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

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For the image in Fig. 8.1(a):

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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

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Fid li C i iFidelity Criteria

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

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Some Basic Compression Methods

Huffman coding:

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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.

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

Chapter 8: Image CompressionChapter 8: Image Compression

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

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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

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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 ..

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

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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

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

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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

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Bl k T f C diBlock Transform Coding:

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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.

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Periodicity of DFT and DCT

Gibbs effect

No Gibbs effect

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Selection of subimage size

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L l di ti diLossless predictive coding

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Lossy predictive codingLossy predictive coding

Delta modulation

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O ti l di tOptimal predictor

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Optimal quantizer

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Wavelet coding

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

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Digital Image Watermarking

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W ki i DCT d iWatermarking in DCT domain

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