Operators

# fuzzy_entropy (Operator)

## Name

fuzzy_entropy — Determine the fuzzy entropy of regions.

## Signature

fuzzy_entropy(Regions, Image : : Apar, Cpar : Entropy)

## Description

fuzzy_entropy calculates the fuzzy entropy of a fuzzy set. To do so, the image is regarded as a fuzzy set. The entropy then is a measure of how well the image approximates a white or black image. It is defined as follows:

```
1     ----
h(x) = --------- \    T (l) h(l)
M N ln(2) /     e
----
```

where MxN is the size of the image, and h(l) is the histogram of the image. Furthermore,

```  T (l) = -u(l) ln(u(l)) - (1-u(l)) ln(1-u(l))
e
```

Here, u(x(m,n)) is a fuzzy membership function defining the fuzzy set (see fuzzy_perimeter). The same restrictions hold as in fuzzy_perimeter.

## Attention

Note that for fuzzy_entropy, the Regions must lie completely within the previously defined domain. Otherwise an exception is raised.

## Parallelization

• Multithreading type: reentrant (runs in parallel with non-exclusive operators).
• Automatically parallelized on tuple level.

## Parameters

Regions (input_object)  region(-array) object

Regions for which the fuzzy entropy is to be calculated.

Image (input_object)  singlechannelimage object (byte)

Input image containing the fuzzy membership values.

Apar (input_control)  integer (integer)

Start of the fuzzy function.

Default value: 0

Suggested values: 0, 5, 10, 20, 50, 100

Typical range of values: 0 ≤ Apar ≤ 255 (lin)

Minimum increment: 1

Recommended increment: 5

Cpar (input_control)  integer (integer)

End of the fuzzy function.

Default value: 255

Suggested values: 50, 100, 150, 200, 220, 255

Typical range of values: 0 ≤ Cpar ≤ 255 (lin)

Minimum increment: 1

Recommended increment: 5

Restriction: Apar <= Cpar

Entropy (output_control)  real(-array) (real)

Fuzzy entropy of a region.

## Example (HDevelop)

```* To find a Fuzzy Entropy from an Image
fuzzy_entropy(Trans,Trans,0,255,Entro)
```

## Result

The operator fuzzy_entropy returns the value 2 (H_MSG_TRUE) if the parameters are correct. Otherwise an exception is raised.