# compression ratio of pixels block

I am new to image compression topic and really appreciate it if someone could help me understand how compression rati works in this case. Assuming I have JPEG lossless coder that encodes the following image:

2 3 4 3
1 A B C


I have used predictive coding and Huffman to obtain the binary representations (codes) for pixels A, B and C:

Which are:

A=0 -> 0
B=3 -> 1101
C=0 -> 0


How can I calculate the compression ratio achieved for coding of the pixels A, B and C (jointly) assuming that the original image has pixel values ranging from 1 to 8?

• The given answer seems quite clear. Do not hesitate to accept it – Laurent Duval Feb 14 '18 at 18:48
• the original image is 256*256 pixel single band (gray scale) 8-bit per pixel this file is 65.536 bytes (64k) after compression the image file is 6.554 byte compression ratio is ? – Ibrahim Shekh Musheer Aug 31 '18 at 12:21

Compression ratio is $$\frac{N_{uncomp}^b}{N_{comp}^b}$$ where ${N_{comp}^b}$ is the total number bits requried to represent those $3$ pixels $A$,$B$, and $C$ while ${N_{uncomp}^b}$ is the total number of bits required when they are not compressed.
Based on your claims, assuming that, those three pixels had $8$ levels with fixed length coding (FLC) of $3$ bits per pixel then; ${N_{uncomp}^b} = 3 \times 3 = 9$ bits in total. And again based on your variable length code (VLC) of the lossless coding scheme which uses $1$ bit for $A$ and $C$ and $4$ bits for $B$ you have ${N_{comp}^b} = 1 + 4 + 1 = 6$ bits in the compressed case, hence the ratio is $$\frac{N_{uncomp}^b}{N_{comp}^b} = \frac{9}{6} = \frac{3}{2}$$
which means a $1.5 \times$ reduction in the number of bits required to represent the same source compared to its uncompressed form.
Note that you can also use the reciprocal of that ratio to indicate a similar metric, which would be $2/3$ in this case indicating the size that compressed form will have compared to the original.