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MaxFilter[data,r]

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

MaxFilter[data,{r1,r2,…}]

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

Details
Details and Options Details and Options
Examples  
Basic Examples  
Scope  
Data  
Parameters  
Applications  
Properties & Relations  
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MaxFilter

MaxFilter[data,r]

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

MaxFilter[data,{r1,r2,…}]

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

Details

  • MaxFilter is a nonlinear filter commonly used to locally smooth data and diminish pepper-like noise, where the amount of smoothing is dependent on the value of r.
  • The function applied to each range-r neighborhood is Max.
  • 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, MaxFilter replaces each pixel by a pixel in its neighborhood that has the maximum total intensity, averaged over all channels.
  • MaxFilter[data,{r1,r2,…}] computes the maximum value in blocks centered on each sample.
  • MaxFilter assumes the index coordinate system for lists and images.
  • At the data boundaries, MaxFilter uses smaller neighborhoods.

Examples

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Basic Examples  (3)

Maximum filter of a list:

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

Filter a TimeSeries:

Wolfram Language code: ts = TemporalData[TimeSeries, {{{0., -0.27267267057145633, -0.6672983789995302, -0.5338541947930846, -0.6117404489279314, -0.6755527076595494, -0.02125421294486496, -0.10792797291843935, -0.6138271235477938, -0.3248568606554575, -0.08843449054 ... 2053424, -0.49980440691873723, -0.5388679788215971, -0.4101602764645551}}, {{0, 1., 0.01}}, 1, {"Continuous", 1}, {"Continuous", 1}, 1, {ValueDimensions -> 1, ResamplingMethod -> {"Interpolation", InterpolationOrder -> 1}}}, False, 10.1];
Wolfram Language code: filtered = MaxFilter[ts, .1]
Wolfram Language code: ListLinePlot[{ts, filtered}, PlotLegends -> {"original data", "filtered"}]

Maximum filtering of a color image:

Wolfram Language code: MaxFilter[[image], 6]

Scope  (13)

Data  (8)

Maximum filtering of a numeric vector:

Wolfram Language code: MinFilter[{0, 3, 8, 2}, 1]

Filter a symbolic array:

Wolfram Language code: MaxFilter[ {a, b, c}, 1]

Maximum filtering of a 2D array:

Wolfram Language code: MaxFilter[(⁠| | | | | | - | - | - | - | | 0 | 3 | 8 | 2 | | 7 | 6 | 9 | 6 | | 5 | 8 | 4 | 0 | | 3 | 5 | 1 | 6 |⁠), 1]//MatrixForm

Maximum filtering of a list of Quantity objects:

Wolfram Language code: data = {Quantity[9, "Feet"], Quantity[86, "Inches"], Quantity[27.1, "Meters"], Quantity[79, "Feet"], Quantity[90, "Feet"], Quantity[41, "Inches"], Quantity[99, "Inches"], Quantity[6, "Feet"], Quantity[38, "Feet"], Quantity[89, "Feet"], Quantity[53, "Feet"], Quantity[85, "Meters"], Quantity[92, "Meters"], Quantity[95, "Meters"], Quantity[49, "Feet"]};
Wolfram Language code: ListLinePlot[{data, MaxFilter[data, 2]}, PlotRange -> All]

Filter an Audio signal:

Wolfram Language code: a = Import["ExampleData/rule30.wav"];
Wolfram Language code: b = MaxFilter[a, 35]
Wolfram Language code: AudioPlot[{a, b}]

Filtering a 2D grayscale image:

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

Filter video frames:

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

Maximum filter of a 3D image:

Wolfram Language code: MaxFilter[[image], 2]

Parameters  (5)

Specify one radius to be used in all directions:

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

Increasing the radius will result in brighter images:

Wolfram Language code: Table[Labeled[MaxFilter[[image], r], Text["*r* = " <> ToString@r]], {r, {1, 2, 4}}]

Maximum filtering just in the first direction:

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

Filtering just in the second direction:

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

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

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

Filtering of a 3D image in the horizontal planes only:

Wolfram Language code: MaxFilter[[image], {0, 3, 3}]

Applications  (4)

Remove pepper noise from an astronomical image:

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

Use a maximum filter to dilate the brighter parts of a color image:

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

Dilate the brighter parts of an image to remove thin, dark features:

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

Use maximum filtering to locate borders in an image:

Wolfram Language code: i = [image]; ImageSubtract[MaxFilter[i, 1], i]

Properties & Relations  (3)

Maximum filtering is the same as Dilation with a box structuring element:

Wolfram Language code: MaxFilter[[image], 1] == Dilation[[image], 1]

Maximum filtering is the same as ImageFilter with function Max:

Wolfram Language code: MaxFilter[[image], 1] == ImageFilter[Max[Flatten[#]]&, [image], 1]

Subsequent application of MaxFilter and MinFilter is the same as Closing:

Wolfram Language code: MinFilter[MaxFilter[[image], 6], 6]
Wolfram Research (2008), MaxFilter, Wolfram Language function, https://reference.wolfram.com/language/ref/MaxFilter.html (updated 2025).

Text

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

CMS

Wolfram Language. 2008. "MaxFilter." Wolfram Language & System Documentation Center. Wolfram Research. Last Modified 2025. https://reference.wolfram.com/language/ref/MaxFilter.html.

APA

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

BibTeX

@misc{reference.wolfram_2026_maxfilter, author="Wolfram Research", title="{MaxFilter}", year="2025", howpublished="\url{https://reference.wolfram.com/language/ref/MaxFilter.html}", note=[Accessed: 12-June-2026]}

BibLaTeX

@online{reference.wolfram_2026_maxfilter, organization={Wolfram Research}, title={MaxFilter}, year={2025}, url={https://reference.wolfram.com/language/ref/MaxFilter.html}, note=[Accessed: 12-June-2026]}