# roofEdge: Edge detection, denoising and deblurring In DRIP: Discontinuous Regression and Image Processing

## Description

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

## Usage

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

## 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. `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.

## 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}). 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.

## Value

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

## References

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

`roofEdgeParSel`, `roofDiff`
 ``` 1 2 3 4 5 6 7 8 9 10 11``` ```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)) ```