Entropy - Maple Help

ImageTools

 Entropy
 compute the entropy of the layers of an image

 Calling Sequence Entropy( img, N, opts )

Parameters

 img - Image; input image N - (optional) posint; number of buckets per layer opts - (optional) equation(s) of the form option = value; specify options for the Entropy command

Options

 • autorange = truefalse
 If true, set the range to the minimum and maximum values that occur in the image (on all layers).  Overrides the range option. The default is false.
 • range = numeric .. numeric
 Assigns the range of values that the buckets cover. The default is 0.0 .. 1.0, which corresponds to the range of values in an unprocessed image.

Description

 • The Entropy command computes the entropy of each layer of an image.
 • The entropy, $H$, of a layer is computed by partitioning the intensities (values) of the pixels in the layer into $N$ buckets, and then computing $H=-\left({\sum }_{i=1}^{N}{P}_{i}{\mathrm{log}}_{2}\left({P}_{i}\right)\right)$, where ${P}_{i}$ is the probability that the intensity of a pixel falls in the $i$-th bucket.
 • The img parameter specifies the image for which the entropy of the layers is computed.
 • The optional N parameter specifies the number of buckets per layer. The default is 256, which is usually suitable for images read from 8-bit per pixel per layer image files.
 • For a single layer (grayscale) image, the Entropy command returns a single value. For 3 or 4 layer images, a list is returned; the i-th element in the list is the entropy of the i-th layer.

Examples

 > $\mathrm{with}\left(\mathrm{ImageTools}\right):$
 > $\mathrm{img}≔\mathrm{Create}\left(100,200,\left(r,c\right)↦\mathrm{evalf}\left(\mathrm{sin}\left(\frac{\mathrm{\pi }\cdot r}{50}\right)\cdot \mathrm{exp}\left(-\frac{c}{50}\right)\right)\right):$
 > $\mathrm{Entropy}\left(\mathrm{img}\right)$
 ${4.17103135635641}$ (1)
 > $\mathrm{Entropy}\left(\mathrm{img},16\right);$$\mathrm{img}≔\mathrm{Create}\left(50,50,\left[\left(r,c\right)↦c\cdot r,\left(r,c\right)↦r+c,\left(r,c\right)↦\mathrm{evalf}\left(\mathrm{sin}\left(\frac{\mathrm{\pi }\cdot r}{25}\right)\right)\right],\mathrm{fit}\right):$
 ${1.65906192348188}$ (2)
 > $\mathrm{Entropy}\left(\mathrm{img}\right)$
 $\left[{7.36142010230650}{,}{6.36454035065060}{,}{4.64385618950637}\right]$ (3)