WOLFRAM

Wolfram Language & System Documentation Center

EntropyFilter[data,r]

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

EntropyFilter[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  
Possible Issues  
See Also
Related Guides
History
Cite this Page

EntropyFilter

EntropyFilter[data,r]

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

EntropyFilter[data,{r1,r2,…}]

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

Details

  • EntropyFilter returns the local randomness of a signal, commonly used to measure textures in an image. The size of the neighborhood is dependent on the value of r.
  • The function applied to each range-r neighborhood is Entropy.
  • 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
  • EntropyFilter[data,{r1,r2,…}] computes the entropy value in blocks centered on each sample.
  • EntropyFilter assumes the index coordinate system for lists and images.
  • At the data boundaries, EntropyFilter uses smaller neighborhoods.

Examples

open all close all

Basic Examples  (3)

Apply an entropy filter to a vector of numbers:

Wolfram Language code: EntropyFilter[{0, 0, 0, 1, 1, 1, 1, 0, 0, 0}, 1] // N

Filter a TimeSeries:

Wolfram Language code: ts = TemporalData[TimeSeries, {{{-5.284299554283819, 2.5633277538370023, 6.579100030714124, -1.968961681799072, -0.4139386346612976, -1.9026234920486018, -0.6119551311215429, 6.658489816525363, -1.1389707331791818, 2.125399040092273, -2.100657 ... -1.0208703378550394, 4.53291764229072, 0.8063886166734048, -0.556998456633081, 5.892989731928727}}, {{0, 100, 1}}, 1, {"Continuous", 1}, {"Discrete", 1}, 1, {ResamplingMethod -> {"Interpolation", InterpolationOrder -> 1}}}, False, 11.1];
Wolfram Language code: filter = EntropyFilter[ts, 5]
Wolfram Language code: ListLinePlot[{ts, filter}, PlotLegends -> {"original data", "filter"}]

Entropy filtering of random disks:

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

Scope  (11)

Data  (7)

Apply a moving entropy filter to a vector:

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

Entropy filtering of a 2D array:

Wolfram Language code: EntropyFilter[(⁠| | | | | | - | - | - | - | | 1 | 1 | 1 | 0 | | 1 | 1 | 1 | 0 | | 1 | 1 | 0 | 0 | | 0 | 0 | 0 | 0 |⁠), 1]//N//MatrixForm

Filter a quantity array:

Wolfram Language code: data = {Quantity[2, "Meters"], Quantity[1, "Meters"], Quantity[0, "Meters"], Quantity[3, "Meters"], Quantity[0, "Meters"], Quantity[1, "Meters"], Quantity[3, "Meters"], Quantity[1, "Meters"], Quantity[1, "Meters"], Quantity[3, "Meters"], Quantity[3, "Meters"], Quantity[1, "Meters"]};
Wolfram Language code: filtered = EntropyFilter[data, 1]//N

Filter an Audio signal:

Wolfram Language code: a = Import["ExampleData/rule30.wav"];
Wolfram Language code: b = EntropyFilter[a, 15]
Wolfram Language code: AudioPlot[{a, b}]

Filtering a 2D grayscale image:

Wolfram Language code: EntropyFilter[[image], 3]//ImageAdjust

Entropy filtering of a 3D image:

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

Filter a symbolic array:

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

Parameters  (4)

Specify one radius to be used in all directions:

Wolfram Language code: EntropyFilter[[image], 5]

Increasing the radius will result in smoother images:

Wolfram Language code: Table[Labeled[EntropyFilter[[image], r], Text["*r* = " <> ToString@r]], {r, {1, 3, 5}}]

Harmonic filtering just in the first direction:

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

Second direction:

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

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

Wolfram Language code: EntropyFilter[[image], {1, 0, 0}]

Filtering of the horizontal planes only:

Wolfram Language code: EntropyFilter[[image], {0, 1, 1}]

Applications  (3)

Apply entropy filtering to show areas of higher information content with higher intensities:

Wolfram Language code: EntropyFilter[[image], 5]// ImageAdjust

Entropy filtering can reveal JPEG compression artifacts:

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

This reveals the presence of padding in an image:

Wolfram Language code: EntropyFilter[[image], 1]// ImageAdjust

Properties & Relations  (2)

Entropy filtering is the same as ArrayFilter with function Entropy:

Wolfram Language code: r = 1; x = {1, 2, -1, 1, 2, 3, 1, -1, 3, 1}; ArrayFilter[Entropy[Flatten[#]]&, x, r, Padding -> None] == EntropyFilter[x, r][[r + 1 ;; -r - 1]]

Entropy filtering is the same as ImageFilter with function Entropy:

Wolfram Language code: ImageCrop[EntropyFilter[[image], 1], 3] == ImageCrop[ImageFilter[Entropy[Flatten[#]]&, [image], 1], 3]

Possible Issues  (1)

The discrete entropy measure does not apply to real-valued images, since distinct pixel values are unlikely to occur more than once:

Wolfram Language code: EntropyFilter[[image], 3]//ImageAdjust

Use ColorQuantize to limit the number of possible pixel values:

Wolfram Language code: EntropyFilter[ColorQuantize[[image], 16], 3]//ImageAdjust
Wolfram Research (2008), EntropyFilter, Wolfram Language function, https://reference.wolfram.com/language/ref/EntropyFilter.html (updated 2025).

Text

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

CMS

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

APA

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

BibTeX

@misc{reference.wolfram_2026_entropyfilter, author="Wolfram Research", title="{EntropyFilter}", year="2025", howpublished="\url{https://reference.wolfram.com/language/ref/EntropyFilter.html}", note=[Accessed: 12-June-2026]}

BibLaTeX

@online{reference.wolfram_2026_entropyfilter, organization={Wolfram Research}, title={EntropyFilter}, year={2025}, url={https://reference.wolfram.com/language/ref/EntropyFilter.html}, note=[Accessed: 12-June-2026]}