lines_gausslines_gaussLinesGausslines_gaussLinesGaussLinesGauss (Operator)

Name

lines_gausslines_gaussLinesGausslines_gaussLinesGaussLinesGauss — Detect lines and their width.

Signature

Description

The operator lines_gausslines_gaussLinesGausslines_gaussLinesGaussLinesGauss can be used to extract lines (curvilinear structures) from the image ImageImageImageImageImageimage. The extracted lines are returned in LinesLinesLinesLinesLineslines as subpixel precise XLD-contours. The parameter LightDarkLightDarkLightDarkLightDarkLightDarklightDark determines, whether bright or dark lines are extracted. If ExtractWidthExtractWidthExtractWidthExtractWidthExtractWidthextractWidth is set to 'true'"true""true""true""true""true" the line width is extracted for each line point. If LineModelLineModelLineModelLineModelLineModellineModel is set to a value different from 'none'"none""none""none""none""none", lines_gausslines_gaussLinesGausslines_gaussLinesGaussLinesGauss 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 LineModelLineModelLineModelLineModelLineModellineModel as bar-shaped lines (LineModelLineModelLineModelLineModelLineModellineModel = 'bar-shaped'"bar-shaped""bar-shaped""bar-shaped""bar-shaped""bar-shaped"), parabolic lines (LineModelLineModelLineModelLineModelLineModellineModel = 'parabolic'"parabolic""parabolic""parabolic""parabolic""parabolic"), and Gaussian lines (LineModelLineModelLineModelLineModelLineModellineModel = 'gaussian'"gaussian""gaussian""gaussian""gaussian""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 LineModelLineModelLineModelLineModelLineModellineModel is only meaningful if ExtractWidthExtractWidthExtractWidthExtractWidthExtractWidthextractWidth='true'"true""true""true""true""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 CompleteJunctionsCompleteJunctionsCompleteJunctionsCompleteJunctionsCompleteJunctionscompleteJunctions is set to 'true'"true""true""true""true""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 SigmaSigmaSigmaSigmaSigmasigma determines the amount of smoothing to be performed. Larger values of SigmaSigmaSigmaSigmaSigmasigma 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_facetlines_facetLinesFacetlines_facetLinesFacetLinesFacet 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 HighHighHighHighHighhigh. Points that have a second derivative smaller than LowLowLowLowLowlow 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_thresholdhysteresis_thresholdHysteresisThresholdhysteresis_thresholdHysteresisThresholdHysteresisThreshold). However, this function is not used internally since it does not allow the extraction of subpixel precise contours.

For the choice of the thresholds HighHighHighHighHighhigh and LowLowLowLowLowlow 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 SigmaSigmaSigmaSigmaSigmasigma. 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 SigmaSigmaSigmaSigmaSigmasigma: The larger SigmaSigmaSigmaSigmaSigmasigma is chosen, the smaller the second derivative will be. This means that for larger smoothing correspondingly smaller values for HighHighHighHighHighhigh and LowLowLowLowLowlow 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 SigmaSigmaSigmaSigmaSigmasigma = 1.5, HighHighHighHighHighhigh should be chosen larger than 14. If, on the other hand, 10 pixel wide lines with an amplitude larger than 100 and a SigmaSigmaSigmaSigmaSigmasigma = 3 are to be detected, HighHighHighHighHighhigh should be chosen larger than 3.5. For the choice of LowLowLowLowLowlow values between 0.25 HighHighHighHighHighhigh and 0.5 HighHighHighHighHighhigh are appropriate.

The extracted lines are returned in a topologically sound data structure in LinesLinesLinesLinesLineslines. This means that lines are correctly split at junction points.

lines_gausslines_gaussLinesGausslines_gaussLinesGaussLinesGauss defines the following attributes for each line point if ExtractWidthExtractWidthExtractWidthExtractWidthExtractWidthextractWidth was set to 'false'"false""false""false""false""false":

'angle'"angle""angle""angle""angle""angle":

The angle of the direction perpendicular to the line

'response'"response""response""response""response""response":

The magnitude of the second derivative

If ExtractWidthExtractWidthExtractWidthExtractWidthExtractWidthextractWidth was set to 'true'"true""true""true""true""true", the following attributes are defined in addition to 'angle'"angle""angle""angle""angle""angle" and 'response'"response""response""response""response""response":

'width_left'"width_left""width_left""width_left""width_left""width_left":

The line width to the left of the line

'width_right'"width_right""width_right""width_right""width_right""width_right":

The line width to the right of the line

If ExtractWidthExtractWidthExtractWidthExtractWidthExtractWidthextractWidth was set to 'true'"true""true""true""true""true" and LineModelLineModelLineModelLineModelLineModellineModel to a value different from 'none'"none""none""none""none""none", the following attributes are defined in addition to 'angle'"angle""angle""angle""angle""angle", 'response'"response""response""response""response""response", 'width_left'"width_left""width_left""width_left""width_left""width_left", and 'width_right'"width_right""width_right""width_right""width_right""width_right":

'asymmetry'"asymmetry""asymmetry""asymmetry""asymmetry""asymmetry":

The asymmetry of the line point

'contrast'"contrast""contrast""contrast""contrast""contrast":

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. All these attributes can be queried via the operator get_contour_attrib_xldget_contour_attrib_xldGetContourAttribXldget_contour_attrib_xldGetContourAttribXldGetContourAttribXld.

lines_gausslines_gaussLinesGausslines_gaussLinesGaussLinesGauss can be executed on OpenCL devices.

Attention

In general, but in particular if the line width is to be extracted, SigmaSigmaSigmaSigmaSigmasigma >= w/sqrt(3) should be selected, where w is the width (half the diameter) of the lines in the image. As the lowest allowable value SigmaSigmaSigmaSigmaSigmasigma >= w/2.5 must be selected. If, for example, lines with a width of 4 pixels (diameter 8 pixels) are to be extracted, SigmaSigmaSigmaSigmaSigmasigma >= 2.3 should be selected.

lines_gausslines_gaussLinesGausslines_gaussLinesGaussLinesGauss uses a special implementation that is optimized using SSE2 instructions if the system parameter 'sse2_enable'"sse2_enable""sse2_enable""sse2_enable""sse2_enable""sse2_enable" is set to 'true'"true""true""true""true""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'"sse2_enable""sse2_enable""sse2_enable""sse2_enable""sse2_enable" to 'false'"false""false""false""false""false" (using set_systemset_systemSetSystemset_systemSetSystemSetSystem) before you call lines_gausslines_gaussLinesGausslines_gaussLinesGaussLinesGauss. This way lines_gausslines_gaussLinesGausslines_gaussLinesGaussLinesGauss does not use SSE2 accelerations. Don't forget to set 'sse2_enable'"sse2_enable""sse2_enable""sse2_enable""sse2_enable""sse2_enable" back to 'true'"true""true""true""true""true" afterwards.

When lines_gausslines_gaussLinesGausslines_gaussLinesGaussLinesGauss is run on OpenCL devices, the same limitations apply as for derivate_gaussderivate_gaussDerivateGaussderivate_gaussDerivateGaussDerivateGauss: SigmaSigmaSigmaSigmaSigmasigma 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.

Parallelization

• 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 internal data level.

Parameters

* 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')
disp_xld(Lines,WindowHandle)

/* 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");
disp_xld(Lines,WindowHandle);

* 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')
disp_xld(Lines,WindowHandle)

/* Detection of lines in an aerial image */
HWindow w(0,0,520,560);
HImage Image("mreut4_3");
HXLDContArray Lines = Image.LinesGauss(1.5,3,8,"light","true",
                                       "bar-shaped","true");
Lines.Display(w);

* 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')
disp_xld(Lines,WindowHandle)

* 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')
disp_xld(Lines,WindowHandle)

Complexity

Let A be the number of pixels in the domain of ImageImageImageImageImageimage. Then the runtime complexity is O(A*Sigma).

The amount of temporary memory required is dependent on the height H of the domain of ImageImageImageImageImageimage and the width W of ImageImageImageImageImageimage. Let S = W*H, then lines_gausslines_gaussLinesGausslines_gaussLinesGaussLinesGauss requires at least 55*S bytes of temporary memory during execution.

Result

lines_gausslines_gaussLinesGausslines_gaussLinesGaussLinesGauss returns 2 (H_MSG_TRUE) if all parameters are correct and no error occurs during execution. If the input is empty the behaviour can be set via set_system(::'no_object_result',<Result>:)set_system("no_object_result",<Result>)SetSystem("no_object_result",<Result>)set_system("no_object_result",<Result>)SetSystem("no_object_result",<Result>)SetSystem("no_object_result",<Result>). If necessary, an exception is raised.

Possible Successors

gen_polygons_xldgen_polygons_xldGenPolygonsXldgen_polygons_xldGenPolygonsXldGenPolygonsXld

Alternatives

lines_facetlines_facetLinesFacetlines_facetLinesFacetLinesFacet

See also

bandpass_imagebandpass_imageBandpassImagebandpass_imageBandpassImageBandpassImage, dyn_thresholddyn_thresholdDynThresholddyn_thresholdDynThresholdDynThreshold, topographic_sketchtopographic_sketchTopographicSketchtopographic_sketchTopographicSketchTopographicSketch

References

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.

Module

2D Metrology