1. HOW JEPG WORKS Presented by: Hao Zhong For 6111 Advanced Algorithm Course

2. What is JPEG? How to “transform”? How to “compress”? How does JPEG works? OUTLINE 2

3. WHAT IS JPEG? It is short for “Joint Photographers Experts Group”. JPEG is a type of transform compression. There are two steps here: – TRANSFORM – COMPRESSION 3

4. HOW TO “TRANSFORM” First, let’s see how TRANSFORM would be. DCT is short for “Discrete Cosine Transform”. There are many versions of DCT. – 1-D – 2-D (used in JPEG) 4

5. HOW TO “TRANSFORM” 1-D DCT – imagine a 129-point signal 5

6. HOW TO “TRANSFORM” 1-D DCT – imagine a 129-point signal – duplicate samples to 256 points 6

7. HOW TO “TRANSFORM” 1-D DCT – imagine a 129-point signal – duplicate samples to 256 points – take the Fourier transform of this 256-point signal 129 points in time domain 129 points in frequency domain 7

8. HOW TO “TRANSFORM” 2-D DCT (used in JPEG) – it is taken of an 8*8 group 8

9. HOW TO “TRANSFORM” 2-D DCT (used in JPEG) – it is taken of an 8*8 group – use 64 basis functions 9

10. HOW TO “TRANSFORM” 2-D DCT (used in JPEG) – it is taken of an 8*8 group – use 64 basis functions one-half cycle 10

11. HOW TO “TRANSFORM” 2-D DCT (used in JPEG) – it is taken of an 8*8 group – use 64 basis functions – in the spectrum, each value is the amplitude of a basis function lowest frequency highest frequency 11 Can you imagine how inverse DCT works?

12. HOW TO “COMPRESS” Then let’s see how COMPRESS would be. Two methods – reducing the number of bits used to represent each value 12

13. HOW TO “COMPRESS” Then let’s see how COMPRESS would be. Two methods – reducing the number of bits used to represent each value – Discarding some of the 64 spectral values nearly all of the signal is contained in the low frequency human eyes are not good at distinguishing a high brightness variation reconstructed image 13

14. HOW DOES JPEG WORKS? 1.image is broken into the 8*8 groups 2.DCT is taken of each group 3.each 8*8 spectrum is compressed by both of the above methods Quantization Table 14

15. HOW DOES JPEG WORKS? 1.image is broken into the 8*8 groups 2.DCT is taken of each group 3.each 8*8 spectrum is compressed by both of the above methods 4.the spectrum is converted from an 8*8 array into a linear sequence We want to get more consecutive ‘zero’s. 15

16. HOW DOES JPEG WORKS? 1.image is broken into the 8*8 groups 2.DCT is taken of each group 3.each 8*8 spectrum is compressed by both of the above methods 4.the spectrum is converted from an 8*8 array into a linear sequence 5.compress these runs of zeros by run-length encoding 6.The sequence is encoded by some method (e.g. Huffman encoding) 16

17. HOW DOES JPEG WORKS? Trade-off – the amount of compression – the image quality 17

18. REFERENCES The Scientist and Engineer’s Guide to Digital Signal processing, By Steven W. Smith, Ph.D. http://www.dspguide.com/ch27/6.htm 18

19. THANK YOU! Any questions?