Image Compression and Watermarking

Image Processing

CSE 166

Lecture 14

Announcements

• Assignment 4 is due May 20, 11:59 PM

• Assignment 5 will be released May 20

– Due May 29, 11:59 PM

• Reading

– Chapter 8: Image Compression and Watermarking

• Sections 8.1, 8.9, 8.10, and 8.12

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Data compression

• Data redundancy

where compression ratio

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where

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

Image information

• Entropy

– It is not possible to encode input image with fewer than bits/pixel

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where

Fidelity criteria,objective (quantitative)

• Total error

• Root-mean-square error

• Mean-square signal to noise ratio (SNR)

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Fidelity criteria,subjective (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

• Example: discrete cosine transform

• Inverse

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where

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

(different watermarks)

Example: DCT-based watermarking

Extracted robust

invisible watermark

Next Lecture

• Morphological image processing

• Reading

– Chapter 9: Morphological image processing

• Sections 9.1, 9.2, 9.3, and 9.5 (through subsection connected components)

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