lines_gauss — Detect lines and their width.
lines_gauss(Image : Lines : Sigma, Low, High, LightDark, ExtractWidth, LineModel, CompleteJunctions : )
The operator lines_gauss can be used to extract lines
(curvilinear structures) from the image Image. The
extracted lines are returned in Lines as subpixel precise
XLD-contours. The parameter LightDark determines, whether
bright or dark lines are extracted. If ExtractWidth is set
to 'true' the line width is extracted for each line point.
If LineModel is set to a value different from
'none', lines_gauss compensates the effect of
asymmetrical lines (lines having different contrast on each side of
the line), and corrects the position and width of the line. The
line model used for the correction can be selected with
LineModel as bar-shaped lines (LineModel =
'bar-shaped'), parabolic lines (LineModel =
'parabolic'), and Gaussian lines (LineModel =
'gaussian'). Bar-shaped lines are the right choice for
most applications. If backlit tubular objects (e.g., blood vessels
in X-ray images) should be extracted, the other two modes can be
used. The parabolic line model should be used in applications where
the lines appear very sharp. The Gaussian line model should be used
in applications where the lines appear less sharp. The parameter
LineModel is only meaningful if
ExtractWidth='true'. Because the line extractor
is unable to extract certain junctions because of differential
geometric reasons, it tries to extract these by different means if
CompleteJunctions is set to 'true'.
The extraction is done by using partial derivatives of a Gaussian
smoothing kernel to determine the parameters of a quadratic
polynomial in x and y for each point of the image. The parameter
Sigma determines the amount of smoothing to be performed.
Larger values of Sigma lead to a larger smoothing of the
image, but can lead to worse localization of the line. Generally,
the localization will be much better than that of lines returned by
lines_facet with comparable parameters. The parameters of
the polynomial are used to calculate the line direction for each
pixel. Pixels which exhibit a local maximum in the second
directional derivative perpendicular to the line direction are
marked as line points. The line points found in this manner are
then linked to contours. This is done by immediately accepting line
points that have a second derivative larger than High.
Points that have a second derivative smaller than Low are
rejected. All other line points are accepted if they are connected
to accepted points by a connected path. This is similar to a
hysteresis threshold operation with infinite path length (see
hysteresis_threshold). However, this function is not used
internally since it does not allow the extraction of subpixel
precise contours.
For the choice of the thresholds High and Low
one has to keep in mind that the second directional derivative
depends on the amplitude and width of the line as well as the choice
of Sigma. The value of the second derivative depends
linearly on the amplitude, i.e., the larger the amplitude, the
larger the response. For the width of the line there is an
approximately inverse exponential dependence: The wider the line is,
the smaller the response gets. This holds analogously for the
dependence on Sigma: The larger Sigma is
chosen, the smaller the second derivative will be. This means that
for larger smoothing correspondingly smaller values for
High and Low have to be chosen. Two examples
help to illustrate this: If 5 pixel wide lines with an amplitude
larger than 100 are to be extracted from an image with a smoothing
of Sigma = 1.5, High should be chosen larger
than 14. If, on the other hand, 10 pixel wide lines with an
amplitude larger than 100 and a Sigma = 3 are to be
detected, High should be chosen larger than 3.5. For the
choice of Low values between 0.25 High and 0.5
High are appropriate.
The parameters Low and High can be calculated from
the respective gray value contrast of the lines to be extracted
(ContrastLow and ContrastHigh) and from the chosen value for
Sigma with the following formula:
The extracted lines are returned in a topologically sound data
structure in Lines. This means that lines are correctly
split at junction points.
lines_gauss defines the following attributes for each
line point if ExtractWidth was set to 'false':
The angle of the direction perpendicular to the line
The magnitude of the second derivative
If ExtractWidth was set to 'true', the following
attributes are defined in addition to 'angle' and
'response':
The line width to the left of the line
The line width to the right of the line
If ExtractWidth was set to 'true' and
LineModel to a value different from 'none', the
following attributes are defined in addition to 'angle',
'response', 'width_left', and
'width_right':
The asymmetry of the line point
The contrast of the line point
Here, the asymmetry is positive if the asymmetric part, i.e., the part with the weaker gradient, is on the right side of the line, while it is negative if the asymmetric part is on the left side of the line.
The contrast results from the difference between the gray value
of the line and the gray value of the background.
The contrast is positive if bright lines are extracted, while it
is negative if dark lines are extracted.
The returned contrast may be larger than the maximum gray value the input
image type is able to represent, especially if the line model specified by
LineModel is not present in the image. For example, for byte images,
the contrast may be greater than 255.
Use get_contour_attrib_xld to obtain attribute values.
See the operator reference of get_contour_attrib_xld for further
information about contour attributes.
lines_gauss can be executed on OpenCL devices.
In general, but in particular if the line width is to be extracted,
should be selected, where w is the width (half the diameter) of
the lines in the image. As the lowest allowable value
must be selected. If, for example, lines with a width of
4 pixels (diameter 8 pixels) are to be extracted, should be selected. Note that the
attributes 'width_left', 'width_right',
'asymmetry', and 'contrast' are set to zero if
Sigma is set too low.
lines_gauss uses a special implementation that is optimized
using SSE2 instructions if the system parameter
'sse2_enable' is set to 'true' (which is default
if SSE2 is available on your machine). This implementation is
slightly inaccurate compared to the pure C version due to numerical
issues. If you prefer accuracy over performance you can set
'sse2_enable' to 'false' (using
set_system) before you call lines_gauss. This way
lines_gauss does not use SSE2 accelerations. Don't forget
to set 'sse2_enable' back to 'true' afterwards.
When lines_gauss is run on OpenCL devices, the same limitations
apply as for derivate_gauss: Sigma must be chosen so that
the required filter mask is smaller than 129 pixels. Also note that the
results can vary compared to 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.
This operator supports cancelling timeouts and interrupts.
Image (input_object) singlechannelimage → object (byte / int1 / int2 / uint2 / int4 / real)
Input image.
Lines (output_object) xld_cont-array → object
Extracted lines.
Sigma (input_control) number → (real / integer)
Amount of Gaussian smoothing to be applied.
Default value: 1.5
Suggested values: 1, 1.2, 1.5, 1.8, 2, 2.5, 3, 4, 5
Typical range of values: 0.7
≤
Sigma
≤
20
Recommended increment: 0.1
Low (input_control) number → (real / integer)
Lower threshold for the hysteresis threshold operation.
Default value: 3
Suggested values: 0, 0.5, 1, 2, 3, 4, 5, 8, 10
Typical range of values: 0
≤
Low
≤
20
Recommended increment: 0.5
Restriction: Low >= 0
High (input_control) number → (real / integer)
Upper threshold for the hysteresis threshold operation.
Default value: 8
Suggested values: 0, 0.5, 1, 2, 3, 4, 5, 8, 10, 12, 15, 18, 20, 25
Typical range of values: 0
≤
High
≤
35
Recommended increment: 0.5
Restriction: High >= 0 && High >= Low
LightDark (input_control) string → (string)
Extract bright or dark lines.
Default value: 'light'
List of values: 'dark', 'light'
ExtractWidth (input_control) string → (string)
Should the line width be extracted?
Default value: 'true'
List of values: 'false', 'true'
LineModel (input_control) string → (string)
Line model used to correct the line position and width.
Default value: 'bar-shaped'
List of values: 'bar-shaped', 'gaussian', 'none', 'parabolic'
CompleteJunctions (input_control) string → (string)
Should junctions be added where they cannot be extracted?
Default value: 'true'
List of values: 'false', 'true'
* Detection of lines in an aerial image read_image(Image,'mreut4_3') lines_gauss(Image,Lines,1.5,3,8,'light','true','bar-shaped','true') dev_display(Lines)
Let A be the number of pixels in the domain of Image.
Then the runtime complexity is O(A*Sigma).
The amount of temporary memory required is dependent on the height
H of the domain of Image and the width W of
Image. Let S = W*H, then lines_gauss requires at
least 55*S bytes of temporary memory during execution.
lines_gauss 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.
bandpass_image,
dyn_threshold,
topographic_sketch
C. Steger: “Extracting Curvilinear Structures: A Differential
Geometric Approach”. In B. Buxton, R. Cipolla, eds., “Fourth
European Conference on Computer Vision”, Lecture Notes in Computer
Science, Volume 1064, Springer Verlag, pp. 630-641, 1996.
C. Steger: “Extraction of Curved Lines from Images”. In “13th
International Conference on Pattern Recognition”, Volume II,
pp. 251-255, 1996.
C. Steger: “An Unbiased Detector of Curvilinear Structures”.
IEEE Transactions on Pattern Analysis and Machine Intelligence,
vol. 20, no. 2, pp. 113-125, 1998.
2D Metrology