Just simply compress the images using a compression algorithm. And what would you do for an 11 dimensional data array? For informational entropy it is measured in bytes. If there was, you'd also have to calculate entropy differently for temporally distributed samples. There is also no such concept of spatial distribution within entropy calculation. That's why your entropy calculation returns the same level of entropy for the two images, even though one is clearly less ordered than the other. You proved this yourself with statement 2. It then gets unwieldy without a computer. If you read Shannon's work you see him do this calculation for plain English considering a tree depth of 3 letters. So you have to create a multi dimensional probability tree considering 1, 2, 3. Pk is all possible combinations of grey levels. You think that you can do it, as you've done by considering the number of grey levels. Identically, when I look at you second image I see that the pixels are sorted by gray value, and therefore it doesn't have the same entropy to me as the image with random noise.ĭoes NOT work in practice, for the simple reason that it's almost impossible to determine $P_k$. FLAC can not get around the Shannon's source coding theorem, that's math, but it can look at the file in a way which reduces the entropy of the file, thus do a better compression. FLAC is lossless so all information is preserved. However, if you know the file is an audio file you can compress it using FLAC instead of some generic compressor. All modern compressors will compress a file close to this limit. This limit depends on the entropy of the file. The maximum compression of a file is dictated by the Shannon's source coding theorem which sets an upper limit for how well a compression algorithm can compress a file. However, you probably know it from compression. It might sound counter intuitive that entropy depends on how you look at the problem. Therefore, the two images do not have the same entropy. , X_B=x_B) \sim 1/N^B \rightarrow H_$ is the same value. gray-scale), but how should one extend it in a statistically correct way to multiple bands? For example, for 2 bands, should one base oneself on $(X_1,X_2)$ and thus on PMF using $P(X_1=x_1,X_2=x_2)$? If one has many ($B$>2) bands then $P(X_1=x_1. There are two problems with this definition: Where $K$ is the number of gray levels and $p_k$ is the probability associated with gray level $k$. One intuitive approach is to consider the image as a bag of pixels and compute What is the most information/physics-theoretical correct way to compute the entropy of an image? I don't care about computational efficiency right now - I want it theoretically as correct as possible.
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