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

Transcription

1 Images with (a) coding redundancy; (b) spatial redundancy; (c) irrelevant information R. C. Gonzalez & R. E. Woods

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3 For the image in Fig. 8.1(a): R. C. Gonzalez & R. E. Woods

4 Measuring Image Information Note that the entropy of Fig.8.1(b) is 8 bits/pixel and that of Fig. 8.1(c) is bits/pixel R. C. Gonzalez & R. E. Woods

5 Fidelity Criteria R. C. Gonzalez & R. E. Woods

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7 The rms of the three images are 5.17, 15.67, and R. C. Gonzalez & R. E. Woods

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10 Huffman coding: Some Basic Compression Methods R. C. Gonzalez & R. E. Woods

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12 Huffman coding example: The entropy of the original image is bits/pixel After compression, the number of bits/pixel is including the code table. Hence, C=8/7.428=1.077, R=1- (1/1.077)= R. C. Gonzalez & R. E. Woods

13 Arithmetic coding: - An entire sequence of source symbols is assigned a single code - No one-to-one correspondence between source symbols and code words R. C. Gonzalez & R. E. Woods

14 The entropy of the original image is 0.58 decimal digits per source symbol. After coding, 3 decimal digits are required for the 5- symbol message 0.6 decimal digits/source symbol R. C. Gonzalez & R. E. Woods

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

16 Construction of a codebook or dictionary containing the source symbol R. C. Gonzalez & R. E. Woods

17 Run-length coding: particularly suitable for binary images BMP file format use 2-byte format (a) encoded mode: 1 st byte shows # of consecutive pixels; and 2 nd byte gives color index. (b) absolute mode: 1 st byte is 0; 2 nd byte is shown below R. C. Gonzalez & R. E. Woods

18 Bit-Plane Coding: Decompose an image into a series of binary images and compress each binary image via one of several well-known binary compression methods R. C. Gonzalez & R. E. Woods

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21 Block Transform Coding: R. C. Gonzalez & R. E. Woods

22 DFT: Hadamard: DCT: R. C. Gonzalez & R. E. Woods

23 The choice of a particular transform in a given application depends on the amount of reconstruction error that can be tolerated and the computational resources available R. C. Gonzalez & R. E. Woods

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27 Periodicity of DFT and DCT Gibbs effect No Gibbs effect R. C. Gonzalez & R. E. Woods

28 Selection of subimage size R. C. Gonzalez & R. E. Woods

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34 Lossless predictive coding R. C. Gonzalez & R. E. Woods

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37 Lossy predictive coding Delta modulation R. C. Gonzalez & R. E. Woods

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39 Optimal predictor R. C. Gonzalez & R. E. Woods

40 Normally, we need R. C. Gonzalez & R. E. Woods

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42 Optimal quantizer R. C. Gonzalez & R. E. Woods

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44 Wavelet coding Wavelet vs. Block: No subdivision of the original image No block artifact R. C. Gonzalez & R. E. Woods

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50 Digital Image Watermarking R. C. Gonzalez & R. E. Woods

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53 Watermarking in DCT domain R. C. Gonzalez & R. E. Woods