# 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 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:
•  list arbitrary-rank numerical array tseries temporal data such as TimeSeries, TemporalData, … image arbitrary Image or Image3D object audio an Audio 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

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## Basic Examples(3)

Apply an entropy filter to a vector of numbers:

Filter a TimeSeries:

Entropy filtering of random disks:

## Scope(11)

### Data(7)

Apply a moving entropy filter to a vector:

Entropy filtering of a 2D array:

Filter a quantity array:

Filter an Audio signal:

Filtering a 2D grayscale image:

Entropy filtering of a 3D image:

Filter a symbolic array:

### Parameters(4)

Specify one radius to be used in all directions:

Increasing the radius will result in smoother images:

Harmonic filtering just in the first direction:

Second direction:

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

Filtering of the horizontal planes only:

## Applications(3)

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

Entropy filtering can reveal JPEG compression artifacts:

This reveals the presence of padding in an image:

## Properties & Relations(2)

Entropy filtering is the same as ArrayFilter with function Entropy:

Entropy filtering is the same as ImageFilter with function Entropy:

## 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:

Use ColorQuantize to limit the number of possible pixel values:

Wolfram Research (2008), EntropyFilter, Wolfram Language function, https://reference.wolfram.com/language/ref/EntropyFilter.html (updated 2016).

#### Text

Wolfram Research (2008), EntropyFilter, Wolfram Language function, https://reference.wolfram.com/language/ref/EntropyFilter.html (updated 2016).

#### CMS

Wolfram Language. 2008. "EntropyFilter." Wolfram Language & System Documentation Center. Wolfram Research. Last Modified 2016. 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_2024_entropyfilter, author="Wolfram Research", title="{EntropyFilter}", year="2016", howpublished="\url{https://reference.wolfram.com/language/ref/EntropyFilter.html}", note=[Accessed: 24-July-2024 ]}

#### BibLaTeX

@online{reference.wolfram_2024_entropyfilter, organization={Wolfram Research}, title={EntropyFilter}, year={2016}, url={https://reference.wolfram.com/language/ref/EntropyFilter.html}, note=[Accessed: 24-July-2024 ]}