roofEdge | R Documentation |

Detect roof/valley edges in an image using piecewise local linear kernel smoothing.

`roofEdge(image, bandwidth, thresh, edge1, blur, plot)`

`image` |
A square matrix object of size n by n, no missing value allowed. |

`bandwidth` |
A positive integer to specify the number of pixels used in the local smoothing. |

`thresh` |
Threshold value used in the edge detection criterion. |

`edge1` |
Step edges. The function excludes step edges when detects roof/valley edges. |

`blur` |
If blur = TRUE, besides the conventional 2-D kernel function, a univariate kernel function is used in the local smoothing to address the issue of blur. |

`plot` |
If plot = TRUE, an image of detected edges is plotted. |

At each pixel, the second-order derivarives (i.e., `f''_{xx}`

,
`f''_{xy}`

, and `f''_{yy}`

) are estimated by
a local quadratic kernel smoothing procedure. Next, the local
neighborhood is first divided into two halves along the direction
perpendicular to (`\widehat{f}''_{xx}`

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

). Then the
one-sided estimates of `f'_{x+}`

and `f'_{x-}`

are obtained
respectively by local linear kernel smoothing. The estimates of
`f'_{y+}`

and `f'_{y-}`

are obtained by the same procedure
except that the neighborhood is divided along the direction
(`\widehat{f}''_{xy}`

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

). The pixel is
flagged as a roof/valley edge pixel if ```
max(|\widehat{f}_{x+} - \widehat{f}_{x-}|,
|\widehat{f}_{y+} - \widehat{f}_{y-}|)>
```

the specified thresh and there is
no step edge pixels in the neighborhood.

Returns a matrix of zeros and ones of the same size as image.

Qiu, P., and Kang, Y. "Blind Image Deblurring Using Jump Regression
Analysis," *Statistica Sinica*, **25**, 2015, 879-899.

`roofEdgeParSel`

, `roofDiff`

```
data(peppers)
# Not run
#step.edges <- stepEdgeLLK(peppers, bandwidth=6, thresh=25, plot=FALSE)
#roof.edges <- roofEdge(image=peppers, bandwidth=9, thresh=3000, edge1=step.edges,
# blur=FALSE, plot=FALSE) # Time consuming
#edges = step.edges + roof.edges
#par(mfrow=c(2,2))
#image(1-step.edges, col=gray(0:1))
#image(1-roof.edges, col=gray(0:1))
#image(1-edges, col=gray(0:1))
#image(peppers, col=gray(c(0:255)/255))
```

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