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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  
See Also
Related Guides
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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:

Kuwahara filtering of a signal:

Scope  (8)

Data  (6)

Filter a numerical list:

Filter a TimeSeries:

Filter an Audio signal:

Smoothing the image, while preserving the edges:

Filter video frames:

Kuwahara filter applied to a 3D image:

Parameters  (2)

Kuwahara filtering just in the vertical direction:

Horizontal direction:

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

Filtering of the horizontal planes only:

Applications  (4)

Use Kuwahara filtering as a preprocessing step for image segmentation:

Remove salt-and-pepper noise:

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

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

Properties & Relations  (2)

Compare Kuwahara to mean filter:

Compare Kuwahara to other edge-preserving filters:

Neat Examples  (1)

Repeatedly apply KuwaharaFilter to an image:

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_2025_kuwaharafilter, author="Wolfram Research", title="{KuwaharaFilter}", year="2025", howpublished="\url{https://reference.wolfram.com/language/ref/KuwaharaFilter.html}", note=[Accessed: 18-August-2025]}

BibLaTeX

@online{reference.wolfram_2025_kuwaharafilter, organization={Wolfram Research}, title={KuwaharaFilter}, year={2025}, url={https://reference.wolfram.com/language/ref/KuwaharaFilter.html}, note=[Accessed: 18-August-2025]}