DRIP (version 2.0)

roofEdge: Roof Edge Detector

Description

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

Usage

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

Value

A matrix of zeros and ones of the same size as the input image.

Arguments

image

A square matrix, no missing value allowed.

bandwidth

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

thresh

Threshold value to use in the edge detection criterion.

edge1

A square matrix representing the image's step edges. The function excludes step edges when detects roof 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 perpendicular to (\(\widehat{f}''_{xy}\), \(\widehat{f}''_{yy}\)). 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 threshold and there is no step edge pixels in the neighborhood.

References

Qiu, P. and Kang, Y. (2015) ``Blind Image Deblurring Using Jump Regression Analysis'', Statistica Sinica, 25, 879 -- 899, tools:::Rd_expr_doi("10.5705/ss.2014.054").

See Also

roofEdgeParSel, roofDiff

Examples

data(peppers)
if (FALSE) {
step.edges <- stepEdge(peppers, bandwidth = 6, thresh = 25, degree = 1)
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))
}