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# Perceptual redundancy perceptual redundancy eye is

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Perceptual Redundancy Perceptual Redundancy Eye is less sensitive to Color High Frequencies So, Allocate more bits/samples to intensity than chromaticity. Allocate more bits to low frequencies than to high frequencies Can play similar tricks with the ear and varying sensitivity to different frequencies (e.g., the “psychoacoustic model” plays a key role in MP3).

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Compression (cont’d) Perceptual Redundancy Block Transform Coding Block Transform Coding Use a transform to convert from spatial domain to another (e.g., a frequency-based one) Win #1: many transforms “pack” the information into parts of the domain better than spatial representations Win #2: Quantize coefficients according to perception (e.g., quantize high frequencies more coarsely than low ones) Problem: artifacts caused by imperfect approximation in one place get spread across the entire image Solution: independently transform and quantize blocks of the image: block transform encoding
Compression (cont’d) Perceptual Redundancy Block Transform Coding Transform Coding: General Structure

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Compression (cont’d) Perceptual Redundancy Block Transform Coding Transform Coding There are many other transforms besides the Fourier Transform, all with the same structure: Forward transform (general form): T ( u , v ) = M X x = 0 N X y = 0 f ( x , y ) g ( x , y , u , v ) Inverse transform (general form): f ( x , y ) = M X u = 0 N X v = 0 T ( u , v ) h ( x , y , u , v ) Most of the time, g ( x , y , u , v ) = h ( x , y , u , v ) (possible normalized, or complex conjugates)
Compression (cont’d) Perceptual Redundancy Block Transform Coding Transform Coding Other basis sets: Walsh-Hadamard Cosine

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Compression (cont’d) Perceptual Redundancy Block Transform Coding Discrete Cosine Transform g ( x , y , u , v ) = h ( x , y , u , v ) = α ( u ) α ( v ) cos ( 2 x + 1 ) u π 2 N cos ( 2 y + 1 ) v π 2 N where α ( u ) = 1 N if u = 0 2 N otherwise
Compression (cont’d) Perceptual Redundancy Block Transform Coding Discrete Cosine Transform How can we get away with cosines and no sines?

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• Winter '08
• Morse,B
• (Cont’d), Codebook, interpixel redundancy, entropy coding

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