image compression and watermarking · 2017. 11. 20. · reading • digital image processing, 4th...
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Image Compression and Watermarking
Image ProcessingCSE 166
Lecture 14
Reading
• Digital Image Processing, 4th edition– Chapter 7: Image Compression and Watermarking
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Data redundancy in images
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Coding redundancy
Spatial redundancy
Irrelevant information
Does not need all 8 bits
Information is unnecessarily replicated
Information is not useful
Fidelity criteriasubjective (qualitative)
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Approximations
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5.17 15.67 14.17
(a) (b) (c)
Objective (quantitative) qualityrms error (in intensity levels)
Subjective (qualitative) quality, relative
Lower is better
(a) is better than (b).
(b) is better than (c)
Compression system
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Compression methods• Huffman coding• Golomb coding• Arithmetic coding• Lempel‐Ziv‐Welch (LZW) coding• Run‐length coding• Symbol‐based coding• Bit‐plane coding• Block transform coding• Predictive coding• Wavelet coding
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Symbol‐based coding
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(0,2) (3,10) …
Block‐transform coding
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Encoder
Decoder
Block‐transform coding
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Discrete cosine transformWalsh‐Hadamard transform
4x4 subimages (4x4 basis images)
Block‐transform coding
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Fourier transform
cosine transform
Walsh‐Hadamardtransform
2.32 1.78 1.13rms error
Retain 32 largest
coefficients
Error image
8x8 subimages
Lower is better
Block‐transform coding
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2x2 4x4 8x8
Reconstruction error versus subimage size
DCT subimage size:
JPEG uses block DCT‐based coding
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Compression reconstruction
Scaled error image
Zoomed compression reconstruction
25:1
52:1
Compression ratio
Predictive coding model
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Encoder
Decoder
Predictive coding
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Input image
Prediction error image
Example: previous pixel coding
Histograms
Wavelet coding
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Encoder
Decoder
Wavelet coding
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Detail coefficients below 25 are truncated to zero
JPEG‐2000 uses wavelet‐based coding
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Compression reconstruction
Scaled error image
Zoomed compression reconstruction
25:1
52:1
Compression ratio
JPEG‐2000 uses wavelet‐based coding
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Compression reconstruction
Scaled error image
Zoomed compression reconstruction
75:1
105:1
Compression ratio
Image watermarking
• Visible watermarks• Invisible watermarks
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Visible watermark
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Original image minus watermark
Watermarked image
Watermark
Invisible image watermarking system
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Encoder
Decoder
Invisible watermark
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Two least significant
bits
JPEGcompressed
Fragile invisible
watermark
Originalimage Extracted
watermark
Example: watermarking using two least significant bits
Invisible watermark
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Watermarked images
Example: DCT‐based watermarking
Extracted robust invisible
watermark