im trying huffman encoding in matlab and reached the part where i get a table with huffman codes, what's next ?

Hello, so i have being trying to implement huffman encoding for an image compression project i got, and in my code im able to reach where i get a table of each symbol and it's code such as the one im posting below, but im not quite sure what i do after this, should i replace each pixel in my image with the new code as a string, or should i combine multiple codes and store each 8 bits on it own, or what ? since you cant save a value as binary in matlab im not quite sure where to go from this

Symbol  Probablity      Code

1	0.947429656982422	"0"
8	0.0165405273437500	"100"
7	0.00766372680664063	"101"
9	0.00628662109375000	"1100"
15	0.00466156005859375	"11010"
6	0.00458145141601563	"11011"
5	0.00319671630859375	"11100"
10	0.00265502929687500	"11101"
4	0.00210571289062500	"111100"
11	0.00152206420898438	"111101"
3	0.00105667114257813	"1111100"
12	0.00102996826171875	"1111101"
13	0.000568389892578125	"1111110"
2	0.000389099121093750	"11111110"
14	0.000308990478515625	"111111110"
0	3.81469726562500e-06	"111111111"

Answer 1

[charan]

Hi,

If you replace the pixel values with the code and store them in order you get a binary representation of image that is shorter than the original image representation, in this way image compression can be achieved. You can refer to the below code that shows similar workflow on a matrix:

img = randi(15,4)

img = 4×4

15 4 11 3 13 8 1 13 1 5 1 1 7 1 4 1

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symbols = unique(img);
counts = histc(img, symbols);
p = counts / sum(counts);
dict = huffmandict(symbols, p) 

dict = 9x2 cell array
    {[ 1]}    {[        1]}
    {[ 3]}    {[0 0 0 0 1]}
    {[ 4]}    {[    0 0 1]}
    {[ 5]}    {[0 0 0 0 0]}
    {[ 7]}    {[0 0 0 1 1]}
    {[ 8]}    {[0 0 0 1 0]}
    {[11]}    {[  0 1 0 1]}
    {[13]}    {[    0 1 1]}
    {[15]}    {[  0 1 0 0]}

img_enc = huffmanenco(img(:), dict)'

img_enc = 1×46

0 1 0 0 0 1 1 1 0 0 0 1 1 0 0 1 0 0 0 1 0 0 0 0 0 0 1 0 1 0

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img2=reshape(huffmandeco(img_enc,dict),4,4)

img2 = 4×4

15 4 11 3 13 8 1 13 1 5 1 1 7 1 4 1

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The "img_enc" shows the encoded image representation. With the dictionary available the image can be decoded from the binary representation.