zero_crossing_sub_pixZeroCrossingSubPixZeroCrossingSubPixzero_crossing_sub_pixzero_crossing_sub_pix🔗

Short description🔗

zero_crossing_sub_pixZeroCrossingSubPixZeroCrossingSubPixzero_crossing_sub_pixzero_crossing_sub_pix — Extract zero crossings from an image with subpixel accuracy.

Signature🔗

zero_crossing_sub_pix( image Image, out xld_cont ZeroCrossings )

HXLDCont HImage.ZeroCrossingSubPix( )

Description🔗

zero_crossing_sub_pixZeroCrossingSubPix extracts the zero crossings of the input image Imageimageimage with subpixel accuracy. The extracted zero crossings are returned as XLD-contours in ZeroCrossingszeroCrossingszero_crossings. Thus, zero_crossing_sub_pixZeroCrossingSubPix can be used as a sub-pixel precise edge extractor if the input image is a Laplace-filtered image (see laplaceLaplace, laplace_of_gaussLaplaceOfGauss, derivate_gaussDerivateGauss).

For the extraction, the input image is regarded as a surface, in which the gray values are interpolated bilinearly between the centers of the individual pixels. Consistent with the surface thus defined, zero crossing lines are extracted for each pixel and linked into topologically sound contours. This means that the zero crossing contours are correctly split at junction points. If the image contains extended areas of constant gray value 0, only the border of such areas is returned as zero crossings.

Execution information🔗

Execution information

Multithreading type: reentrant (runs in parallel with non-exclusive operators).
Multithreading scope: global (may be called from any thread).
Processed without parallelization.

Parameters🔗

Imageimageimage (input_object) singlechannelimage → object (int1 / int2 / int4 / real)HObject (int1 / int2 / int4 / real)HImage (int1 / int2 / int4 / real)HObject (int1 / int2 / int4 / real)Hobject (int1 / int2 / int4 / real)

Input image.

ZeroCrossingszeroCrossingszero_crossings (output_object) xld_cont-array → objectHObjectHXLDContHObjectHobject *

Extracted zero crossings.

Example🔗

(HDevelop)


* Detection zero crossings of the Laplacian-of-Gaussian
* of an aerial image
read_image(Image,'mreut')
derivate_gauss(Image,Laplace,3,'laplace')
zero_crossing_sub_pix(Laplace,ZeroCrossings)
dev_display(ZeroCrossings)

* Detection of edges, i.e, zero crossings of the Laplacian-of-Gaussian
* that have a large gradient magnitude, in an aerial image
read_image(Image,'mreut')
Sigma := 1.5
* Compensate the threshold for the fact that derivate_gauss(...,'gradient')
* calculates a Gaussian-smoothed gradient, in which the edge amplitudes
* are too small because of the Gaussian smoothing, to correspond to a true
* edge amplitude of 20.
Threshold := 20/(Sigma*sqrt(2*3.1415926))
derivate_gauss(Image,Gradient,Sigma,'gradient')
threshold(Gradient,Region,Threshold,255)
reduce_domain(Image,Region,ImageReduced)
derivate_gauss(ImageReduced,Laplace,Sigma,'laplace')
zero_crossing_sub_pix(Laplace,Edges)
dev_display(Edges)

(C)

/* Detection zero crossings of the Laplacian-of-Gaussian of aerial image */
read_image(&Image,"mreut")\;
derivate_gauss(Image,&Laplace,3,"laplace")\;
zero_crossing_sub_pix(Laplace,&ZeroCrossings)\;
disp_xld(ZeroCrossings,WindowHandle)\;

/* Detection of edges, i.e, zero crossings of the Laplacian-of-Gaussian
   that have a large gradient magnitude, in an aerial image */
read_image(&Image,"mreut")\;
Sigma = 1.5\;
/* Compensate the threshold for the fact that derivate_gauss(...,'gradient')
   calculates a Gaussian-smoothed gradient, in which the edge amplitudes
   are too small because of the Gaussian smoothing, to correspond to a true
   edge amplitude of 20. */
Threshold = 20/(Sigma*sqrt(2*PI))\;
derivate_gauss(Image,&Gradient,Sigma,"gradient")\;
threshold(Gradient,&Region,Threshold,255)\;
reduce_domain(Image,Region,&ImageReduced)\;
derivate_gauss(ImageReduced,&Laplace,Sigma,"laplace")\;
zero_crossing_sub_pix(Laplace,&Edges)\;
disp_xld(Edges,WindowHandle)\;

(C++)

/* Detection zero crossings of the Laplacian-of-Gaussian of aerial image */
HWindow Window(0,0,512,512)\;
HImage Image("mreut")\;
HImage Laplace = Image.DerivateGauss(3,"laplace")\;
HXLDContArray ZeroCrossings = Laplace.ZeroCrossingsSubPix()\;
ZeroCrossings.Display(Window)\;

/* Detection of edges, i.e, zero crossings of the Laplacian-of-Gaussian
   that have a large gradient magnitude, in an aerial image */
HWindow Window(0,0,512,512)\;
HImage Image("mreut")\;
Sigma = 1.5\;
/* Compensate the threshold for the fact that derivate_gauss(...,'gradient')
   calculates a Gaussian-smoothed gradient, in which the edge amplitudes
   are too small because of the Gaussian smoothing, to correspond to a true
   edge amplitude of 20. */
Threshold = 20/(Sigma*sqrt(2*PI))\;
HImage Gradient = Image.DerivateGauss(Sigma,"gradient")\;
HRegion Region = Gradient.Threshold(Threshold,255)\;
HImage ImageReduced = Image.ReduceDomain(Region)\;
HImage Laplace = ImageReduced.DerivateGauss(Sigma,"laplace")\;
HXLDContArray Edges = Laplace.ZeroCrossingSubPix()\;
Edges.Display(Window)\;

Result🔗

zero_crossing_sub_pixZeroCrossingSubPix usually returns the value 2 (H_MSG_TRUE). If necessary, an exception is raised.

Combinations with other operators🔗

Combinations

Possible predecessors

laplaceLaplace, laplace_of_gaussLaplaceOfGauss, diff_of_gaussDiffOfGauss, derivate_gaussDerivateGauss

Alternatives

zero_crossingZeroCrossing

See also

threshold_sub_pixThresholdSubPix

Module🔗

2D Metrology