X, reflect(Y))`

.

##### Value

A pixel image (an object of class `"im"`

) representing the
convolution of `X`

and `Y`

.

##### See Also

##### Examples

```
# NOT RUN {
X <- as.im(letterR)
Y <- as.im(square(1))
plot(convolve.im(X, Y))
plot(convolve.im(X, Y, reflectX=TRUE))
plot(convolve.im(X))
# }
```

*Documentation reproduced from package spatstat, version 1.59-0, License: GPL (>= 2)*