Extract zero crossings from an image with subpixel accuracy.

zero_crossing_sub_pix extracts the zero crossings of the input image Image with subpixel accuracy. The extracted zero crossings are returned as XLD-contours in ZeroCrossings. Thus, zero_crossing_sub_pix can be used as a sub-pixel precise edge extractor if the input image is a Laplace-filtered image (see laplace, laplace_of_gauss, derivate_gauss).

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.

/* 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)
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*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)
disp_xld(Edges,WindowHandle)

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

zero_crossing_sub_pix is reentrant and automatically parallelized (on tuple level).

laplace, laplace_of_gauss, diff_of_gauss, derivate_gauss

zero_crossing

threshold_sub_pix

2D Metrology