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GeometricMeanFilter[data,r]

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

GeometricMeanFilter[data,{r1,r2,…}]

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

Details
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Examples  
Basic Examples  
Scope  
Data  
Parameters  
Applications  
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GeometricMeanFilter

GeometricMeanFilter[data,r]

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

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
    videoa Video 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

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Basic Examples  (3)

Geometric mean filtering of a list:

Wolfram Language code: GeometricMeanFilter[ {1, 2, 4, 8, 16}, 1]

Filter a TimeSeries:

Wolfram Language code: ts = TemporalData[TimeSeries, {{{1.6822413925758568, 1.5219174391144983, 1.9973736747454531, 1.6415040132205478, 2.343217089768049, 2.084783743067781, 1.1351714143749005, 2.002767932712488, 2.252258418508231, 1.3441535276154277, 1.591914032996 ... 0014642836, 2.04651425850399, 1.8547408293958698, 1.4796960501647136}}, {{0, 1., 0.01}}, 1, {"Continuous", 1}, {"Continuous", 1}, 1, {ValueDimensions -> 1, ResamplingMethod -> {"Interpolation", InterpolationOrder -> 1}}}, False, 10.1];
Wolfram Language code: filtered = GeometricMeanFilter[ts, 0.1]
Wolfram Language code: ListLinePlot[{ts, filtered}, PlotLegends -> {"original data", "filtered"}]

Geometric mean filtering of an image:

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

Scope  (13)

Data  (8)

Apply a moving geometric mean filter to a vector:

Wolfram Language code: GeometricMeanFilter[{1, 2, 3, 2, 1}, 1]

Filter a symbolic array:

Wolfram Language code: GeometricMeanFilter[{a, a^2, a^3, a^4, a^5}, 1]

Filter a 2D array:

Wolfram Language code: GeometricMeanFilter[(⁠| | | | | | - | -- | -- | -- | | 1 | 2 | 4 | 8 | | 2 | 4 | 8 | 16 | | 4 | 8 | 16 | 32 | | 8 | 16 | 32 | 64 |⁠), 1]//MatrixForm

Filter a quantity array:

Wolfram Language code: data = Quantity[RandomReal[1, 8], "Meters"]; filtered = GeometricMeanFilter[data, 1]

Filter an Audio signal:

Wolfram Language code: a = Import["ExampleData/rule30.wav"];
Wolfram Language code: b = GeometricMeanFilter[a, 15]
Wolfram Language code: AudioPlot[{a, b}]

Filtering a 2D grayscale image:

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

Filter video frames:

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

Geometric mean filtering of a 3D volume:

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

Parameters  (5)

Specify one radius to be used in all directions:

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

Increasing the radius will result in smoother images:

Wolfram Language code: Table[Labeled[GeometricMeanFilter[[image], r], Text["*r* = " <> ToString@r]], {r, {1, 3, 6}}]

Geometric mean filtering just in the first direction:

Wolfram Language code: GeometricMeanFilter[[image], {5, 0}]

Second direction:

Wolfram Language code: GeometricMeanFilter[[image], {0, 5}]

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

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

Filtering of the horizontal planes only:

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

Use a quantity parameter with a TimeSeries input:

Wolfram Language code: data = TimeSeries[FinancialData["AAPL", {{2016, 7, 1}, {2017, 1, 1}, "Day"}]]
Wolfram Language code: DateListPlot[{data, GeometricMeanFilter[data, Quantity[5, "Days"]]}]

Applications  (3)

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

Wolfram Language code: ts = TemporalData[TimeSeries, {{{80.89576922254395, 81.84000090895346, 83.03432343926568, 83.72564812358453, 85.38980344510735, 86.30217405399064, 87.99223737435075, 90.20650621756305, 92.11188729177361, 90.59502815354307, 91.21680329850624, 9 ... 51.88204639122333, 152.98259712435015, 154.5669904898752, 153.14375080767493, 153.9422804090023, 153.59498797717634}}, {{0, 782, 1}}, 1, {"Continuous", 1}, {"Discrete", 1}, 1, {ValueDimensions -> 1, ResamplingMethod -> None}}, False, 11.1];
Wolfram Language code: res = Table[GeometricMeanFilter[ts, r], {r, {10, 50, 100}}];
Wolfram Language code: ListLinePlot[Join[{ts}, res], PlotLegends -> {"data", "r = 10", "r = 50", "r = 100"}]

Reduce noise using geometric mean filtering:

Wolfram Language code: GeometricMeanFilter[[image], 1]

Unsharp masking using geometric mean filtering:

Wolfram Language code: i = [image]; ImageAdd[i, ImageSubtract[i, GeometricMeanFilter[i, 3]]]

Properties & Relations  (3)

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

Wolfram Language code: data = RandomReal[1, 50]; ListLinePlot[{MeanFilter[data, 5], GeometricMeanFilter[data, 5], HarmonicMeanFilter[data, 5]}, PlotRange -> {0, 1}, PlotLegends -> {"mean", "geometric mean", "harmonic mean"}]

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

Wolfram Language code: r = 1; x = {1, 2, -1, 1, 2, 3, 1, -1, 3, 1}; ArrayFilter[GeometricMean[Flatten[#]]&, x, r, Padding -> None] == GeometricMeanFilter[x, r][[r + 1 ;; -r - 1]]

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

Wolfram Language code: ImageCrop[GeometricMeanFilter[[image], 1], 3] == ImageCrop[ImageFilter[GeometricMean[Flatten[#]]&, [image], 1], 3]
Wolfram Research (2008), GeometricMeanFilter, Wolfram Language function, https://reference.wolfram.com/language/ref/GeometricMeanFilter.html (updated 2025).

Text

Wolfram Research (2008), GeometricMeanFilter, Wolfram Language function, https://reference.wolfram.com/language/ref/GeometricMeanFilter.html (updated 2025).

CMS

Wolfram Language. 2008. "GeometricMeanFilter." Wolfram Language & System Documentation Center. Wolfram Research. Last Modified 2025. 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

BibTeX

@misc{reference.wolfram_2026_geometricmeanfilter, author="Wolfram Research", title="{GeometricMeanFilter}", year="2025", howpublished="\url{https://reference.wolfram.com/language/ref/GeometricMeanFilter.html}", note=[Accessed: 12-June-2026]}

BibLaTeX

@online{reference.wolfram_2026_geometricmeanfilter, organization={Wolfram Research}, title={GeometricMeanFilter}, year={2025}, url={https://reference.wolfram.com/language/ref/GeometricMeanFilter.html}, note=[Accessed: 12-June-2026]}