edges_image — Extract edges using Deriche, Lanser, Shen, or Canny filters.
edges_image detects step edges using recursively implemented
filters (according to Deriche, Lanser and Shen) or the
conventionally implemented “derivative of Gaussian” filter (using
filter masks) proposed by Canny. Furthermore, a very fast variant
of the Sobel filter can be used. Thus, the following edge operators
are available:
'deriche1', 'lanser1', 'deriche1_int4', 'deriche2', 'lanser2', 'deriche2_int4', 'shen', 'mshen', 'canny', and 'sobel_fast'
(parameter Filter).
The edge amplitudes (gradient magnitude) are returned in
ImaAmp.
For all filters except 'sobel_fast', the edge directions
are returned in ImaDir. For 'sobel_fast', the
edge direction is not computed to speed up the filter.
Consequently, ImaDir is an empty image object.
The edge operators 'deriche1' respectively 'deriche2' are
also available for int4-images, and return the signed filter response instead
of its absolute value. This behavior can be obtained for byte-images as
well by selecting 'deriche1_int4' respectively
'deriche2_int4' as filter.
This can be used to calculate the second derivative of an image by
applying edges_image (with parameter value 'lanser2') to the
signed first derivative. Edge directions 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).
The “filter width” (i.e., the amount of smoothing) can be chosen
arbitrarily for all filters except 'sobel_fast' (where the
filter width is 3x3 and Alpha is
ignored), and can be estimated by calling info_edges for
concrete values of the parameter Alpha. It decreases for
increasing Alpha for the Deriche, Lanser and Shen filters
and increases for the Canny filter, where it is the standard
deviation of the Gaussian on which the Canny operator is based.
“Wide” filters exhibit a larger invariance to noise, but also a
decreased ability to detect small details. Non-recursive filters,
such as the Canny filter, are realized using filter masks, and thus
the execution time increases for increasing filter width. In
contrast, the execution time for recursive filters does not depend
on the filter width. Thus, arbitrary filter widths are possible
using the Deriche, Lanser and Shen filters without increasing the
run time of the operator. The resulting advantage in speed compared
to the Canny operator naturally increases for larger filter widths.
As border treatment, the recursive operators assume that the images
to be zero outside of the image, while the Canny operator repeats
the gray value at the image's border. The signal-noise-ratio of the
filters is comparable for the following choices of Alpha:
Alpha('lanser1') = Alpha('deriche1'),
Alpha('deriche2') = Alpha('deriche1') / 2,
Alpha('lanser2') = Alpha('deriche2'),
Alpha('shen') = Alpha('deriche1') / 2,
Alpha('mshen') = Alpha('shen'),
Alpha('canny') = 1.77 / Alpha('deriche1').
The originally proposed recursive filters
('deriche1', 'deriche2', 'shen') return a biased
estimate of the amplitude of diagonal edges.
This bias is removed in the corresponding modified version
of the operators
('lanser1', 'lanser2' and 'mshen'),
while maintaining the same execution speed.
For relatively small filter widths (11 x 11),
i.e., for
Alpha('lanser2') = 0.5,
all filters yield similar results.
Only for “wider” filters differences begin to appear:
the Shen filters begin to yield qualitatively inferior results.
However, they are the fastest of the implemented operators ---
closely followed by the Deriche operators.
edges_image optionally offers to apply a
non-maximum-suppression
(NMS = 'nms'/'inms'/'hvnms';
'none'
if not desired) and hysteresis threshold operation
(Low,High; at least one negative if not
desired) to the resulting edge image.
Conceptually, this corresponds to the following calls:
Note that the hysteresis threshold operation is not applied
if NMS is set to 'none'.
For 'sobel_fast', the same non-maximum-suppression is
performed for all values of NMS except 'none'.
Additionally, for 'sobel_fast' the resulting edges are
thinned to a width of one pixel.
edges_image can be executed on OpenCL devices for the filter
types 'canny' and 'sobel_fast'.
The OpenCL implementation of edges_image will generally compute
results that differ somewhat from the CPU implementation.
Since edges_image uses Gauss convolution internally for the
'canny' filter, the same limitations for OpenCL apply as for
derivate_gauss: Alpha must be chosen small enough that
the required filter mask is less than 129 pixels in size.
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) singlechannelimage(-array) → object (byte / uint2 / int4 / real)
Input image.
ImaAmp (output_object) (multichannel-)image(-array) → object (byte / uint2 / int4 / real)
Edge amplitude (gradient magnitude) image.
ImaDir (output_object) image(-array) → object (direction)
Edge direction image.
Filter (input_control) string → (string)
Edge operator to be applied.
Default value: 'canny'
List of values: 'canny', 'deriche1', 'deriche1_int4', 'deriche2', 'deriche2_int4', 'lanser1', 'lanser2', 'mshen', 'shen', 'sobel_fast'
List of values (for compute devices): 'canny', 'sobel_fast'
Alpha (input_control) real → (real)
Filter parameter: small values result in strong smoothing, and thus less detail (opposite for 'canny').
Default value: 1.0
Suggested values: 0.1, 0.2, 0.3, 0.4, 0.5, 0.7, 0.9, 1.1
Typical range of values: 0.2
≤
Alpha
≤
50.0
Minimum increment: 0.01
Recommended increment: 0.1
Restriction: Alpha > 0.0
NMS (input_control) string → (string)
Non-maximum suppression ('none', if not desired).
Default value: 'nms'
List of values: 'hvnms', 'inms', 'nms', 'none'
Low (input_control) integer → (integer / real)
Lower threshold for the hysteresis threshold operation (negative, if no thresholding is desired).
Default value: 20
Suggested values: 5, 10, 15, 20, 25, 30, 40
Typical range of values: 1
≤
Low
≤
255
Minimum increment: 1
Recommended increment: 5
Restriction: Low > 1 || Low < 0
High (input_control) integer → (integer / real)
Upper threshold for the hysteresis threshold operation (negative, if no thresholding is desired).
Default value: 40
Suggested values: 10, 15, 20, 25, 30, 40, 50, 60, 70
Typical range of values: 1
≤
High
≤
255
Minimum increment: 1
Recommended increment: 5
Restriction: High > 1 || High < 0 && High >= Low
read_image(Image,'fabrik') edges_image(Image,Amp,Dir,'lanser2',0.5,'none',-1,-1) hysteresis_threshold(Amp,Margin,20,30,30)
edges_image returns TRUE if all parameters are correct
and no error occurs during execution. If the input is empty the
behavior can be set via
set_system('no_object_result',<Result>). If
necessary, an exception is raised.
threshold,
hysteresis_threshold,
close_edges_length
sobel_dir,
frei_dir,
kirsch_dir,
prewitt_dir,
robinson_dir
info_edges,
nonmax_suppression_amp,
hysteresis_threshold,
bandpass_image
S.Lanser, W.Eckstein: “Eine Modifikation des Deriche-Verfahrens zur
Kantendetektion”; 13. DAGM-Symposium, München; Informatik
Fachberichte 290; Seite 151 - 158; Springer-Verlag; 1991.
S.Lanser: “Detektion von Stufenkanten mittels rekursiver Filter
nach Deriche”; Diplomarbeit; Technische Universität München,
Institut für Informatik, Lehrstuhl Prof. Radig; 1991.
J.Canny: “Finding Edges and Lines in Images”; Report, AI-TR-720;
M.I.T. Artificial Intelligence Lab., Cambridge; 1983.
J.Canny: “A Computational Approach to Edge Detection”; IEEE
Transactions on Pattern Analysis and Machine Intelligence; PAMI-8,
vol. 6; S. 679-698; 1986.
R.Deriche: “Using Canny's Criteria to Derive a Recursively
Implemented Optimal Edge Detector”; International Journal of
Computer Vision; vol. 1, no. 2; S. 167-187; 1987.
R.Deriche: “Optimal Edge Detection Using Recursive Filtering”;
Proc. of the First International Conference on Computer Vision,
London; S. 501-505; 1987.
R.Deriche: “Fast Algorithms for Low-Level Vision”; IEEE
Transactions on Pattern Analysis and Machine Intelligence; PAMI-12,
no. 1; S. 78-87; 1990.
S.Castan, J.Zhao und J.Shen: “Optimal Filter for Edge Detection
Methods and Results”; Proc. of the First European Conference on
Computer Vision, Antibes; Lecture Notes on computer Science;
no. 427; S. 12-17; Springer-Verlag; 1990.
Foundation