sobel_dirSobelDirSobelDirsobel_dirsobel_dir🔗

Short description🔗

sobel_dirSobelDirSobelDirsobel_dirsobel_dir — Detect edges (amplitude and direction) using the Sobel operator.

Signature🔗

sobel_dir( image Image, out image EdgeAmplitude, out image EdgeDirection, string FilterType, integer Size )

Description🔗

sobel_dirSobelDir 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'"sum_sqrt": \(\sqrt{a^2 + b^2} / 4\)
'sum_abs'"sum_abs": \((| a | + | b |) / 4\)

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_imageGaussImage) or a binomial filter (see binomial_filterBinomialFilter) of size Sizesizesize-2. The Gaussian filter is selected for the above values of FilterTypefilterTypefilter_type. Here, Sizesizesize = 5, 7, 9, 11, or 13 must be used. The binomial filter is selected by appending '_binomial'"_binomial" to the above values of FilterTypefilterTypefilter_type. Here, Sizesizesize 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 Sizesizesize. Here, the first value of Sizesizesize 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 Sizesizesize \(>\) 33 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 EdgeDirectionedgeDirectionedge_direction, 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 \([E_{x},E_{y}]\) denote the image gradient. Then the following edge directions \(r\) are returned as \(r/2\):

intensity increase	\(E_x / E_y\)	edge direction \(r\) [deg]
from bottom to top	0 / +	0
from lower right to upper left	- / +	]0,90[
from right to left	- / 0	90
from upper right to lower left	- / -	]90,180[
from top to bottom	0 / -	180
from upper left to lower right	+ / -	]180,270[
from left to right	+ / 0	270
from lower left to upper right	+ / +	]270,360[.

Points with edge amplitude 0 are assigned the edge direction 255 (undefined direction).

sobel_ampSobelAmp can be executed on OpenCL devices. Note that when using Gaussian filtering for Sizesizesize \(>\) 3, the results can vary from the CPU implementation.

Attention🔗

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.

Execution information🔗

Execution information

Supports OpenCL compute devices.
Multithreading type: reentrant (runs in parallel with non-exclusive operators).
Multithreading scope: global (may be called from any thread).
Automatically parallelized on tuple level.
Automatically parallelized on channel level.
Automatically parallelized on domain level.

Parameters🔗

Imageimageimage (input_object) (multichannel-)image(-array) → object (byte / int2 / uint2 / real)HObject (byte / int2 / uint2 / real)HImage (byte / int2 / uint2 / real)HObject (byte / int2 / uint2 / real)Hobject (byte / int2 / uint2 / real)

Input image.

EdgeAmplitudeedgeAmplitudeedge_amplitude (output_object) (multichannel-)image(-array) → object (byte / int2 / uint2 / real)HObject (byte / int2 / uint2 / real)HImage (byte / int2 / uint2 / real)HObject (byte / int2 / uint2 / real)Hobject * (byte / int2 / uint2 / real)

Edge amplitude (gradient magnitude) image.

EdgeDirectionedgeDirectionedge_direction (output_object) (multichannel-)image(-array) → object (direction)HObject (direction)HImage (direction)HObject (direction)Hobject * (direction)

Edge direction image.

FilterTypefilterTypefilter_type (input_control) string → (string)HTuple (HString)HTuple (string)strHtuple (char*)

Filter type.

Default: 'sum_abs'"sum_abs"
List of values: 'sum_abs', 'sum_abs_binomial', 'sum_sqrt', 'sum_sqrt_binomial'
List of values (for compute devices): 'sum_abs', 'sum_abs_binomial', 'sum_sqrt', 'sum_sqrt_binomial'

Sizesizesize (input_control) integer(-array) → (integer)HTuple (Hlong)HTuple (int / long)MaybeSequence[int]Htuple (Hlong)

Size of filter mask.

Default: 33
List of values: 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 33, 35, 37, 39

Example🔗

(HDevelop)

read_image(Image,'fabrik')
sobel_dir(Image,Amp,Dir,'sum_abs',3)
threshold(Amp,Edg,128,255)

(C)

read_image(&Image,"fabrik")\;
sobel_dir(Image,&Amp,&Dir,"sum_abs",3)\;
threshold(Amp,&Edg,128.0,255.0)\;

Result🔗

sobel_dirSobelDir returns 2 (H_MSG_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.

Combinations with other operators🔗

Combinations

Possible predecessors

binomial_filterBinomialFilter, gauss_filterGaussFilter, mean_imageMeanImage, anisotropic_diffusionAnisotropicDiffusion, sigma_imageSigmaImage

Possible successors

nonmax_suppression_dirNonmaxSuppressionDir, hysteresis_thresholdHysteresisThreshold, thresholdThreshold

Alternatives

edges_imageEdgesImage, frei_dirFreiDir, kirsch_dirKirschDir, prewitt_dirPrewittDir, robinson_dirRobinsonDir

Module🔗

Foundation