entropy2__ ( Regions, Image : : : Entropy, Anisotropy )

Determine the entropy and anisotropy of images.

The operator entropy2__ creates the histogram of relative frequencies of the gray values in the input image and calculates from these frequencies the entropy and the anisotropy coefficient for each region from Regions according to the following formulae:

    Entropy:
                                 255
                                 ----
                                 \
                Entropy  =     - /     rel[i]  *  ld(rel[i])
                                 ----
                                  0

    Anisotropiy coefficient:
                                  k
                                 ----
                                 \
                                 /     rel[i]  *  ld(rel[i])
                                 ----
                                  0
                Anisotropy  =  -----------------------------
                                        Entropy

        where
                rel[i]  histogram of relative gray value frequencies
                i       Gray value of input image (0..255)
        and     k       smallest possible gray value with sum(rel[i]) >= 0.5


Parameters

Regions (input_object)
region(-array) -> object
Regions where the features are to be determined.

Image (input_object)
image -> object : byte
Gray value image.

Entropy (output_control)
real(-array) -> real
Information content (entropy) of the gray values.
Assertion: (0 <= Entropy) && (Entropy <= 8)

Anisotropy (output_control)
real(-array) -> real
Measure of the symmetry of gray value distribution.


Complexity

If F is the area of the region the runtime complexity is O(F + 255).


Result

The operator entropy2__ returns the value TRUE if an image with defined gray values is entered and the parameters are correct. The behavior in case of empty input (no input images available) is set via the operator set_system(::'no_object_result',<Result>:), the behavior in case of empty region is set via set_system(::'empty_region_result',<Result>:). If necessary an exception is raised.


Alternatives

select_grey__


See also

entropy1__, histo__, fuzzy_entropy, fuzzy_perimeter



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