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MeanShiftFilter
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MeanShiftFilter

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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.

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MeanShiftFilter[data,{r1,r2,…},d]

uses ri for filtering the ^(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.
  • The function applied to each range-r neighborhood is MeanShift.
  • 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, the distance is computed between channel vectors.
  • MeanShiftFilter[data,{r1,r2,…},d] computes the mean shift value in blocks centered on each sample.
  • MeanShiftFilter assumes the index coordinate system for lists and images.
  • At the data boundaries, MeanShiftFilter uses smaller neighborhoods.
  • The following options can be given:
  • DistanceFunction EuclideanDistancehow to compute the distance between values
    MaxIterations 1maximum 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

Examples

open allclose all

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

Mean-shift filtering of a vector:

In[1]:=1
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https://wolfram.com/xid/0fq3vtnyg10bu-s47pnq
Out[1]=1

Filter a TimeSeries:

In[1]:=1
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https://wolfram.com/xid/0fq3vtnyg10bu-wxgjw
In[2]:=2
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https://wolfram.com/xid/0fq3vtnyg10bu-g9fo2
Out[2]=2
In[3]:=3
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https://wolfram.com/xid/0fq3vtnyg10bu-dulvtd
Out[3]=3

Mean-shift filtering of a color image:

In[1]:=1
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https://wolfram.com/xid/0fq3vtnyg10bu-oefipw
Out[1]=1

Scope  (11)Survey of the scope of standard use cases

Data  (6)

Mean-shift filtering of data:

In[1]:=1
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https://wolfram.com/xid/0fq3vtnyg10bu-39jnjr
Out[1]=1

Mean-shift filtering of a 2D array:

In[1]:=1
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https://wolfram.com/xid/0fq3vtnyg10bu-cxywqj

Filter a TimeSeries:

In[1]:=1
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https://wolfram.com/xid/0fq3vtnyg10bu-62t833
In[2]:=2
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https://wolfram.com/xid/0fq3vtnyg10bu-77v7p5
Out[2]=2
In[3]:=3
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https://wolfram.com/xid/0fq3vtnyg10bu-18tdm0
Out[3]=3

Filter an Audio signal:

In[1]:=1
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https://wolfram.com/xid/0fq3vtnyg10bu-p90slf
In[2]:=2
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https://wolfram.com/xid/0fq3vtnyg10bu-o6g2aw
Out[2]=2
In[3]:=3
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https://wolfram.com/xid/0fq3vtnyg10bu-j5yrn4
Out[3]=3

Mean-shift filtering of a grayscale image:

In[1]:=1
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https://wolfram.com/xid/0fq3vtnyg10bu-nddd2h
Out[1]=1

Mean-shift filtering of a 3D image:

In[1]:=1
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https://wolfram.com/xid/0fq3vtnyg10bu-bjekx4
Out[1]=1

Parameters  (5)

Specify one radius to be used in all directions:

In[11]:=11
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https://wolfram.com/xid/0fq3vtnyg10bu-tlzgi7
Out[11]=11

Mean-shift filtering in just the first direction:

In[1]:=1
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https://wolfram.com/xid/0fq3vtnyg10bu-gdx3zh
Out[1]=1

Filtering in just the second direction:

In[1]:=1
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https://wolfram.com/xid/0fq3vtnyg10bu-79md3z
Out[1]=1

Mean-shift filtering of a 3D image in the vertical direction only:

In[1]:=1
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https://wolfram.com/xid/0fq3vtnyg10bu-camcbp
Out[1]=1

Mean-shift filtering of a 3D image in the horizontal planes only:

In[2]:=2
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https://wolfram.com/xid/0fq3vtnyg10bu-5u7xo
Out[2]=2

Mean-shift filter averages only over pixels that differ in value by less than d:

In[1]:=1
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https://wolfram.com/xid/0fq3vtnyg10bu-e9uvy3
Out[1]=1

Options  (3)Common values & functionality for each option

DistanceFunction  (2)

By default, EuclideanDistance is used:

In[29]:=29
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https://wolfram.com/xid/0fq3vtnyg10bu-vy4lw
Out[29]=29

Specify the distance function:

In[1]:=1
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https://wolfram.com/xid/0fq3vtnyg10bu-4g3vi2
Out[1]=1

MaxIterations  (1)

By default, only one iteration of mean shift is applied to input:

In[1]:=1
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https://wolfram.com/xid/0fq3vtnyg10bu-fnsh5o
Out[1]=1

Use MaxIterations to specify the number of iterations:

In[1]:=1
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https://wolfram.com/xid/0fq3vtnyg10bu-zzjjv
Out[1]=1

Applications  (2)Sample problems that can be solved with this function

Use mean-shift filtering to smooth an image while preserving the edges:

In[6]:=6
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https://wolfram.com/xid/0fq3vtnyg10bu-328wxm
Out[6]=6

Use mean-shift filtering as a preprocessing step for image segmentation:

In[1]:=1
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https://wolfram.com/xid/0fq3vtnyg10bu-b0tv2
Out[1]=1

Properties & Relations  (1)Properties of the function, and connections to other functions

MeanShiftFilter is equivalent to MeanFilter for distance d greater than the data dynamic range:

In[23]:=23
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https://wolfram.com/xid/0fq3vtnyg10bu-eoy13k
In[25]:=25
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https://wolfram.com/xid/0fq3vtnyg10bu-1qqmmg
Out[25]=25

Neat Examples  (1)Surprising or curious use cases

Show how MeanShiftFilter iteratively shifts values until they converge:

In[1]:=1
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https://wolfram.com/xid/0fq3vtnyg10bu-2q9fdn
In[2]:=2
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https://wolfram.com/xid/0fq3vtnyg10bu-2g9n2v
Out[2]=2
In[3]:=3
✖
https://wolfram.com/xid/0fq3vtnyg10bu-v27t6q
In[4]:=4
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https://wolfram.com/xid/0fq3vtnyg10bu-w91jgl
Out[4]=4
Wolfram Research (2010), MeanShiftFilter, Wolfram Language function, https://reference.wolfram.com/language/ref/MeanShiftFilter.html (updated 2016).
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Wolfram Research (2010), MeanShiftFilter, Wolfram Language function, https://reference.wolfram.com/language/ref/MeanShiftFilter.html (updated 2016).

Text

Wolfram Research (2010), MeanShiftFilter, Wolfram Language function, https://reference.wolfram.com/language/ref/MeanShiftFilter.html (updated 2016).

✖
Wolfram Research (2010), MeanShiftFilter, Wolfram Language function, https://reference.wolfram.com/language/ref/MeanShiftFilter.html (updated 2016).

CMS

Wolfram Language. 2010. "MeanShiftFilter." Wolfram Language & System Documentation Center. Wolfram Research. Last Modified 2016. https://reference.wolfram.com/language/ref/MeanShiftFilter.html.

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Wolfram Language. 2010. "MeanShiftFilter." Wolfram Language & System Documentation Center. Wolfram Research. Last Modified 2016. https://reference.wolfram.com/language/ref/MeanShiftFilter.html.

APA

Wolfram Language. (2010). MeanShiftFilter. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/MeanShiftFilter.html

✖
Wolfram Language. (2010). MeanShiftFilter. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/MeanShiftFilter.html

BibTeX

@misc{reference.wolfram_2025_meanshiftfilter, author="Wolfram Research", title="{MeanShiftFilter}", year="2016", howpublished="\url{https://reference.wolfram.com/language/ref/MeanShiftFilter.html}", note=[Accessed: 29-March-2025 ]}

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@misc{reference.wolfram_2025_meanshiftfilter, author="Wolfram Research", title="{MeanShiftFilter}", year="2016", howpublished="\url{https://reference.wolfram.com/language/ref/MeanShiftFilter.html}", note=[Accessed: 29-March-2025 ]}

BibLaTeX

@online{reference.wolfram_2025_meanshiftfilter, organization={Wolfram Research}, title={MeanShiftFilter}, year={2016}, url={https://reference.wolfram.com/language/ref/MeanShiftFilter.html}, note=[Accessed: 29-March-2025 ]}

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@online{reference.wolfram_2025_meanshiftfilter, organization={Wolfram Research}, title={MeanShiftFilter}, year={2016}, url={https://reference.wolfram.com/language/ref/MeanShiftFilter.html}, note=[Accessed: 29-March-2025 ]}