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sobel_amp — Detect edges (amplitude) using the Sobel operator.
sobel_amp(Image : EdgeAmplitude : FilterType, Size : )
sobel_amp calculates first derivative of an image and is used as an edge detector. The filter is based on the following filter masks:
A =
1 2 1
0 0 0
-1 -2 -1
B =
1 0 -1
2 0 -2
1 0 -1
These masks are used differently, according to the selected filter type. (In the following, a and b denote the results of convolving an image with A and B for one particular pixel.)
'sum_sqrt' sqrt(a^2 + b^2) / 4
'sum_abs' (|a| + |b|) / 4
'thin_sum_abs' (thin(|a|) + thin(|b|)) / 4
'thin_max_abs' max(thin(|a|),thin(|b|)) / 4
'x' b / 4
'y' a / 4
Here, thin(x) is equal to x for a vertical maximum (mask A) and a horizontal maximum (mask B), respectively, and 0 otherwise. Thus, for 'thin_sum_abs' and 'thin_max_abs' the gradient image is thinned. For the filter types 'x' and 'y' if the input image is of type byte the output image is of type int1, of type int2 otherwise. For a Sobel operator with size 3x3, the corresponding filters A and B are applied directly, while for larger filter sizes the input image is first smoothed using a Gaussian filter (see gauss_image) or a binomial filter (see binomial_filter) of size Size-2. The Gaussian filter is selected for the above values of FilterType. Here, Size = 5, 7, 9, 11, or 13 must be used. The binomial filter is selected by appending '_binomial' to the above values of FilterType. Here, Size can be selected between 5 and 39. Furthermore, it is possible to select different amounts of smoothing the column and row direction by passing two values in Size. Here, the first value of Size corresponds to the mask width (smoothing in the column direction), while the second value corresponds to the mask height (smoothing in the row direction) of the binomial filter. The binomial filter can only be used for images of type byte, uint2 and real. Since smoothing reduces the edge amplitudes, in this case the edge amplitudes are multiplied by a factor of 2 to prevent information loss. Therefore,
sobel_amp(I,E,FilterType,S)
for Size > 3 is conceptually equivalent to
scale_image(I,F,2,0)
gauss_image(F,G,S-2)
sobel_amp(G,E,FilterType,3)
or to
scale_image(I,F,2,0)
binomial_filter(F,G,S[0]-2,S[1]-2)
sobel_amp(G,E,FilterType,3).
For sobel_amp special optimizations are implemented FilterType = 'sum_abs' that use SIMD technology. The actual application of these special optimizations is controlled by the system parameter 'mmx_enable' (see set_system). If 'mmx_enable' is set to 'true' (and the SIMD instruction set is available), the internal calculations are performed using SIMD technology. Note that SIMD technology performs best on large, compact input regions. Depending on the input region and the capabilities of the hardware the execution of sobel_amp might even take significantly more time with SIMD technology than without.
sobel_amp can be executed on OpenCL devices for the filter types 'sum_abs', 'sum_sqrt', 'x' and 'y' (as well as their binomial variants). Note that when using gaussian filtering for Size > 3, the results can vary from the CPU implementation.
Input image.
Edge amplitude (gradient magnitude) image.
Filter type.
Default value: 'sum_abs'
List of values: 'sum_abs', 'thin_sum_abs', 'thin_max_abs', 'sum_sqrt', 'x', 'y', 'sum_abs_binomial', 'thin_sum_abs_binomial', 'thin_max_abs_binomial', 'sum_sqrt_binomial', 'x_binomial', 'y_binomial'
List of values (for compute devices): 'sum_abs', 'sum_sqrt', 'x', 'y', 'sum_abs_binomial', 'sum_sqrt_binomial', 'x_binomial', 'y_binomial'
Size of filter mask.
Default value: 3
List of values: 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 33, 35, 37, 39
read_image(Image,'fabrik') sobel_amp(Image,Amp,'sum_abs',3) threshold(Amp,Edg,128,255)
sobel_amp returns 2 (H_MSG_TRUE) if all parameters are correct. If the input is empty the behaviour can be set via set_system('no_object_result',<Result>). If necessary, an exception is raised.
binomial_filter, gauss_image, mean_image, anisotropic_diffusion, sigma_image
threshold, nonmax_suppression_amp, gray_skeleton
frei_amp, roberts, kirsch_amp, prewitt_amp, robinson_amp
laplace, highpass_image, bandpass_image
Foundation
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