roofDiff | R Documentation |

Compute difference between two one-sided gradient estimators.

roofDiff(image, bandwidth, blur)

`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. |

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

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}*).

Returns a matrix where each entry is the maximum of the
differences: *|\widehat{f}_{x+} - \widehat{f}_{x-}|* and
*|\widehat{f}_{y+} - \widehat{f}_{y-}|* at each pixel.

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

`roofEdgeParSel`

, `roofEdge`

data(peppers) #diff = roofDiff(image = peppers, bandwidth = 8) # Time consuming

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