Arithmetic coding for image compression

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haithem abdelghany 2017-7-25

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评论： Walter Roberson 2021-7-16

I am working on the topic of image compression I found built in matlab function for arithmetic coding which is arithenco I want to use it in image compression can any give me example on how to this function for image compression.

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Answer 1

Walter Roberson 2017-7-25

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reshape() the image into a vector. Apply arithmetic encoding.

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Walter Roberson 2017-7-28

在 MATLAB Online 中打开

The size of a .mat can be larger or smaller than the size of the data being saved. You should save into .mat files for ease of recalling data exactly was it was saved; you should not save into .mat files expecting them to be any particular size.

If you are looking at the file size from a data compression point of view, you should be using something like,

fid = fopen('compressed_data.dat', 'w');
fwrite(fid, uint8(length(unique_symbols)) );
fwrite(fid, uint8(unique_symbols));
coded_as_uint8 = uint8(bin2dec(char(buffer(coded_result,8) + '0').'));
unused_bits_of_last_byte = uint8(length(coded_as_uint8) * 8 - length(coded_result) );
fwrite(fid, unused_bits_of_last_byte);
fwrite(fid, coded_as_uint8);
fclose(fid);

This creates a file with the following structure:

a single byte that gives the length of the symbol table
a vector that length of bytes that are the symbols being encoded
a single byte that gives the number of unused bits in the last byte of the data that follows
a vector of the arithenco results converted from a vector of double(0) and double(1) into a stream of bytes by packing 8 bits per byte

The "number of unused bits in the last byte" is there because the conversion of a stream of bits into bytes has a problem if the number of bits being converted is not an exact multiple of 8. The buffer() call (from the Signal Processing Toolbox) puts in 0s for the extra bits and when decoding you need a way to know when to stop decoding and ignore the final few 0s.

There are other approaches that can be used instead of coding the number of unused bits, and some of the other approaches can be pretty useful in some situations, but they are more complicated to decode.

Astha Singh 2021-7-16

can you tell how to save this as an image

Walter Roberson 2021-7-16

在 MATLAB Online 中打开

bytes = uint8([]);
bytes = [bytes, uint8(length(unique_symbols)) ];
bytes = [bytes, uint8(unique_symbols)];
coded_as_uint8 = uint8(bin2dec(char(buffer(coded_result,8) + '0').'));
unused_bits_of_last_byte = uint8(length(coded_as_uint8) * 8 - length(coded_result) );
bytes = [bytes, unused_bits_of_last_byte];
bytes = [bytes, coded_as_uint8];
imwrite(bytes, 'useless_image.tif');

The above will fail if the encoding requires more than 4 gigabytes. You must use .tif to be able to handle that size; if you can be sure that the encoding will be no more than 2 gigabytes (minus one byte) then you can use .png .

.tif and .png files can be used to store arbitrary bytes without loss. (.bmp too, but .bmp has a limit of 30000 bytes for this purpose.)

You will not get any useful output if you ask to display an image created in this way: if the arithematic encoding worked properly, then the output will look pretty much random. Just because you can create an image file does not mean that the image file is understandable to humans.

People keep expecting that compressed images look like... I don't know. A distorted but partly recognizable version of the original, I guess? A smaller and possibly recolored version of the original?

But compression theory says that you can continue to compress until one of two things happens:

the compressed values become statistically indistinguishable from random; or
the overhead needed to describe the data transformations to apply more compression starts to take more space than just listing the compressed bytes as they are.

If you could still make out any resemblence between the original image and the data representing the compressed image, then you did not do a good enough job of compression !!

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Arithmetic coding for image compression

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