Image Compression (in addition to notes) - BGUiip/slides/compression.pdf · Image Compression (in...
Transcript of Image Compression (in addition to notes) - BGUiip/slides/compression.pdf · Image Compression (in...
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IIP1
Image Compression (in addition to notes)
• Motivation/application/Taxonomy
• Redundant vs. irrelevant information
• Lossless compression techniques
• Lossy compression techniques
• Graphics file formats
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Image Compression – Motivation
Example: A video-based CD-ROM application
• Full-motion video, 30 fps, 720x480 resolution
generates 20.736 Mbytes/s
• Storing 31 s of video on a 650 Mbytes CD-ROM
• Compression increases storage capacity to
74 min for VHS-grade video quality
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Applications of Image, Video & Audio Compression
Bhaskaran & Konstantinides, 1997
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A Taxonomy of Image, Video & Audio Compression Methods
Bhaskaran & Konstantinides, 1997Bhaskaran & Konstantinides, 1997
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IIP5
Redundant vs. IrrelevantInformation
: הודעה למשהתפגוש אותך בשדה התעופה , שו לה, אשתך ה יקרה ". " מחר בע רב6- דקות ל 5-גוריון ב לוד ב -בן
5-גורי ון ב -שולה תפגוש אותך בשדה התעופה בן " . " מחר בע רב6-דקות ל
." מחר ב ע רב6-גוריון ב -שו לה תפגוש אותך ב בן "
IIP6
Lossless vs. Lossy Image Compression
• Lossless compression techniques (dictionary: RLE, LZW; statistical: Huffman) – only redundant; small ratios (less than 3:1)
• Lossy compression techniques (scalar quantization; transform image coding (DFT, DCT, Hadamard)) – also irrelevant; larger ratios (even more than 100:1)
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Lossless & Lossy Compression –Coding Framework
Note: Most compression standards employ both lossy the losslessschemes to achieve high coding efficiency
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Lossless Compression (1) –Differential Coding (1)
• If pixels are in the order x1,…,xN, then instead of compressing the pixels, compress the prediction residuals
0 and
,1 ,
0
1
==−= −
x
Nixxy iii
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Lossless Compression (2)–Differential Coding (2)
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1~ 8 for the image ( ) no compression1
( ) log 255
8 for the residual image ( ) compression
ii
ii
bits pI s
pbits p
≈ →= = < ↑ →
residualspixel
values
the residual has smaller entropy thus higher compression ratios may be obtained
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Lossless Compression (3) – Run-Length Encoding (RLE) (1)
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Lossless Compression (4) –RLE (2): An Example
0
20
40
60
80
100
120
1 3 5 7 9 11 13 15 17 19
pixel number
grey
leve
l
The RLE code of the given section of raw image is: 4,30;3,50;2,25;7,100;1,50;2,0
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Lossless Compression (5) –Lempel-Ziv-Welch (LZW)
Compression• LZ77 LZ78 LZW
• Builds up a code during file encoding
• In the first time a string appears it is stored with its code, thereafter only the code
• No separate dictionary is needed (as for RLE) since the code is part of the file
• GIF, TIFF, modem & text compression, PS level 2 (photoshop)
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Lossless Compression (6)–Huffman Coding (1)
• The main idea behind statistical encoding techniques is to represent frequently occurring characters in the file with fewer bits than less commonly occurring ones.
• A good example is Morse coding invented for telegraph coding. Morse codes often used letters (e.g., the letter e) using single symbols (dot in the case of e) and much less common letters using a sequence of symbols (e.g., dash, dash, dot, dot for z).
• Huffman Coding uses a binary encoding tree for representing commonly occurring values in few bits and less common values in more bits.
D. Huffman, 1952
IIP14
Lossless Compression (7)–Huffman Coding (2)
Construction procedure:1. Arrange symbols s1,…,sN with probabilities of
occurrence p1,…,pN such that .Assign a tree leaf node to each symbol
2. Merge 2 nodes with the smallest probabilities by replacing sN-1 & sN with HN-1 that has a probability of occurrence pN-1 + pN (sN-1 & sN are mutually exclusive thus )
3. Arbitrarily assign 1 & 0 to each pair of branches merging into a node
4. Repeat the previous steps until the final set has only one member (establishing a binary tree)
Npppp ≥≥≥≥ ...321
1 1( ) ( ) ( )N N N NP S S P S P S− −+ = +
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Lossless Compression (8)– Huffman Codeword Construction (3)
Bhaskaran & Konstantinides, 1997
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Lossless Compression (9)–Huffman Coding (4)
• Facsimile compression standards (Group 3, Group 4 etc.) yield compression ratios of 20:1 to 50:1
(B/W run-length encoding + Huffman coding)
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Lossy Compression (1) – DPCM
Jain, 1989
e
e*
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Lossy Compression (2) –Transform Image Coding (1)
• Transform the image; discard near zero coefficients; quantize small coefficients coarsely; repeat for blocks; transmit/store large coefficients
• As block size increases, higher compression ratios are achieved for the same distortion level
• Spatial-domain block coding: pixels are grouped into blocks which are then compressed
• Transform-domain block coding: blocks are first transformed to another domain and less important information in the transformed domain is discarded (DFT, DCT, DHT)
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Lossy Compression (3) –Transform Image Coding (2): DCT-Based Coding System
Bhaskaran & Konstantinides, 1997
IIP20
Lossy Compression (4) – DCT (2)
• See previous lectures
• DCT has high compaction level and is image independent
• Used in almost all image & video compression methods
• Block size of 8x8; 64 waveforms
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IIP21
Lossy Video Compression (1)
• 1st, reduce temporal redundancy
(the difference frame has many pixels near zero high compression ratios)
interframe coder
• 2nd, reduce spatial redundancy (as for still image; e.g., DCT)
intraframe coder
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Lossy Video Compression (2) –Motion Compensation
coder
decoder
Bhaskaran & Konstantinides, 1997
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Lossy Video Compression (3) –Motion Estimation
N=M=16
p=15 head & shoulder
p=63 sporting events
Bhaskaran & Konstantinides, 1997
IIP24
Data Types
Vector Data
Bitmap Data
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Graphics File Formats (1)• TIFF, GIF
• BMP, PCX
• JPEG (still images)
• MPEG-1, MPEG-2 (video storage & broadcasting)
• H.261 & H.263 (video conferencing)
• MPEG-4, MPEG-7 (next generation of audiovisual coding standard)
• MPEG & Dolby AC-3 (audio coding)
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Graphics File Formats (2) – TIFF (1)
Murray & vanRyper, 1996
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Graphics File Formats (3) – TIFF (2)
Murray & vanRyper, 1996
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Graphics File Formats (4) –The JPEG Standard (1)
• Joint Photographic Experts Group (1980; 1992)
• Continuous effort to establish state of the art image compression
• Tradeoff easily between compression and image quality
• Modest computational complexity (software-only implementation)
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Graphics File Formats (5) –The JPEG Standard (2)
Murray & vanRyper, 1996
IIP30
JPEG (3)Castleman, 1996
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Graphics File Formats (7)
Castleman, 1996
compression statistics for previous picture
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The MPEG Video Standards (1)
• MPEG-1 (1991) – coding video+audio ≤ 1.5 Mbit/s (CD-ROM)
• MPEG-2 (1994) – ≤ 100 Mbit/s (HDTV)• MPEG-4 (1999) – various communication paradigms
(interactive telecommunication broadcast & internet); object-based paradigm for scene representation (compared to frame-based of MPEG-1&2)
• MPEG-7 – associate with the content allowing search; description of shape, size, texture and color (digital libraries, multimedia directory services (yellow pages),…)
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The MPEG Video Standards (2)
Compression functions:
• Sample rate reduction in spatial & temporal domains of both luminance & chrominance
• Block-based DCT for the intraframes & interframes
• Block-based motion compensation
• Huffman coding for the lossless compression of motion vectors & quantised DCT coefficients
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The MPEG Video Standards (3) –MPEG-1 Encoder
Bhaskaran & Konstantinides, 1997
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The MPEG Video Standards (4) –MPEG-4
Bhaskaran & Konstantinides, 1997
VOP –video object
plane