shock_filter — Apply a shock filter to an image.
shock_filter(Image : SharpenedImage : Theta, Iterations, Mode, Sigma : )
The operator shock_filter applies a shock filter to the
input image Image to sharpen the edges contained in it.
The principle of the shock filter is based on the transport of the
gray values of the image towards an edge from both sides through
dilation and erosion and satisfies the differential equation
on the function u defined by the gray values in Image at
a time . The discretized equation is solved
in Iterations time steps of length Theta, so that
the output image SharpenedImage contains the gray value
function at the time .
The decision between dilation and erosion is made using the sign
function s with values {-1,0,+1} on a
conventional edge detector. The detector of Canny
is available with Mode='canny' and the detector
of Marr/Hildreth (the Laplace operator)
can be selected by Mode='laplace'.
To make the edge detection more robust, in particular on noisy
images, it can be performed on a smoothed image matrix. This is done
by giving the standard deviation of a Gaussian kernel for
convolution with the image matrix in the parameter Sigma.
Note that filter operators may return unexpected results if an image with a reduced domain is used as input. Please refer to the chapter Filters.
Image (input_object) (multichannel-)image(-array) → object (byte / uint2 / real)
Input image.
SharpenedImage (output_object) image(-array) → object (byte / uint2 / real)
Output image.
Theta (input_control) real → (real)
Time step.
Default: 0.5
Suggested values: 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7
Restriction:
0 < Theta <= 0.7
Iterations (input_control) integer → (integer)
Number of iterations.
Default: 10
Suggested values: 1, 3, 10, 100
Restriction:
Iterations >= 1
Mode (input_control) string → (string)
Type of edge detector.
Default: 'canny'
List of values: 'canny', 'laplace'
Sigma (input_control) real → (real)
Smoothing of edge detector.
Default: 1.0
Suggested values: 0.0, 0.5, 1.0, 2.0, 5.0
Restriction:
Theta >= 0
F. Guichard, J. Morel; “A Note on Two Classical Shock Filters and
Their Asymptotics”; Michael Kerckhove (Ed.): Scale-Space and
Morphology in Computer Vision, LNCS 2106, pp. 75-84; Springer, New
York; 2001.
G. Aubert, P. Kornprobst; “Mathematical Problems in Image
Processing”; Applied Mathematical Sciences 147; Springer, New
York; 2002.
Foundation