Smoothing

List of Operators ↓

This chapter contains operators for smoothing filters. Further information about filtering can be found at the introduction to the chapter Filters.

General information about smoothing filters

Smoothing operators are filters that help to suppress noise in an image. For this purpose it is assumed, that in the undisturbed or true image the gray value of a given data point does not completely differ from its surroundings, ideally even varies only little. Thus, to suppress noise, it can be useful to replace the measured gray value with an estimate based on surrounding data points. Such an estimate can be done in different ways, so HALCON provides different smoothing operators.

The operators differ in speed and suitability for different kinds of noise. Information like the complexity (runtime dependence on the image size) is, if available, given in the operator reference. While most operators treat a single image, some can process depending images (e.g., multichannel filters like mean_nmean_nMeanNMeanNMeanNmean_n and rank_nrank_nRankNRankNRankNrank_n, or edge-preserving filters like guided_filterguided_filterGuidedFilterGuidedFilterGuidedFilterguided_filter and bilateral_filterbilateral_filterBilateralFilterBilateralFilterBilateralFilterbilateral_filter, which additionally use guidance images). Please note that some filters have both possibilities and more information is given in the specific operator reference.

Smoothing filters for single images with random noise

These smoothing filters apply their smoothing function on each channel of the input image separately and return a smoothed image with the same number of channels. In the following table we list implemented variants of smoothing filters for a single image with random noise and apply them for three different variants of random noise. The images in the table shall give an idea of the operators capability, but please note that the smoothed images highly depend on the input parameters and the individual image for every operator. For comparison, the different noisy images without filtering are given in the first row of the table. The undisturbed image without noise is shown in the following figure ((1) the full image as well as (2) its part by means of which possible effects on edges and remains from Salt & Pepper noise are visualized more clearly).

(1) (2)
(1) Undisturbed image, (2) part of the image chosen for the visualization of the filter capabilities

We marked filters recommended due to their special suitability concerning speed (S), edge-preservation (E), or a compromise between these two (C). The numbers in square brackets refer to further information that is given in a list below the table.

White Noise Gaussian Noise Salt & Pepper Noise Time[1] Alternatives
noisy image
binomial_filterbinomial_filterBinomialFilterBinomialFilterBinomialFilterbinomial_filter(S)
1|2 gauss_filtergauss_filterGaussFilterGaussFilterGaussFiltergauss_filter, smooth_imagesmooth_imageSmoothImageSmoothImageSmoothImagesmooth_image, derivate_gaussderivate_gaussDerivateGaussDerivateGaussDerivateGaussderivate_gauss, isotropic_diffusionisotropic_diffusionIsotropicDiffusionIsotropicDiffusionIsotropicDiffusionisotropic_diffusion
smooth_imagesmooth_imageSmoothImageSmoothImageSmoothImagesmooth_image
2 | 9 binomial_filterbinomial_filterBinomialFilterBinomialFilterBinomialFilterbinomial_filter, gauss_filtergauss_filterGaussFilterGaussFilterGaussFiltergauss_filter, mean_imagemean_imageMeanImageMeanImageMeanImagemean_image, derivate_gaussderivate_gaussDerivateGaussDerivateGaussDerivateGaussderivate_gauss, isotropic_diffusionisotropic_diffusionIsotropicDiffusionIsotropicDiffusionIsotropicDiffusionisotropic_diffusion
mean_imagemean_imageMeanImageMeanImageMeanImagemean_image(S)
1 | 1 binomial_filterbinomial_filterBinomialFilterBinomialFilterBinomialFilterbinomial_filter, gauss_filtergauss_filterGaussFilterGaussFilterGaussFiltergauss_filter, smooth_imagesmooth_imageSmoothImageSmoothImageSmoothImagesmooth_image, mean_image_shapemean_image_shapeMeanImageShapeMeanImageShapeMeanImageShapemean_image_shape
anisotropic_diffusionanisotropic_diffusionAnisotropicDiffusionAnisotropicDiffusionAnisotropicDiffusionanisotropic_diffusion(E)[2]
805|2568 bilateral_filterbilateral_filterBilateralFilterBilateralFilterBilateralFilterbilateral_filter, guided_filterguided_filterGuidedFilterGuidedFilterGuidedFilterguided_filter
guided_filterguided_filterGuidedFilterGuidedFilterGuidedFilterguided_filter(E)[2,3]
13 | 62 bilateral_filterbilateral_filterBilateralFilterBilateralFilterBilateralFilterbilateral_filter, anisotropic_diffusionanisotropic_diffusionAnisotropicDiffusionAnisotropicDiffusionAnisotropicDiffusionanisotropic_diffusion, median_imagemedian_imageMedianImageMedianImageMedianImagemedian_image
bilateral_filterbilateral_filterBilateralFilterBilateralFilterBilateralFilterbilateral_filter(E)[3]
16 | 54 guided_filterguided_filterGuidedFilterGuidedFilterGuidedFilterguided_filter, anisotropic_diffusionanisotropic_diffusionAnisotropicDiffusionAnisotropicDiffusionAnisotropicDiffusionanisotropic_diffusion, median_imagemedian_imageMedianImageMedianImageMedianImagemedian_image
gauss_filtergauss_filterGaussFilterGaussFilterGaussFiltergauss_filter
1 | 4 binomial_filterbinomial_filterBinomialFilterBinomialFilterBinomialFilterbinomial_filter, smooth_imagesmooth_imageSmoothImageSmoothImageSmoothImagesmooth_image, derivate_gaussderivate_gaussDerivateGaussDerivateGaussDerivateGaussderivate_gauss, isotropic_diffusionisotropic_diffusionIsotropicDiffusionIsotropicDiffusionIsotropicDiffusionisotropic_diffusion
isotropic_diffusionisotropic_diffusionIsotropicDiffusionIsotropicDiffusionIsotropicDiffusionisotropic_diffusion(E)[2]
11 | 51
sigma_imagesigma_imageSigmaImageSigmaImageSigmaImagesigma_image
10 | 33 anisotropic_diffusionanisotropic_diffusionAnisotropicDiffusionAnisotropicDiffusionAnisotropicDiffusionanisotropic_diffusion, rank_imagerank_imageRankImageRankImageRankImagerank_image
midrange_imagemidrange_imageMidrangeImageMidrangeImageMidrangeImagemidrange_image
3 | 11 sigma_imagesigma_imageSigmaImageSigmaImageSigmaImagesigma_image
median_imagemedian_imageMedianImageMedianImageMedianImagemedian_image(E)
3 | 4 median_rectmedian_rectMedianRectMedianRectMedianRectmedian_rect, rank_imagerank_imageRankImageRankImageRankImagerank_image, rank_rectrank_rectRankRectRankRectRankRectrank_rect
median_rectmedian_rectMedianRectMedianRectMedianRectmedian_rect(C)
2 | 3 median_imagemedian_imageMedianImageMedianImageMedianImagemedian_image, rank_rectrank_rectRankRectRankRectRankRectrank_rect, rank_imagerank_imageRankImageRankImageRankImagerank_image
median_separatemedian_separateMedianSeparateMedianSeparateMedianSeparatemedian_separate(C)
7 | 24 median_imagemedian_imageMedianImageMedianImageMedianImagemedian_image
median_weightedmedian_weightedMedianWeightedMedianWeightedMedianWeightedmedian_weighted
14 | 47 median_imagemedian_imageMedianImageMedianImageMedianImagemedian_image, trimmed_meantrimmed_meanTrimmedMeanTrimmedMeanTrimmedMeantrimmed_mean, sigma_imagesigma_imageSigmaImageSigmaImageSigmaImagesigma_image
rank_rectrank_rectRankRectRankRectRankRectrank_rect(E)
2 | 8 rank_imagerank_imageRankImageRankImageRankImagerank_image, median_rectmedian_rectMedianRectMedianRectMedianRectmedian_rect, median_imagemedian_imageMedianImageMedianImageMedianImagemedian_image
rank_imagerank_imageRankImageRankImageRankImagerank_image(E)
3 | 15 rank_rectrank_rectRankRectRankRectRankRectrank_rect, median_imagemedian_imageMedianImageMedianImageMedianImagemedian_image, median_rectmedian_rectMedianRectMedianRectMedianRectmedian_rect
mean_spmean_spMeanSpMeanSpMeanSpmean_sp
4 | 9 mean_imagemean_imageMeanImageMeanImageMeanImagemean_image, median_imagemedian_imageMedianImageMedianImageMedianImagemedian_image, median_separatemedian_separateMedianSeparateMedianSeparateMedianSeparatemedian_separate, eliminate_min_maxeliminate_min_maxEliminateMinMaxEliminateMinMaxEliminateMinMaxeliminate_min_max
eliminate_min_maxeliminate_min_maxEliminateMinMaxEliminateMinMaxEliminateMinMaxeliminate_min_max
11 | 42
eliminate_speliminate_spEliminateSpEliminateSpEliminateSpeliminate_sp
1 | 10 mean_spmean_spMeanSpMeanSpMeanSpmean_sp, mean_imagemean_imageMeanImageMeanImageMeanImagemean_image, median_imagemedian_imageMedianImageMedianImageMedianImagemedian_image, eliminate_min_maxeliminate_min_maxEliminateMinMaxEliminateMinMaxEliminateMinMaxeliminate_min_max
trimmed_meantrimmed_meanTrimmedMeanTrimmedMeanTrimmedMeantrimmed_mean
7 | 29 sigma_imagesigma_imageSigmaImageSigmaImageSigmaImagesigma_image, median_weightedmedian_weightedMedianWeightedMedianWeightedMedianWeightedmedian_weighted, median_imagemedian_imageMedianImageMedianImageMedianImagemedian_image
Further information related to the numbers in square brackets used in the table above:
  1. The numbers in the column 'Time' are indications about the time the operator uses to process an image. The numbers are obtained from averaging over multiple runs on the three different noise images and given in arbitrary units. Note also that the runtime of an operator depends on many factors, not at least on the used parameters and the image size. For each filter, the first number is for an image of size 800x600, the second for an image of size 1497x1160. The shown images are parts of the smaller image with parameters reasonable to us (we do not claim to have found the parameters resulting neither necessarily in the best image smoothing nor the smallest runtime). Even if two filters have the same parameter name as input, we did not necessarily use the same parameter value for both of them. Therefore, these numbers are to be understood as an indicator only.

  2. This operator can be used iteratively.

  3. This operator uses a guidance image (which can be the ImageImageImageImageimageimage itself).

Smoothing filters for single images with systematic noise

Video images composed of two half images can have systematic errors. In such a case, the operator fill_interlacefill_interlaceFillInterlaceFillInterlaceFillInterlacefill_interlace can help.

Operators designed for smoothing over multiple channels

These smoothing filters take an image with multiple channels as input and return a single channel (gray value) image. In HALCON, the following filters of this group are implemented:

Further operators

In addition to the smoothing filters, this chapter contains the following operator: info_smoothinfo_smoothInfoSmoothInfoSmoothInfoSmoothinfo_smooth, which returns information related to the different filters used by the operator smooth_imagesmooth_imageSmoothImageSmoothImageSmoothImagesmooth_image.

Glossary

In the following, the most important terms that are used in the context of smoothing filters are described:

smoothing

Smoothing means to apply a filter function on the given data to capture the main data patterns while removing noise.

random noise

Random noise is a stationary variation of brightness or color information by a small random amount for every pixel with an assumed mean of 0 over the total image.

systematic noise

Systematic noise is predictable noise, caused, e.g., by the specific setup used to acquire the images.


List of Operators

anisotropic_diffusionAnisotropicDiffusionanisotropic_diffusionAnisotropicDiffusionanisotropic_diffusion
Perform an anisotropic diffusion of an image.
bilateral_filterBilateralFilterbilateral_filterBilateralFilterbilateral_filter
bilateral filtering of an image.
binomial_filterBinomialFilterbinomial_filterBinomialFilterbinomial_filter
Smooth an image using the binomial filter.
eliminate_min_maxEliminateMinMaxeliminate_min_maxEliminateMinMaxeliminate_min_max
Smooth an image in the spatial domain to suppress noise.
eliminate_spEliminateSpeliminate_spEliminateSpeliminate_sp
Replace values outside of thresholds with average value.
fill_interlaceFillInterlacefill_interlaceFillInterlacefill_interlace
Interpolate 2 video half images.
gauss_filterGaussFiltergauss_filterGaussFiltergauss_filter
Smooth using discrete Gauss functions.
guided_filterGuidedFilterguided_filterGuidedFilterguided_filter
Guided filtering of an image.
info_smoothInfoSmoothinfo_smoothInfoSmoothinfo_smooth
Information on smoothing filter smooth_imagesmooth_imageSmoothImageSmoothImageSmoothImagesmooth_image.
isotropic_diffusionIsotropicDiffusionisotropic_diffusionIsotropicDiffusionisotropic_diffusion
Perform an isotropic diffusion of an image.
mean_imageMeanImagemean_imageMeanImagemean_image
Smooth by averaging.
mean_image_shapeMeanImageShapemean_image_shapeMeanImageShapemean_image_shape
Smooth image using a mean filter with arbitrary mask.
mean_nMeanNmean_nMeanNmean_n
Average gray values over several channels.
mean_spMeanSpmean_spMeanSpmean_sp
Suppress salt and pepper noise.
median_imageMedianImagemedian_imageMedianImagemedian_image
Compute a median filter with various masks.
median_rectMedianRectmedian_rectMedianRectmedian_rect
Compute a median filter with rectangular masks.
median_separateMedianSeparatemedian_separateMedianSeparatemedian_separate
Separated median filtering with rectangle masks.
median_weightedMedianWeightedmedian_weightedMedianWeightedmedian_weighted
Weighted median filtering with different rank masks.
midrange_imageMidrangeImagemidrange_imageMidrangeImagemidrange_image
Calculate the average of maximum and minimum inside any mask.
rank_imageRankImagerank_imageRankImagerank_image
Compute a rank filter with arbitrary masks.
rank_nRankNrank_nRankNrank_n
Return gray values with given rank from multiple channels.
rank_rectRankRectrank_rectRankRectrank_rect
Compute a rank filter with rectangular masks.
sigma_imageSigmaImagesigma_imageSigmaImagesigma_image
Non-linear smoothing with the sigma filter.
smooth_imageSmoothImagesmooth_imageSmoothImagesmooth_image
Smooth an image using various filters.
trimmed_meanTrimmedMeantrimmed_meanTrimmedMeantrimmed_mean
Smooth an image with an arbitrary rank mask.