# roofDiff: roof/valley edge detection In DRIP: Discontinuous Regression and Image Processing

## Description

Compute difference between two one-sided gradient estimators.

## Usage

 `1` ``` roofDiff(image, bandwidth, blur) ```

## Arguments

 `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.

## Details

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}).

## Value

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.

## References

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

`roofEdgeParSel`, `roofEdge`
 ```1 2``` ``` data(peppers) #diff = roofDiff(image = peppers, bandwidth = 8) # Time consuming ```