Chapter 8: Image Compression - Concordia Universityusers.encs.concordia.ca/~weiping/DIP W12/New...

Chapter 8: Image CompressionChapter 8: Image Compression

Images with (a) coding redundancy; (b) spatial redundancy; (c) irrelevant information

© 1992–2008 R. C. Gonzalez & R. E. Woods


For the image in Fig. 8.1(a):



M i I I f tiMeasuring Image Information

Note that the entropy of Fig.8.1(b) is 8 bits/pixel and that of Fig. 8.1(c) is 1.566 bits/pixel



Fid li C i iFidelity Criteria



The rms of the three images are 5.17, 15.67, and 14.17.



Some Basic Compression Methods

Huffman coding:



Huffman coding example:

The entropy of the original image is 7.3838 bits/pixelAfter compression, the number of bits/pixel is 7.428 including the code table.


Hence, C=8/7.428=1.077, R=1- (1/1.077)=0.0715


A ith ti diArithmetic coding: - An entire sequence of source symbols is assigned a single code- No one-to-one correspondence between source symbols and code

dwords



The entropy of the original image is 0.58 decimal digits per source symbol.

After coding 3 decimal digits are required for the 5-After coding, 3 decimal digits are required for the 5symbol message – 0.6 decimal digits/source symbol



LZW coding:-Assigns fixed-length code words to variable-length source sequence- Spatial redundancy is exploited- Spatial redundancy is exploited- Used in a number of imaging file formats like GIF, TIFF, PDF ..



Construction of a codebook or “dictionary” containing the source symbol.



R l th di ti l l it bl f bi iRun-length coding: particularly suitable for binary images

BMP file format – use 2-byte format(a) encoded mode: 1st byte shows # of consecutive pixels;

and 2nd byte gives color index.(b) absolute mode: 1st byte is 0; 2nd byte is shown below( ) y ; y



Bit Pl C diBit-Plane Coding:Decompose an image into a series of binary images and compress each binary image via one of several well-known p y gbinary compression methods



Bl k T f C diBlock Transform Coding:



The choice of a particular transform in a given application depends on the amount ofapplication depends on the amount of reconstruction error that can be tolerated and the computational resources available.



Periodicity of DFT and DCT

Gibbs effect

No Gibbs effect



Selection of subimage size



L l di ti diLossless predictive coding



Lossy predictive codingLossy predictive coding

Delta modulation



O ti l di tOptimal predictor



Optimal quantizer



Wavelet coding

W l t Bl kWavelet vs. Block No subdivision of the original imageNo block artifact



Digital Image Watermarking



W ki i DCT d iWatermarking in DCT domain


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