sobel_dir ( Image : EdgeAmplitude, EdgeDirection : FilterType, Size : )

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

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 und b denote the results of convolving an image with A und B for one particular pixel.) 'sum_sqrt' sqrt(a^2 + b^2) 'sum_abs' (|a| + |b|) / 2 For a Sobel operator with size 3x3, the corresponding filters A and B are applied directly, while for larger filter sizes (Size = 5,7,9 and 11) the input image is first smoothed using a Gaussian filter of size Size-2. Therefore,
     sobel_dir(I:Amp,Dir:FilterType,S)

for Size > 3 is equivalent to

     gauss__(I:G:S-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 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 [Ex,Ey] denote the image gradient. Then the following edge directions are returned as r/2:
intensity increase                     Ex / Ey        edge direction r

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).


Parameters

Image (input_object)
image(-array) -> object : byte
Input image.

EdgeAmplitude (output_object)
image(-array) -> object : byte
Edge amplitude (gradient magnitude) image.

EdgeDirection (output_object)
image(-array) -> object : direction
Edge direction image.

FilterType (input_control)
string -> string
Filter type.
Default value: 'sum_abs'
List of values: 'sum_abs', 'sum_sqrt'

Size (input_control)
integer -> integer
Size of filter mask.
Default value: 3
List of values: 3, 5, 7, 9, 11, 13


Example
read_image(:Image:'fabrik':) >
sobel_dir(Image:Amp,Dir:'sum_abs',3:) >
threshold__(Amp:Edg:128,255:).

Result

sobel_dir returns 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.


Possible Predecessors

gauss__, mean__, anisotrope_diff__, sigma__


Possible Successors

nonmax_suppression_dir, hysteresis_threshold__, threshold__


Alternatives

edges__, frei_dir, kirsch_dir, prewitt_dir, robinson_dir


See also

roberts__, laplace__, highpass__, bandpass__



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