| roofDiff {DRIP} | R Documentation |
Roof Edge Detection Statistics
Description
Compute the difference between two one-sided gradient estimates.
Usage
roofDiff(image, bandwidth, blur)
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. |
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 perpendicular to (\widehat{f}''_{xy},
\widehat{f}''_{yy}).
Value
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 location.
References
Qiu, P. and Kang, Y. (2015) "Blind Image Deblurring Using Jump Regression Analysis", Statistica Sinica, 25, 879 – 899, doi:10.5705/ss.2014.054.
See Also
Examples
data(peppers)
diff <- roofDiff(image = peppers, bandwidth = 8) # Time consuming