# 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 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:
•  list arbitrary-rank numerical array tseries temporal data such as TimeSeries, TemporalData, … image arbitrary Image or Image3D object audio an 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

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## Basic Examples(3)

Geometric mean filtering of a list:

Filter a TimeSeries:

Geometric mean filtering of an image:

## Scope(12)

### Data(7)

Apply a moving geometric mean filter to a vector:

Geometric mean filtering of a 2D array:

Filter a quantity array:

Filter an Audio signal:

Filtering a 2D grayscale image:

Geometric mean filtering of a 3D volume:

Filter a symbolic array:

### Parameters(5)

Specify one radius to be used in all directions:

Increasing the radius will result in smoother images:

Geometric mean filtering just in the first direction:

Second direction:

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

Filtering of the horizontal planes only:

Use a quantity parameter with a TimeSeries input:

## Applications(3)

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

Reduce noise using geometric mean filtering:

Unsharp masking using geometric mean filtering:

## Properties & Relations(3)

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

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

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

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).

#### CMS

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

#### BibTeX

@misc{reference.wolfram_2023_geometricmeanfilter, author="Wolfram Research", title="{GeometricMeanFilter}", year="2016", howpublished="\url{https://reference.wolfram.com/language/ref/GeometricMeanFilter.html}", note=[Accessed: 21-March-2023 ]}

#### BibLaTeX

@online{reference.wolfram_2023_geometricmeanfilter, organization={Wolfram Research}, title={GeometricMeanFilter}, year={2016}, url={https://reference.wolfram.com/language/ref/GeometricMeanFilter.html}, note=[Accessed: 21-March-2023 ]}