stepDiff | R Documentation |

Compute difference between two one-sided local kernel estimates along the gradient direction.

```
stepDiff(image, bandwidth, degree = 1, blur = FALSE, plot = FALSE)
```

`image` |
A square matrix, no missing value allowed. |

`bandwidth` |
A positive integer that specifies the number of pixels to use in the local smoothing. |

`degree` |
An integer equal to 0 for local constant kernel smoothing or 1 for local linear kernel smoothing. The default value is 1. |

`blur` |
If blur = TRUE, in addition to a conventional 2-D kernel function, a 1-D kernel is used in local smoothing to address the issue of blur. The default value is FALSE. |

`plot` |
If plot = TRUE, an image of the detection statistics at each pixel is plotted. |

At each pixel, the gradient is estimated by a local linear
kernel smoothing procedure. Next, the local neighborhood is
divided into two halves along the direction perpendicular to
(`\widehat{f}'_{x}`

, `\widehat{f}'_{y}`

). Then the one-
sided local kernel estimates are obtained in the two half
neighborhoods respectively.

A matrix of the estimated difference, `|\widehat{f}_+ - \widehat{f}_-|`

,
at each pixel.

Kang, Y. and Qiu, P. (2014) "Jump Detection in Blurred Regression
Surfaces," *Technometrics*, **56**(4), 539 – 550,
\Sexpr[results=rd]{tools:::Rd_expr_doi("10.1080/00401706.2013.844732")}.

`roofDiff`

```
data(sar) # SAR image is bundled with the package and it is a
# standard test image in statistics literature.
diff <- stepDiff(image = sar, bandwidth = 4, degree = 0)
```

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