sobel_dir — Detect edges (amplitude and direction) using the Sobel operator.
sobel_dir(Image : EdgeAmplitude, EdgeDirection : FilterType, Size : )
sobel_dir 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.)
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_dir(I,Amp,Dir,FilterType,S)
for Size > 3 is conceptually equivalent to
scale_image(I,F,2,0)
gauss_image(F,G,S-2)
sobel_dir(G,Amp,Dir,FilterType,3)
or to
scale_image(I,F,2,0)
binomial_filter(F,G,S[0]-2,S[1]-2)
sobel_dir(G,Amp,Dir,FilterType,3).
The edge directions are returned in EdgeDirection, and
are stored in 2-degree steps, i.e., an edge direction of x
degrees in mathematically positive sense and with respect to the
horizontal axis is stored as x / 2
in the edge direction image. Furthermore, the direction
of the change of intensity is taken into account. Let
denote the image gradient. Then the
following edge directions are returned as r/2:
Points with edge amplitude 0 are assigned the edge direction 255
(undefined direction).
sobel_amp can be executed on OpenCL devices. Note that when using
gaussian filtering for Size > 3, the results can vary from the
CPU implementation.
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 / int2 / uint2 / real)
Input image.
EdgeAmplitude (output_object) (multichannel-)image(-array) → object (byte / int2 / uint2 / real)
Edge amplitude (gradient magnitude) image.
EdgeDirection (output_object) (multichannel-)image(-array) → object (direction)
Edge direction image.
FilterType (input_control) string → (string)
Filter type.
Default value: 'sum_abs'
List of values: 'sum_abs', 'sum_abs_binomial', 'sum_sqrt', 'sum_sqrt_binomial'
List of values (for compute devices): 'sum_abs', 'sum_sqrt', 'sum_abs_binomial', 'sum_sqrt_binomial'
Size (input_control) integer(-array) → (integer)
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_dir(Image,Amp,Dir,'sum_abs',3) threshold(Amp,Edg,128,255)
sobel_dir returns TRUE if all parameters are
correct. If the input is empty the behavior can be set via
set_system('no_object_result',<Result>). If
necessary, an exception is raised.
binomial_filter,
gauss_filter,
mean_image,
anisotropic_diffusion,
sigma_image
nonmax_suppression_dir,
hysteresis_threshold,
threshold
edges_image,
frei_dir,
kirsch_dir,
prewitt_dir,
robinson_dir
roberts,
laplace,
highpass_image,
bandpass_image
Foundation