--- title: "MeanShiftFilter" language: "en" type: "Symbol" summary: "MeanShiftFilter[data, r, d] filters data by replacing every value by the mean of the pixels in a range-r neighborhood and whose value is within a distance d. MeanShiftFilter[data, {r1, r2, ...}, d] uses ri for filtering the i\\[Null]^thdimension in data." keywords: - mean-shift - meanshift - mean shift - cluster analysis - feature space - noise removal - denoising canonical_url: "https://reference.wolfram.com/language/ref/MeanShiftFilter.html" source: "Wolfram Language Documentation" related_guides: - title: "Image Restoration" link: "https://reference.wolfram.com/language/guide/ImageRestoration.en.md" - title: "Linear and Nonlinear Filters" link: "https://reference.wolfram.com/language/guide/LinearAndNonlinearFilters.en.md" - title: "Image Processing & Analysis" link: "https://reference.wolfram.com/language/guide/ImageProcessing.en.md" - title: "Image Filtering & Neighborhood Processing" link: "https://reference.wolfram.com/language/guide/ImageFilteringAndNeighborhoodProcessing.en.md" - title: "Video Computation: Update History" link: "https://reference.wolfram.com/language/guide/VideoComputation-UpdateHistory.en.md" related_functions: - title: "MeanFilter" link: "https://reference.wolfram.com/language/ref/MeanFilter.en.md" - title: "MeanShift" link: "https://reference.wolfram.com/language/ref/MeanShift.en.md" - title: "BilateralFilter" link: "https://reference.wolfram.com/language/ref/BilateralFilter.en.md" - title: "GuidedFilter" link: "https://reference.wolfram.com/language/ref/GuidedFilter.en.md" - title: "TrimmedMean" link: "https://reference.wolfram.com/language/ref/TrimmedMean.en.md" --- # MeanShiftFilter MeanShiftFilter[data, r, d] filters data by replacing every value by the mean of the pixels in a range-r neighborhood and whose value is within a distance d. MeanShiftFilter[data, {r1, r2, …}, d] uses ri for filtering the $i$$$^{\text{th}}$$dimension in data. ## Details and Options * ``MeanShiftFilter`` is used to locally smooth data and diminish noise while preserving significant jumps such as edges in images, where the amount of smoothing is dependent on the values of ``r`` and ``d``. [image] * The function applied to each range-``r`` neighborhood is ``MeanShift``. * 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 | | video | a Video object | * For multichannel images and audio signals, the distance is computed between channel vectors. * ``MeanShiftFilter[data, {r1, r2, …}, d]`` computes the mean shift value in $\left(2 r_1+1\right)\times \left(2 r_2+1\right)\times \ldots$ blocks centered on each sample. * ``MeanShiftFilter`` assumes the index coordinate system for lists and images. [image] * At the data boundaries, ``MeanShiftFilter`` uses smaller neighborhoods. * The following options can be given: | | | | | ----------------- | ----------------- | -------------------------------------------- | | DistanceFunction | EuclideanDistance | how to compute the distance between values | | MaxIterations | 1 | maximum number of iterations to be performed | * For a complete list of possible settings for ``DistanceFunction``, see the reference page for ``MeanShift``. * The possible range for the distance parameter ``d`` depends on the distance function as well as the dimension of the color space. --- ## Background & Context ``MeanShiftFilter`` is a filter for smoothing images to remove local variations typically caused by noise, rough textures, etc. ``MeanShiftFilter`` is often used as a preprocessing step before doing other image analysis operations such as segmentation. Unlike most other noise-removing filters (e.g. ``MeanFilter``), ``MeanShiftFilter`` preserves edges in the image. Other similar functions include ``PeronaMalikFilter``, ``BilateralFilter``, and ``NonlocalMeansFilter``. --- ## Examples (22) ### Basic Examples (3) Mean-shift filtering of a vector: ```wl In[1]:= MeanShiftFilter[ {1, 0, 1, 4, 4, 5, 2, 1}, 2, 1] Out[1]= {0.666667, 0.666667, 0.666667, 4.33333, 4.33333, 4.33333, 1.5, 1.5} ``` --- Filter a ``TimeSeries`` : ```wl In[1]:= ts = TemporalData[TimeSeries, {CompressedData["«1188»"], {{0., 10., 0.1}}, 1, {"Continuous", 1}, {"Continuous", 1}, 1, {ValueDimensions -> 1, ResamplingMethod -> {"Interpolation", InterpolationOrder -> 1}}}, False, 10.]; In[2]:= filtered = MeanShiftFilter[ts, 5, 2] Out[2]= TemporalData[TimeSeries, {CompressedData["«1186»"], {{0., 10., 0.1}}, 1, {"Continuous", 1}, {"Continuous", 1}, 1, {ValueDimensions -> 1, ResamplingMethod -> {"Interpolation", InterpolationOrder -> 1}}}, False, 14.3] In[3]:= ListLinePlot[{ts, filtered}, PlotLegends -> {"original data", "filtered"}] Out[3]= [image] ``` --- Mean-shift filtering of a color image: ```wl In[1]:= MeanShiftFilter[[image], 10, .5] Out[1]= [image] ``` ### Scope (12) #### Data (7) Mean-shift filtering of data: ```wl In[1]:= MeanShiftFilter[ {0, 1, 10, 11}, 1, 1] Out[1]= {0.5, 0.5, 10.5, 10.5} ``` --- Mean-shift filtering of a 2D array: ```wl In[1]:= MeanShiftFilter[(⁠| | | | | | - | - | - | - | | 0 | 3 | 2 | 2 | | 3 | 9 | 9 | 6 | | 5 | 8 | 7 | 0 | | 3 | 1 | 1 | 2 |⁠), 1, 2]//MatrixForm Out[1]//MatrixForm= (⁠| | | | | | ------- | ------- | ------- | --- | | 0. | 2.66667 | 2.33333 | 2. | | 3.66667 | 8.25 | 8.25 | 6.5 | | 3.66667 | 8.25 | 7.8 | 1. | | 3. | 1.66667 | 1. | 1. |⁠) ``` --- Filter a ``TimeSeries`` : ```wl In[1]:= ts = TemporalData[TimeSeries, {CompressedData["«1188»"], {{0, 1., 0.01}}, 1, {"Continuous", 1}, {"Continuous", 1}, 1, {ValueDimensions -> 1, ResamplingMethod -> {"Interpolation", InterpolationOrder -> 1}}}, False, 10.1]; In[2]:= filtered = MeanShiftFilter[ts, 5, 1, MaxIterations -> 100] Out[2]= TemporalData[TimeSeries, {CompressedData["«1076»"], {{0, 1., 0.01}}, 1, {"Continuous", 1}, {"Continuous", 1}, 1, {ValueDimensions -> 1, ResamplingMethod -> {"Interpolation", InterpolationOrder -> 1}}}, False, 14.3] In[3]:= ListLinePlot[{ts, filtered}, PlotLegends -> {"original data", "filtered"}] Out[3]= [image] ``` --- Filter an ``Audio`` signal: ```wl In[1]:= a = Import["ExampleData/rule30.wav"]; In[2]:= b = MeanShiftFilter[a, 25, 0.5] Out[2]= [image] In[3]:= AudioPlot[{a, b}] Out[3]= [image] ``` --- Mean-shift filtering of a grayscale image: ```wl In[1]:= MeanShiftFilter[[image], 5, 0.1] Out[1]= [image] ``` --- Filter video frames: ```wl In[1]:= MeanShiftFilter[Video["ExampleData/fish.mp4"], 3, .02] Out[1]= \!\(\*VideoBox["![Embedded Video Player](video://content-709q3)"]\) ``` --- Mean-shift filtering of a 3D image: ```wl In[1]:= MeanShiftFilter[[image], 6, 0.1] Out[1]= [image] ``` #### Parameters (5) Specify one radius to be used in all directions: ```wl In[1]:= MeanShiftFilter[[image], 5, 1] Out[1]= [image] ``` --- Mean-shift filtering in just the first direction: ```wl In[1]:= MeanShiftFilter[[image], {5, 0}, 1] Out[1]= [image] ``` --- Filtering in just the second direction: ```wl In[1]:= MeanShiftFilter[[image], {0, 5}, 1] Out[1]= [image] ``` --- Mean-shift filtering of a 3D image in the vertical direction only: ```wl In[1]:= MeanShiftFilter[[image], {5, 0, 0}, 1] Out[1]= [image] ``` Mean-shift filtering of a 3D image in the horizontal planes only: ```wl In[2]:= MeanShiftFilter[[image], {0, 5, 5}, 1] Out[2]= [image] ``` --- Mean-shift filter averages only over pixels that differ in value by less than ``d`` : ```wl In[1]:= Labeled[MeanShiftFilter[[image], 5, #], #]& /@ {0.1, 0.3, 0.5} Out[1]= [image] ``` ### Options (3) #### DistanceFunction (2) By default, ``EuclideanDistance`` is used: ```wl In[1]:= MeanShiftFilter[[image], 10, .5] Out[1]= [image] ``` --- Specify the distance function: ```wl In[1]:= MeanShiftFilter[[image], 10, .5, DistanceFunction -> ManhattanDistance] Out[1]= [image] ``` #### MaxIterations (1) By default, only one iteration of mean shift is applied to input: ```wl In[1]:= MeanShiftFilter[[image], 3, .1] Out[1]= [image] ``` Use ``MaxIterations`` to specify the number of iterations: ```wl In[2]:= MeanShiftFilter[[image], 3, .1, MaxIterations -> 100] Out[2]= [image] ``` ### Applications (2) Use mean-shift filtering to smooth an image while preserving the edges: ```wl In[1]:= MeanShiftFilter[[image], 4, 0.05, MaxIterations -> 30] Out[1]= [image] ``` --- Use mean-shift filtering as a preprocessing step for image segmentation: ```wl In[1]:= ClusteringComponents[MeanShiftFilter[[image], 3, 0.2], 5]// Colorize Out[1]= [image] ``` ### Properties & Relations (1) ``MeanShiftFilter`` is equivalent to ``MeanFilter`` for distance ``d`` greater than the data dynamic range: ```wl In[1]:= r = 1; data = RandomReal[{0, r}, 100]; In[2]:= MeanShiftFilter[data, 1, r + $MachineEpsilon] == MeanFilter[data, 1] Out[2]= True ``` ### Neat Examples (1) Show how ``MeanShiftFilter`` iteratively shifts values until they converge: ```wl In[1]:= data = Join[RandomReal[NormalDistribution[0, .4], {500, 2}], RandomReal[NormalDistribution[1, .4], {500, 2}]]; In[2]:= ListPlot[data] Out[2]= [image] In[3]:= ms = NestList[MeanShiftFilter[#, 1000, {.6, .6}]&, data, 5]; In[4]:= ListLinePlot[Transpose[ms]] Out[4]= [image] ``` ## See Also * [`MeanFilter`](https://reference.wolfram.com/language/ref/MeanFilter.en.md) * [`MeanShift`](https://reference.wolfram.com/language/ref/MeanShift.en.md) * [`BilateralFilter`](https://reference.wolfram.com/language/ref/BilateralFilter.en.md) * [`GuidedFilter`](https://reference.wolfram.com/language/ref/GuidedFilter.en.md) * [`TrimmedMean`](https://reference.wolfram.com/language/ref/TrimmedMean.en.md) ## Related Guides * [Image Restoration](https://reference.wolfram.com/language/guide/ImageRestoration.en.md) * [Linear and Nonlinear Filters](https://reference.wolfram.com/language/guide/LinearAndNonlinearFilters.en.md) * [Image Processing & Analysis](https://reference.wolfram.com/language/guide/ImageProcessing.en.md) * [Image Filtering & Neighborhood Processing](https://reference.wolfram.com/language/guide/ImageFilteringAndNeighborhoodProcessing.en.md) * [Video Computation: Update History](https://reference.wolfram.com/language/guide/VideoComputation-UpdateHistory.en.md) ## History * [Introduced in 2010 (8.0)](https://reference.wolfram.com/language/guide/SummaryOfNewFeaturesIn80.en.md) \| [Updated in 2015 (10.2)](https://reference.wolfram.com/language/guide/SummaryOfNewFeaturesIn102.en.md) ▪ [2016 (11.0)](https://reference.wolfram.com/language/guide/SummaryOfNewFeaturesIn110.en.md) ▪ [2025 (14.3)](https://reference.wolfram.com/language/guide/SummaryOfNewFeaturesIn143.en.md)