Shannon's entropy is a byproduct of information, which, like happiness, is pursued.
Information entropy code#
Once the signals are completely decoded, putting aside any semantic content, they are entropy to the code breakers. So if decoding cryptographic signals, the apparently random inputs are not entropy, but information. Information is found in unexpected signals, which is why newspapers will print an article about a man biting a dog, not the other way around. A sentence "dog bites man" has more entropy than "man bites dog," because the latter is more unexpected. If a signal is predictable it is redundant, and redundancy, under scarce resources, is waste. "Entropy, as defined in information theory, is a measure of how random the message is." Perhaps the writer means a measure of how unpredictable it is, and uses random as a synonym. Just wanted to point out that the last comment may mislead people. * or, if we're thinking in terms of quantum mechanics rather than classical mechanics, it's the amount of information you would gain if you made a measurement such that the system was put into a pure state after the measurement. If you would like to have a deep understanding of the relationship between Shannon entropy and thermodynamics, it is highly recommended that you read this long but awesome paper by Edwin Jaynes. But the only way its entropy can decrease is if we make a measurement, and this decrease in entropy is typically so small it can be neglected. This increases our uncertainty about the system, i.e. The second law of thermodynamics arises because there are a lot of ways we can lose information about a system, for example if the motions of its particles become correlated with the motions of particles in its surroundings. Because you don't know the answer, you can use a probability distribution: $p(\text$ bits or more. For example: suppose you ask me a question to which the possible answers are "yes" and "no", and you have no idea what my answer will be. The entropy only comes in when you don't know which message will be sent. For example, you talk about "the entropy of a message", but what could that mean? Shannon's entropy is a property of a probability distribution, but a message isn't a probability distribution, so a message does not in itself have an entropy. entropy = -np.sum(glcm*np.You have to be careful when thinking about this. If we set to 2, the result is expressed in bits. Where represents the entries of the GLCM. The GLCM (corresponding to the pixel to the right) of the image above is computed as follows: glcm = np.squeeze(greycomatrix(img, distances=,Īnd finally we apply this formula to calculate the entropy: Then we read the image: img = io.imread('') Take a look at this post to learn more.Īs per your request, I'm attaching an example of how the entropy of a GLCM is computed:įirst we import the necessary modules: import numpy as np Notice that the entropy of an image is rather different from the entropy feature extracted from the GLCM (Gray-Level Co-occurrence Matrix) of an image. Where is the number of gray levels (256 for 8-bit images), is the probability of a pixel having gray level, and is the base of the logarithm function. The entropy of an image is defined as follows: