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HarmonicMeanFilter
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HarmonicMeanFilter

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filters data by replacing every value by the harmonic mean value in its range-r neighborhood.

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HarmonicMeanFilter[data,{r1,r2,…}]

uses ri for filtering the ^(th)dimension in data.

Details

  • HarmonicMeanFilter is used to locally smooth data, particularly when extreme values are present, where the amount of smoothing is dependent on the value of r.
  • The function applied to each range-r neighborhood is HarmonicMean.
  • 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
  • For multichannel images and audio signals, HarmonicMeanFilter operates separately on each channel.
  • HarmonicMeanFilter[data,{r1,r2,…}] computes the harmonic mean value in blocks centered on each sample.
  • HarmonicMeanFilter assumes the index coordinate system for lists and images.
  • At the data boundaries, HarmonicMeanFilter uses smaller neighborhoods.

Examples

open allclose all

Basic Examples  (3)Summary of the most common use cases

Harmonic mean filtering of a list:

In[6]:=6
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https://wolfram.com/xid/0cptyoea8obhuy-s47pnq
Out[6]=6

Filter a TimeSeries:

In[1]:=1
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https://wolfram.com/xid/0cptyoea8obhuy-ctzx4
In[2]:=2
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https://wolfram.com/xid/0cptyoea8obhuy-77v7p5
Out[2]=2
In[3]:=3
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https://wolfram.com/xid/0cptyoea8obhuy-18tdm0
Out[3]=3

Harmonic mean filtering applied to a color image:

In[1]:=1
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https://wolfram.com/xid/0cptyoea8obhuy-hz36oe
Out[1]=1

Scope  (12)Survey of the scope of standard use cases

Data  (8)

Apply a moving harmonic mean filter to a vector:

In[1]:=1
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https://wolfram.com/xid/0cptyoea8obhuy-wfj9re
Out[1]=1

Harmonic mean filtering of a 2D array:

In[1]:=1
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https://wolfram.com/xid/0cptyoea8obhuy-cxywqj

Filter a TimeSeries:

In[1]:=1
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https://wolfram.com/xid/0cptyoea8obhuy-cx9jy
In[2]:=2
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https://wolfram.com/xid/0cptyoea8obhuy-4amfq
Out[2]=2
In[3]:=3
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https://wolfram.com/xid/0cptyoea8obhuy-cv7xrc
Out[3]=3

Filter a quantity array:

In[1]:=1
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https://wolfram.com/xid/0cptyoea8obhuy-jopin9
Out[1]=1

Filter an Audio signal:

In[1]:=1
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https://wolfram.com/xid/0cptyoea8obhuy-dflgzt
In[2]:=2
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https://wolfram.com/xid/0cptyoea8obhuy-em7h2s
Out[2]=2
In[3]:=3
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https://wolfram.com/xid/0cptyoea8obhuy-ndwk9g
Out[3]=3

Filtering a 2D grayscale image:

In[1]:=1
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https://wolfram.com/xid/0cptyoea8obhuy-dc0gtv
Out[1]=1

Harmonic mean filtering of a 3D volume:

In[1]:=1
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https://wolfram.com/xid/0cptyoea8obhuy-6jwd04
Out[1]=1

Filter a symbolic array:

In[1]:=1
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https://wolfram.com/xid/0cptyoea8obhuy-lm9bsz
Out[1]=1

Parameters  (4)

Specify one radius to be used in all directions:

In[2]:=2
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https://wolfram.com/xid/0cptyoea8obhuy-tlzgi7
Out[2]=2

Increasing the radius will result in smoother images:

In[1]:=1
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https://wolfram.com/xid/0cptyoea8obhuy-ibus74
Out[1]=1

Harmonic mean filtering just in the first direction:

In[1]:=1
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https://wolfram.com/xid/0cptyoea8obhuy-gdx3zh
Out[1]=1

Second direction:

In[2]:=2
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https://wolfram.com/xid/0cptyoea8obhuy-hzoyls
Out[2]=2

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

In[1]:=1
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https://wolfram.com/xid/0cptyoea8obhuy-37xttb
Out[1]=1

Filtering of the horizontal planes only:

In[2]:=2
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https://wolfram.com/xid/0cptyoea8obhuy-5u7xo
Out[2]=2

Applications  (3)Sample problems that can be solved with this function

Blur a grayscale image:

In[1]:=1
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https://wolfram.com/xid/0cptyoea8obhuy-e400fa
Out[1]=1

Use harmonic mean filtering if your data has outliers:

In[1]:=1
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https://wolfram.com/xid/0cptyoea8obhuy-ioz7qz
Out[1]=1
In[2]:=2
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https://wolfram.com/xid/0cptyoea8obhuy-icwggl
Out[2]=2

Reduce effect of outliers in an image:

In[1]:=1
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https://wolfram.com/xid/0cptyoea8obhuy-e5xtyf
Out[1]=1

Properties & Relations  (4)Properties of the function, and connections to other functions

The harmonic mean is the reciprocal of the mean of reciprocals of the given data:

In[1]:=1
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https://wolfram.com/xid/0cptyoea8obhuy-cqzltl
Out[2]=2

For positive data, HarmonicMeanFilter[data,r]≤GeometricMeanFilter[data,r]≤MeanFilter[data,r]:

In[1]:=1
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https://wolfram.com/xid/0cptyoea8obhuy-i40d86
Out[1]=1

Harmonic mean filtering is the same as ArrayFilter with function HarmonicMean:

In[1]:=1
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https://wolfram.com/xid/0cptyoea8obhuy-fns4nv
Out[1]=1

Harmonic mean filtering is the same as ImageFilter with function HarmonicMean:

In[1]:=1
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https://wolfram.com/xid/0cptyoea8obhuy-dhww66
Out[1]=1
Wolfram Research (2008), HarmonicMeanFilter, Wolfram Language function, https://reference.wolfram.com/language/ref/HarmonicMeanFilter.html (updated 2016).
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Wolfram Research (2008), HarmonicMeanFilter, Wolfram Language function, https://reference.wolfram.com/language/ref/HarmonicMeanFilter.html (updated 2016).

Text

Wolfram Research (2008), HarmonicMeanFilter, Wolfram Language function, https://reference.wolfram.com/language/ref/HarmonicMeanFilter.html (updated 2016).

✖
Wolfram Research (2008), HarmonicMeanFilter, Wolfram Language function, https://reference.wolfram.com/language/ref/HarmonicMeanFilter.html (updated 2016).

CMS

Wolfram Language. 2008. "HarmonicMeanFilter." Wolfram Language & System Documentation Center. Wolfram Research. Last Modified 2016. https://reference.wolfram.com/language/ref/HarmonicMeanFilter.html.

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Wolfram Language. 2008. "HarmonicMeanFilter." Wolfram Language & System Documentation Center. Wolfram Research. Last Modified 2016. https://reference.wolfram.com/language/ref/HarmonicMeanFilter.html.

APA

Wolfram Language. (2008). HarmonicMeanFilter. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/HarmonicMeanFilter.html

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Wolfram Language. (2008). HarmonicMeanFilter. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/HarmonicMeanFilter.html

BibTeX

@misc{reference.wolfram_2025_harmonicmeanfilter, author="Wolfram Research", title="{HarmonicMeanFilter}", year="2016", howpublished="\url{https://reference.wolfram.com/language/ref/HarmonicMeanFilter.html}", note=[Accessed: 30-April-2025 ]}

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@misc{reference.wolfram_2025_harmonicmeanfilter, author="Wolfram Research", title="{HarmonicMeanFilter}", year="2016", howpublished="\url{https://reference.wolfram.com/language/ref/HarmonicMeanFilter.html}", note=[Accessed: 30-April-2025 ]}

BibLaTeX

@online{reference.wolfram_2025_harmonicmeanfilter, organization={Wolfram Research}, title={HarmonicMeanFilter}, year={2016}, url={https://reference.wolfram.com/language/ref/HarmonicMeanFilter.html}, note=[Accessed: 30-April-2025 ]}

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@online{reference.wolfram_2025_harmonicmeanfilter, organization={Wolfram Research}, title={HarmonicMeanFilter}, year={2016}, url={https://reference.wolfram.com/language/ref/HarmonicMeanFilter.html}, note=[Accessed: 30-April-2025 ]}