# dilation: Compute a morphological dilation of a signal In VPdtw: Variable Penalty Dynamic Time Warping

 dilation R Documentation

## Compute a morphological dilation of a signal

### Description

A dilation is a moving local maximum over a window of specific fixed width specified by span. This dilation is computed first in one direction and then in the other.

### Usage

```dilation(y, span)
```

### Arguments

 `y` signal, a numeric vector `span` the width of the moving window, integer

### Details

A dilation is a method often used in mathematical morphology and image analysis (Soille 1999). This function is for vectors not matrices or images though applying it to rows and columns of a matrix will give the corresponding results.

An erosion of a vector or image can also be computed easily from this by computing the dilation of -1 times the vector and transforming back.

We recommend using a dilation to form a `penalty` for use in `VPdtw`.

### Value

 `res` Dilation of y with width span

David Clifford

### References

Soille, P. Morphological Image Analysis: Principles and Applications; Springer: New York, 1999.

### Examples

```
## Example 1 - dilation of a signal
data(reference)
dref <- dilation(reference,150)
plot(reference,log="y",type="l")
lines(dref,col=2)

## Example 2 - dilation of an image
BIN <- (volcano>177)
dBIN <- t(apply(BIN,1,dilation,span=5))
dBIN <- apply(dBIN,2,dilation,span=5)