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GeometricMeanFilter
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GeometricMeanFilter

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

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GeometricMeanFilter[data,{r1,r2,…}]

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

Details

  • GeometricMeanFilter is used to locally smooth data by using geometric mean as opposed to arithmetic mean, where the amount of smoothing is dependent on the value of r.
  • The function applied to each range-r neighborhood is GeometricMean.
  • 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, GeometricMeanFilter operates separately on each channel.
  • GeometricMeanFilter[data,{r1,r2,…}] computes the geometric mean value in blocks centered on each sample.
  • GeometricMeanFilter assumes the index coordinate system for lists and images.
  • At the data boundaries, GeometricMeanFilter uses smaller neighborhoods.

Examples

open allclose all

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

Geometric mean filtering of a list:

In[4]:=4
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https://wolfram.com/xid/0bh1qzixdnik9m-la5ph
Out[4]=4

Filter a TimeSeries:

In[1]:=1
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https://wolfram.com/xid/0bh1qzixdnik9m-fx6jf7
In[2]:=2
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https://wolfram.com/xid/0bh1qzixdnik9m-g9fo2
Out[2]=2
In[3]:=3
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https://wolfram.com/xid/0bh1qzixdnik9m-dulvtd
Out[3]=3

Geometric mean filtering of an image:

In[1]:=1
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https://wolfram.com/xid/0bh1qzixdnik9m-6y1vk2
Out[1]=1

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

Data  (7)

Apply a moving geometric mean filter to a vector:

In[4]:=4
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https://wolfram.com/xid/0bh1qzixdnik9m-s47pnq
Out[4]=4

Geometric mean filtering of a 2D array:

In[1]:=1
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https://wolfram.com/xid/0bh1qzixdnik9m-cxywqj

Filter a quantity array:

In[1]:=1
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https://wolfram.com/xid/0bh1qzixdnik9m-jopin9
Out[1]=1

Filter an Audio signal:

In[1]:=1
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https://wolfram.com/xid/0bh1qzixdnik9m-dflgzt
In[2]:=2
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https://wolfram.com/xid/0bh1qzixdnik9m-em7h2s
Out[2]=2
In[3]:=3
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https://wolfram.com/xid/0bh1qzixdnik9m-ndwk9g
Out[3]=3

Filtering a 2D grayscale image:

In[1]:=1
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https://wolfram.com/xid/0bh1qzixdnik9m-dc0gtv
Out[1]=1

Geometric mean filtering of a 3D volume:

In[1]:=1
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https://wolfram.com/xid/0bh1qzixdnik9m-6jwd04
Out[1]=1

Filter a symbolic array:

In[1]:=1
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https://wolfram.com/xid/0bh1qzixdnik9m-f3jfe5
Out[1]=1

Parameters  (5)

Specify one radius to be used in all directions:

In[1]:=1
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https://wolfram.com/xid/0bh1qzixdnik9m-tlzgi7
Out[1]=1

Increasing the radius will result in smoother images:

In[1]:=1
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https://wolfram.com/xid/0bh1qzixdnik9m-ibus74
Out[1]=1

Geometric mean filtering just in the first direction:

In[1]:=1
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https://wolfram.com/xid/0bh1qzixdnik9m-gdx3zh
Out[1]=1

Second direction:

In[2]:=2
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https://wolfram.com/xid/0bh1qzixdnik9m-hzoyls
Out[2]=2

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

In[1]:=1
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https://wolfram.com/xid/0bh1qzixdnik9m-37xttb
Out[1]=1

Filtering of the horizontal planes only:

In[2]:=2
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https://wolfram.com/xid/0bh1qzixdnik9m-5u7xo
Out[2]=2

Use a quantity parameter with a TimeSeries input:

In[1]:=1
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https://wolfram.com/xid/0bh1qzixdnik9m-icrqve
Out[1]=1
In[2]:=2
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https://wolfram.com/xid/0bh1qzixdnik9m-l1vae5
Out[2]=2

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

Use GeometricMeanFilter to smooth a positive-valued time series and identify the trend:

In[1]:=1
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https://wolfram.com/xid/0bh1qzixdnik9m-djyxka
In[2]:=2
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https://wolfram.com/xid/0bh1qzixdnik9m-5bdacu
In[3]:=3
✖
https://wolfram.com/xid/0bh1qzixdnik9m-b97dk3
Out[3]=3

Reduce noise using geometric mean filtering:

In[1]:=1
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https://wolfram.com/xid/0bh1qzixdnik9m-hb1cuf
Out[1]=1

Unsharp masking using geometric mean filtering:

In[1]:=1
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https://wolfram.com/xid/0bh1qzixdnik9m-jekwvj
Out[1]=1

Properties & Relations  (3)Properties of the function, and connections to other functions

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

In[3]:=3
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https://wolfram.com/xid/0bh1qzixdnik9m-i40d86
Out[4]=4

Geometric mean filtering is the same as ArrayFilter with function GeometricMean:

In[1]:=1
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https://wolfram.com/xid/0bh1qzixdnik9m-fns4nv
Out[1]=1

Geometric mean filtering is the same as ImageFilter with function GeometricMean:

In[1]:=1
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https://wolfram.com/xid/0bh1qzixdnik9m-dhww66
Out[1]=1
Wolfram Research (2008), GeometricMeanFilter, Wolfram Language function, https://reference.wolfram.com/language/ref/GeometricMeanFilter.html (updated 2016).
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Wolfram Research (2008), GeometricMeanFilter, Wolfram Language function, https://reference.wolfram.com/language/ref/GeometricMeanFilter.html (updated 2016).

Text

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

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

CMS

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

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

APA

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

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

BibTeX

@misc{reference.wolfram_2025_geometricmeanfilter, author="Wolfram Research", title="{GeometricMeanFilter}", year="2016", howpublished="\url{https://reference.wolfram.com/language/ref/GeometricMeanFilter.html}", note=[Accessed: 29-March-2025 ]}

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@misc{reference.wolfram_2025_geometricmeanfilter, author="Wolfram Research", title="{GeometricMeanFilter}", year="2016", howpublished="\url{https://reference.wolfram.com/language/ref/GeometricMeanFilter.html}", note=[Accessed: 29-March-2025 ]}

BibLaTeX

@online{reference.wolfram_2025_geometricmeanfilter, organization={Wolfram Research}, title={GeometricMeanFilter}, year={2016}, url={https://reference.wolfram.com/language/ref/GeometricMeanFilter.html}, note=[Accessed: 29-March-2025 ]}

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@online{reference.wolfram_2025_geometricmeanfilter, organization={Wolfram Research}, title={GeometricMeanFilter}, year={2016}, url={https://reference.wolfram.com/language/ref/GeometricMeanFilter.html}, note=[Accessed: 29-March-2025 ]}