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BilateralFilter
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BilateralFilter

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BilateralFilter[data,σ,μ]

applies a bilateral filter of spatial spread σ and pixel value spread μ to data.

Details and Options

  • BilateralFilter is a nonlinear local filter used for edge-preserving smoothing. The amount of smoothing is dependent on the values of σ and μ.
  • BilateralFilter replaces each pixel by a weighted average of its neighbors, using normalized Gaussian matrices as weights.
  • 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
  • When applied to multichannel audio signals and images, the Euclidean distance between channel vectors is computed.
  • At the data boundaries, BilateralFilter uses smaller neighborhoods.
  • The following options can be given:
  • MaxIterations 1maximum number of iterations
    WorkingPrecision MachinePrecisionthe precision to use
  • BilateralFilter uses a Gaussian matrix of spatial radius 5/2 σ.
  • BilateralFilter always returns an image of a real type.
  • For large values of μ, bilateral filtering yields results similar to Gaussian filtering.

Background & Context

  • BilateralFilter is a filter for smoothing images to remove local variations typically caused by noise, rough textures, etc. BilateralFilter is often used as a preprocessing step before doing other image analysis operations, such as segmentation. Bilateral filtering can also be used to perform unsharp masking by subtracting the filtered image from the original and then adding the original back in.
  • BilateralFilter performs a nonlinear edge-preserving smoothing. The smoothing is done by replacing each pixel with a weighted average of its neighbors, where weights are taken from a normalized Gaussian distribution based on color value similarity. Here, the standard deviation σ and mean μ of the Gaussian distribution are specified as arguments.
  • BilateralFilter works with arbitrary grayscale and color images, as well as with 3D and 2D images. When applied to multichannel images, BilateralFilter does not operate channel-by-channel but rather uses the Euclidean distance between channel vectors.
  • Other edge-preserving filters include MeanShiftFilter and PeronaMalikFilter. Similar filters that are not edge preserving include MeanFilter and GaussianFilter. For large values of the Gaussian distribution mean, bilateral filtering yields results similar to Gaussian filtering.

Examples

open allclose all

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

Bilateral filtering of a vector:

In[5]:=5
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https://wolfram.com/xid/0rkspu6rwxu4h0a-s47pnq
Out[5]=5

Filter a TimeSeries:

In[1]:=1
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https://wolfram.com/xid/0rkspu6rwxu4h0a-wxgjw
In[2]:=2
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https://wolfram.com/xid/0rkspu6rwxu4h0a-g9fo2
Out[2]=2
In[3]:=3
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https://wolfram.com/xid/0rkspu6rwxu4h0a-dulvtd
Out[3]=3

Smooth details in a color image:

In[1]:=1
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https://wolfram.com/xid/0rkspu6rwxu4h0a-w48w8
Out[1]=1

Scope  (7)Survey of the scope of standard use cases

Data  (7)

Bilateral filtering of a list:

In[1]:=1
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https://wolfram.com/xid/0rkspu6rwxu4h0a-txn89d
Out[1]=1

Bilateral filtering of a 2D array:

In[1]:=1
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https://wolfram.com/xid/0rkspu6rwxu4h0a-cxywqj

Filter a TimeSeries:

In[1]:=1
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https://wolfram.com/xid/0rkspu6rwxu4h0a-62t833
In[2]:=2
✖
https://wolfram.com/xid/0rkspu6rwxu4h0a-77v7p5
Out[2]=2
In[3]:=3
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https://wolfram.com/xid/0rkspu6rwxu4h0a-18tdm0
Out[3]=3

Filter an Audio signal:

In[1]:=1
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https://wolfram.com/xid/0rkspu6rwxu4h0a-p90slf
In[2]:=2
✖
https://wolfram.com/xid/0rkspu6rwxu4h0a-o6g2aw
Out[2]=2
In[3]:=3
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https://wolfram.com/xid/0rkspu6rwxu4h0a-j5yrn4
Out[3]=3

Bilateral filtering smooths an image while preserving edges:

In[1]:=1
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https://wolfram.com/xid/0rkspu6rwxu4h0a-c8ikmi
Out[1]=1

Denoise a 3D image:

In[1]:=1
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https://wolfram.com/xid/0rkspu6rwxu4h0a-6llc2h
Out[1]=1

Symbolic computation of a bilateral filter:

In[1]:=1
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https://wolfram.com/xid/0rkspu6rwxu4h0a-lhzs1x
Out[1]=1

Options  (6)Common values & functionality for each option

MaxIterations  (2)

By default, one iteration of bilateral filtering is performed:

In[1]:=1
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https://wolfram.com/xid/0rkspu6rwxu4h0a-h209k4
Out[2]=2

Run more iterations:

In[3]:=3
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https://wolfram.com/xid/0rkspu6rwxu4h0a-0tw4f9
Out[3]=3

Repeatedly filter a TimeSeries:

In[1]:=1
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https://wolfram.com/xid/0rkspu6rwxu4h0a-ovnshr
In[2]:=2
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https://wolfram.com/xid/0rkspu6rwxu4h0a-cg8j2w
Out[2]=2
In[3]:=3
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https://wolfram.com/xid/0rkspu6rwxu4h0a-m0dp7
Out[3]=3

WorkingPrecision  (4)

By default, MachinePrecision is used with integer arrays:

In[9]:=9
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https://wolfram.com/xid/0rkspu6rwxu4h0a-cdrg18
Out[9]=9

Perform exact computation instead:

In[10]:=10
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https://wolfram.com/xid/0rkspu6rwxu4h0a-jt3a9c
Out[10]=10

By default, the precision of the input is used for real arrays:

In[1]:=1
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https://wolfram.com/xid/0rkspu6rwxu4h0a-2q79si
Out[1]=1

Specify the precision to use:

In[2]:=2
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https://wolfram.com/xid/0rkspu6rwxu4h0a-7f69wx
Out[2]=2

With symbolic arrays, exact computation is used:

In[1]:=1
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https://wolfram.com/xid/0rkspu6rwxu4h0a-djfeg5
Out[1]=1

WorkingPrecision is ignored when filtering images:

In[1]:=1
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https://wolfram.com/xid/0rkspu6rwxu4h0a-pc6p9y
Out[1]=1

An image of a real type is always returned:

In[2]:=2
✖
https://wolfram.com/xid/0rkspu6rwxu4h0a-o6dztt
Out[2]=2

Applications  (5)Sample problems that can be solved with this function

Removing noise:

In[1]:=1
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https://wolfram.com/xid/0rkspu6rwxu4h0a-db1px6
Out[1]=1

Create a posterization effect by performing multiple iterations:

In[1]:=1
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https://wolfram.com/xid/0rkspu6rwxu4h0a-bsda0u
Out[1]=1

Bilateral filtering with a large color spread value, used for background removal:

In[1]:=1
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https://wolfram.com/xid/0rkspu6rwxu4h0a-o73w7s
Out[1]=1

Bilateral filtering as a preprocessing step for image segmentation:

In[1]:=1
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https://wolfram.com/xid/0rkspu6rwxu4h0a-qvmskg
Out[1]=1

Unsharp masking using bilateral filtering:

In[1]:=1
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https://wolfram.com/xid/0rkspu6rwxu4h0a-jekwvj
Out[1]=1

Properties & Relations  (2)Properties of the function, and connections to other functions

Bilateral filtering performs noise reduction while preserving edges:

In[1]:=1
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https://wolfram.com/xid/0rkspu6rwxu4h0a-s15v2m
Out[2]=2

MeanFilter also reduces noise, but does not preserve edges:

In[3]:=3
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https://wolfram.com/xid/0rkspu6rwxu4h0a-1qbjvp
Out[3]=3

For large values of the Gaussian distribution mean, bilateral filtering yields results similar to Gaussian filtering:

In[1]:=1
✖
https://wolfram.com/xid/0rkspu6rwxu4h0a-vy4lw
Out[1]=1
Wolfram Research (2010), BilateralFilter, Wolfram Language function, https://reference.wolfram.com/language/ref/BilateralFilter.html (updated 2016).
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Wolfram Research (2010), BilateralFilter, Wolfram Language function, https://reference.wolfram.com/language/ref/BilateralFilter.html (updated 2016).

Text

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

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

CMS

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

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

APA

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

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

BibTeX

@misc{reference.wolfram_2025_bilateralfilter, author="Wolfram Research", title="{BilateralFilter}", year="2016", howpublished="\url{https://reference.wolfram.com/language/ref/BilateralFilter.html}", note=[Accessed: 25-March-2025 ]}

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@misc{reference.wolfram_2025_bilateralfilter, author="Wolfram Research", title="{BilateralFilter}", year="2016", howpublished="\url{https://reference.wolfram.com/language/ref/BilateralFilter.html}", note=[Accessed: 25-March-2025 ]}

BibLaTeX

@online{reference.wolfram_2025_bilateralfilter, organization={Wolfram Research}, title={BilateralFilter}, year={2016}, url={https://reference.wolfram.com/language/ref/BilateralFilter.html}, note=[Accessed: 25-March-2025 ]}

✖
@online{reference.wolfram_2025_bilateralfilter, organization={Wolfram Research}, title={BilateralFilter}, year={2016}, url={https://reference.wolfram.com/language/ref/BilateralFilter.html}, note=[Accessed: 25-March-2025 ]}