1. I MAGE C OMPRESSION

2. The goal of image compression is to reduce the amount of data required to represent a digital image.

3. I MAGE C OMPRESSION ( CONT ’ D ) Lossless Information preserving Low compression ratios Lossy Not information preserving High compression ratios Trade-off: information loss vs compression ratio

4. D ATA ≠ I NFORMATION Data and information are not synonymous terms! Data is the means by which information is conveyed. Data compression aims to reduce the amount of data while preserving as much information as possible.

5. D ATA VS I NFORMATION ( CONT ’ D ) The same information can be represented by different amount of data – for example: Your wife, Helen, will meet you at Logan Airport in Boston at 5 minutes past 6:00 pm tomorrow night Your wife will meet you at Logan Airport at 5 minutes past 6:00 pm tomorrow night Helen will meet you at Logan at 6:00 pm tomorrow night Ex1: Ex2: Ex3:

6. C OMPRESSION R ATIO compression Compression ratio:

7. R ELEVANT D ATA R EDUNDANCY Example:

8. T YPES OF D ATA R EDUNDANCY (1) Coding Redundancy (2) Interpixel Redundancy (3) Psychovisual Redundancy Data compression attempts to reduce one or more of these redundancy types.

9. C ODING - D EFINITIONS Code: a list of symbols (letters, numbers, bits etc.) Code word: a sequence of symbols used to represent some information (e.g., gray levels). Code word length: number of symbols in a code word.

10. C ODING - D EFINITIONS ( CONT ’ D ) N x M image r k : k-th gray level l(r k ): # of bits for r k P(r k ): probability of r k Expected value:

11. C ODING R EDUNDANCY Case 1: l(r k ) = constant length Example:

12. C ODING R EDUNDANCY ( CONT ’ D ) Case 2: l(r k ) = variable length variable length Total number of bits: 2.7NM

13. I NTERPIXEL REDUNDANCY Interpixel redundancy implies that pixel values are correlated (i.e., a pixel value can be reasonably predicted by its neighbors). auto-correlation: f(x)=g(x) histograms auto-correlation

14. I NTERPIXEL REDUNDANCY ( CONT ’ D ) To reduce interpixel redundancy, some kind of transformation must be applied on the data (e.g., thresholding, DFT, DWT) Example: original thresholded threshold (1+10) bits/pair 11 ……………0000……………………..11…..000…..

15. P SYCHOVISUAL REDUNDANCY The human eye is more sensitive to the lower frequencies than to the higher frequencies in the visual spectrum. Idea: discard data that is perceptually insignificant!

16. P SYCHOVISUAL REDUNDANCY ( CONT ’ D ) 256 gray levels 16 gray levels + random noise 16 gray levels C=8/4 = 2:1 add a small pseudo-random number to each pixel prior to quantization Example: quantization

17. R EFERENCES CS474/674 – Prof. Bebis