compression

compression - CS148: Introduction to Computer Graphics and...

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CS148: Introduction to Computer Graphics and Imaging Compression
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CS148 Lecture 16 Pat Hanrahan, Winter 2009 Key Concepts Lossless vs. lossy compression Kolmolgorev complexity Predictive coding / Hu f man coding JPEG / Discrete cosine transform (DCT) JPEG2000 / Wavelets
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CS148 Lecture 16 Pat Hanrahan, Winter 2009 Image and Video Data Rates Image 640x480x24b = ~3/4 MB Full screen Image 1024x768x24b = ~2.5MB DVD 720x480x24bx30f/s = ~30 MB/s High Definition DVD 1920x1080x24bx30f/s = ~178MB/s Film 4000x3000x36bx30f/s = ~1.5GB/s 8 TB for one 90 minute movie!
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CS148 Lecture 16 Pat Hanrahan, Winter 2009 Lossless vs. Lossy Compression Lossless All information stored Exact original can be reconstructed Lossy Some information discarded Goal: discard information humans won’t notice Much higher compression ratios possible
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CS148 Lecture 16 Pat Hanrahan, Winter 2009 Kolmogorov Complexity What is the shortest program that can generate the data? 17 KB JPEG Re(c), Im(c), xmin, xmax, ymin, ymax (24B) z 0 = x + iy z n +1 = z 2 n + c
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CS148 Lecture 16 Pat Hanrahan, Winter 2009 Run Length Encoding BWBBBBBBBBBBBBWWWWWWBBBW BW\{12}B\{6}W\{3}BW
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CS148 Lecture 16 Pat Hanrahan, Winter 2009 Code Book Alphabet: A, B, C, D Frequencies: ¼ , ¼ , ¼ , ¼ Code: 00, 01, 10, 11 ABCDBDAC = 8 characters 00 01 10 11 01 11 00 11 = 16 bits ¼ * 2 + ¼ * 2 + ¼ * 2 + ¼ * 2 = 2 bits/ch on average
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CS148 Lecture 16 Pat Hanrahan, Winter 2009 Code Book Alphabet: A, B, C, D Frequencies: ½ , ¼ , 1/8, 1/8 Code: 0, 10, 110, 111 ABACADAB = 8 characters 0 10 0 110 0 111 0 10 = 14 bits ½ * 1 + ¼ * 2 +1/8 * 3 +1/8 * 3 = 1 ¾ bits/ch on average
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CS148 Lecture 16 Pat Hanrahan, Winter 2009 Entropy
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CS148 Lecture 16 Pat Hanrahan, Winter 2009 Hu f man Coding A (.10) B (.15) C (.30) D (.16) E (.29)
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CS148 Lecture 16 Pat Hanrahan, Winter 2009 Hu f man Coding A (.10) B (.15) C (.30) D (.16) E (.29) AB (.25) 0 1
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compression - CS148: Introduction to Computer Graphics and...

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