How can I apply Huffman coding correctly? - matlab

Question

I applied the zigzag function after quantization to an image block, and I want to compute the Huffman coding of this block. I understand that the input argument must be a vector, and that the histogram should be calculated.
I wrote the following code, but it doesn't seem to work:
[M N]=size(yce);
fun1=zigzag(yce);
count1 = imhist(fun1);
p1 = count1/ numel(fun1);
[dict1,avglen1]=huffmandict(count1,p1);
comp1= huffmanenco(fun1,dict1);
Im1 = huffmandeco(comp1,dict1);
I get the following error with the huffmandict function:
Error in project at 65
[dict1,avglen1]=huffmandict(count1,p1);
Source symbols repeat.
zigzag.m is a written function in a matlab file.it converts a matrix into a vector,thus eliminating long sequences of zeros.

Answer 1

The Huffman encoding function (huffmandict) in MATLAB requires that the symbols vector (first argument of the function) must all be unique values. This symbols vector is a list of all possible symbols that are seen in your data that you want to encode / compress. As such, it wouldn't make sense to have a list of all symbols to be encountered if there are duplicates. This is much like a dictionary of words, where it wouldn't make sense to see the same word twice in this dictionary. The second parameter of the function is the associated probabilities of occurrence for each symbol in your sequence.
With huffmandict, what you are doing is you are creating a dictionary for Huffman encoding that consists of all possible unique symbols to be encountered when encoding/decoding as well as their associated probabilities. Therefore, by examining your code, you need to extract both the bin locations as well as the probabilities of occurrence when using imhist. Essentially, you need to call the two element output version of imhist. The second output of imhist gives you a list of all possible intensities / symbols that were encountered in the data, while the first element gives you the frequency of each these intensities / symbols in your data. You then normalize the first output element by the total number of symbols / intensities in your data to get the probabilities (assuming equiprobable encounters of course). Once this is complete, you use both of these as input into huffmandict.
In other words, you need to change only two lines of code, thus:
[M N]=size(yce);
fun1=zigzag(yce);
[count1,x] = imhist(fun1); %// Change
p1 = count1/ numel(fun1);
[dict1,avglen1]=huffmandict(x,p1); %// Change
comp1= huffmanenco(fun1,dict1);
Im1 = huffmandeco(comp1,dict1);
Edit
Knowing how fun1 is structured now, do not use imhist. imhist assumes that you are putting in image data, but it doesn't look like that's the case. Instead, try using histc instead to compute the frequency of occurrence. As such, simply modify your code to this:
[M N]=size(yce);
fun1=zigzag(yce);
bins = unique(fun1); %// Change
count1 = histc(fun1, bins); %// Change
p1 = count1/ numel(fun1);
[dict1,avglen1]=huffmandict(bins,p1); %// Change
comp1= huffmanenco(fun1,dict1);
Im1 = huffmandeco(comp1,dict1);
unique finds those unique values that are in your vector so that we can use these as bins to calculate our frequencies. This also figures out the all possible symbols seen in the data.