Image Compression and Watermarking
Image Processing CSE 166 Lecture 13 Announcements
• Assignment 5 is due Nov 23, 11:59 PM • Quiz 5 is Nov 25 • Assignment 6 will be released Nov 23 – Due Dec 2, 11:59 PM • Reading – Chapter 8: Image Compression and Watermarking • Sections 8.1, 8.9, 8.10, and 8.12
CSE 166, Fall 2020 2 Data compression
• Data redundancy
where compression ratio
where
CSE 166, Fall 2020 3 Data redundancy in images
Coding Spatial Irrelevant redundancy redundancy information
Does not need all Information is Information is 8 bits unnecessarily not useful replicated
CSE 166, Fall 2020 4 Image information
• Entropy
where
– It is not possible to encode input image with fewer than bits/pixel
CSE 166, Fall 2020 5 Fidelity criteria, objective (quantitative) • Total error
• Root-mean-square error
• Mean-square signal to noise ratio (SNR)
CSE 166, Fall 2020 6 Fidelity criteria, subjective (qualitative)
CSE 166, Fall 2020 7 Approximations Objective (quantitative) quality rms error (in intensity levels) Lower is 5.17 15.67 14.17 better
(a) (b) (c) (a) is better Subjective (qualitative) quality, relative than (b), (b) is better CSE 166, Fall 2020 than (c)8 Compression system
CSE 166, Fall 2020 9 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
CSE 166, Fall 2020 10 Symbol-based coding
(0,2) (3,10) …
CSE 166, Fall 2020 11 Block-transform coding
Encoder
Decoder
CSE 166, Fall 2020 12 Block-transform coding
• Example: discrete cosine transform
where
• Inverse
CSE 166, Fall 2020 13 Block-transform coding 4x4 subimages (4x4 basis images)
Walsh-Hadamard transform Discrete cosine transform
CSE 166, Fall 2020 14 Block-transform coding 8x8 Walsh- subimages Fourier Hadamard cosine transform transform transform
Retain 32 largest coefficients
Error image
Lower is rms error 2.32 1.78 1.13 CSE 166, Fall 2020 better 15 Block-transform coding
Reconstruction error versus subimage size
DCT subimage size: 2x2 4x4 8x8 CSE 166, Fall 2020 16 JPEG uses block DCT-based coding Zoomed Compression Scaled error compression reconstruction image reconstruction
25:1
Compression ratio
52:1
CSE 166, Fall 2020 17 Predictive coding model
Encoder
Decoder
CSE 166, Fall 2020 18 Predictive coding Example: previous pixel coding
Input image
Histograms
Prediction error image
CSE 166, Fall 2020 19 Wavelet coding
Encoder
Decoder
CSE 166, Fall 2020 20 Wavelet coding
Detail coefficients below 25 are truncated to zero
CSE 166, Fall 2020 21 JPEG-2000 uses wavelet-based coding Zoomed Compression Scaled error compression reconstruction image reconstruction
25:1
Compression ratio
52:1
CSE 166, Fall 2020 22 JPEG-2000 uses wavelet-based coding Zoomed Compression Scaled error compression reconstruction image reconstruction
75:1
Compression ratio
105:1
CSE 166, Fall 2020 23 Image watermarking
• Visible watermarks • Invisible watermarks
CSE 166, Fall 2020 24 Visible watermark Watermark
Watermarked Original image image minus watermark CSE 166, Fall 2020 25 Invisible image watermarking system
Encoder
Decoder
CSE 166, Fall 2020 26 Invisible watermark Example: watermarking using two least significant bits
Original image Extracted watermark Two least significant bits
JPEG Fragile compressed invisible watermark
CSE 166, Fall 2020 27 Invisible watermark Example: DCT-based watermarking
Watermarked Extracted images robust (different invisible watermarks) watermark
CSE 166, Fall 2020 28 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)
CSE 166, Fall 2020 29