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KuwaharaFilter[data,r]

computes for each element p in data the variance of the values in the four (r+1)×(r+1) squares that have p as a corner, and replaces p with the mean of the values of the square with least variance.

Details
Details and Options Details and Options
Examples  
Basic Examples  
Scope  
Data  
Parameters  
Applications  
Properties & Relations  
Neat Examples  
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KuwaharaFilter

KuwaharaFilter[data,r]

computes for each element p in data the variance of the values in the four (r+1)×(r+1) squares that have p as a corner, and replaces p with the mean of the values of the square with least variance.

Details

  • KuwaharaFilter is a nonlinear local filter typically used for edge-preserving smoothing.
  • The data can be any of the following:
  • listarbitrary-rank numerical array
    tseriestemporal data such as TimeSeries, TemporalData, …
    imagearbitrary Image or Image3D object
    audioan Audio object
    videoa Video object
  • For multi-channel data, KuwaharaFilter computes the sum of the variances in each channel.
  • KuwaharaFilter[data,{r1,r2,…}] uses blocks.
  • KuwaharaFilter assumes the index coordinate system for lists and images.
  • At the data boundaries, KuwaharaFilter uses smaller neighborhoods.

Examples

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Basic Examples  (2)

Kuwahara filtering of an image:

Wolfram Language code: KuwaharaFilter[[image], 3]

Kuwahara filtering of a signal:

Wolfram Language code: data = TemporalData[TimeSeries, {{{-0.1807621426976858, 0.1413032974253584, 0.14787020336891699, -0.18283488261794334, -0.03389990261702913, -0.01981257214348542, 0.030642813601194474, 0.16788346166120727, -0.12656460929996266, 0.097159702207544 ... 32831686447162, 0.08706753196133699, -0.054206874420813844, 0.1733508109246914, 0.033414574408857645}}, {{0, 100, 1}}, 1, {"Continuous", 1}, {"Discrete", 1}, 1, {ResamplingMethod -> {"Interpolation", InterpolationOrder -> 1}}}, False, 12.]; ListLinePlot[{data, KuwaharaFilter[data, 10]}]

Scope  (8)

Data  (6)

Filter a numerical list:

Wolfram Language code: KuwaharaFilter[{1, 2, 1, -1, 0, 2}, 1]

Filter a TimeSeries:

Wolfram Language code: ts = TemporalData[TimeSeries, {{{0., -0.054108337548928784, 0.1280211704499059, 0.28162021808461324, -0.2057320325139802, -0.4871901025739722, -0.7154387408784426, -0.7399660905024047, -0.6981022018441507, -0.7178077145466483, -0.8034462541874 ... 7894984276149, 1.8851123992920942, 1.8341759268762767, 2.0335844117979263}}, {{0., 10., 0.1}}, 1, {"Continuous", 1}, {"Continuous", 1}, 1, {ValueDimensions -> 1, ResamplingMethod -> {"Interpolation", InterpolationOrder -> 1}}}, False, 10.]; filtered = KuwaharaFilter[ts, 5]
Wolfram Language code: ListLinePlot[{ts, filtered}, PlotLegends -> {"original data", "filtered"}]

Filter an Audio signal:

Wolfram Language code: a = Import["ExampleData/rule30.wav"]; b = KuwaharaFilter[a, 40]
Wolfram Language code: AudioPlot[{a, b}]

Smoothing the image, while preserving the edges:

Wolfram Language code: KuwaharaFilter[[image], 3]

Filter video frames:

Wolfram Language code: KuwaharaFilter[Video["ExampleData/fish.mp4"], 3]

Kuwahara filter applied to a 3D image:

Wolfram Language code: KuwaharaFilter[[image], 3]

Parameters  (2)

Kuwahara filtering just in the vertical direction:

Wolfram Language code: KuwaharaFilter[[image], {10, 0}]

Horizontal direction:

Wolfram Language code: KuwaharaFilter[[image], {0, 10}]

Kuwahara filtering of a 3D image in the vertical direction only:

Wolfram Language code: KuwaharaFilter[[image], {4, 0, 0}]

Filtering of the horizontal planes only:

Wolfram Language code: KuwaharaFilter[[image], {0, 4, 4}]

Applications  (4)

Use Kuwahara filtering as a preprocessing step for image segmentation:

Wolfram Language code: ClusteringComponents[KuwaharaFilter[[image], 2], 6]// Colorize

Remove salt-and-pepper noise:

Wolfram Language code: KuwaharaFilter[[image], 2]

Use a Kuwahara filter to remove smaller stars from an astronomical image:

Wolfram Language code: KuwaharaFilter[[image], 2]

Use a Kuwahara filter to create an artistic oil painting effect:

Wolfram Language code: KuwaharaFilter[[image], 4]

Properties & Relations  (2)

Compare Kuwahara to mean filter:

Wolfram Language code: i = [image];{KuwaharaFilter[i, 2], MeanFilter[i, 2]}

Compare Kuwahara to other edge-preserving filters:

Wolfram Language code: i = [image]; {KuwaharaFilter[i, 5], MeanShiftFilter[i, 5, 0.1], BilateralFilter[i, 5, 0.1]}

Neat Examples  (1)

Repeatedly apply KuwaharaFilter to an image:

Wolfram Language code: FixedPoint[KuwaharaFilter[#, 5]&, [image], 150]
Wolfram Research (2010), KuwaharaFilter, Wolfram Language function, https://reference.wolfram.com/language/ref/KuwaharaFilter.html (updated 2025).

Text

Wolfram Research (2010), KuwaharaFilter, Wolfram Language function, https://reference.wolfram.com/language/ref/KuwaharaFilter.html (updated 2025).

CMS

Wolfram Language. 2010. "KuwaharaFilter." Wolfram Language & System Documentation Center. Wolfram Research. Last Modified 2025. https://reference.wolfram.com/language/ref/KuwaharaFilter.html.

APA

Wolfram Language. (2010). KuwaharaFilter. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/KuwaharaFilter.html

BibTeX

@misc{reference.wolfram_2026_kuwaharafilter, author="Wolfram Research", title="{KuwaharaFilter}", year="2025", howpublished="\url{https://reference.wolfram.com/language/ref/KuwaharaFilter.html}", note=[Accessed: 12-June-2026]}

BibLaTeX

@online{reference.wolfram_2026_kuwaharafilter, organization={Wolfram Research}, title={KuwaharaFilter}, year={2025}, url={https://reference.wolfram.com/language/ref/KuwaharaFilter.html}, note=[Accessed: 12-June-2026]}