lecture10_TransformCoding_JPEG

lecture10_TransformCoding_JPEG - 1 Lossy Image Compression...

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Unformatted text preview: 1 Lossy Image Compression and JPEG standard Yao Wang Polytechnic University, Brooklyn, NY 11201 With contribution from Zhu Liu, and Gonzalez/Woods, Digital Image Processing, 2ed and A. K. Jain, Fundamentals of Digital Image Processing Yao Wang, NYU-Poly EL5123: Transform Coding and JPEG 2 Lecture Outline • Introduction • Quantization Revisited – General description of quantizer – Uniform quantization • Transform coding – Review of linear and unitary transform, 1D and 2D – DCT – Quantization of transform coefficients – Runlength coding of DCT coefficients • JPEG standard overview 2 Yao Wang, NYU-Poly EL5123: Transform Coding and JPEG 3 A Typical Compression System Transfor- mation Quanti- zation Binary Encoding Prediction Transforms Model fitting …... Scalar Q Vector Q Fixed length Variable length (Huffman, arithmetic, LZW) Input Samples Transformed parameters Quantized parameters Binary bitstreams • Motivation for transformation --- To yield a more efficient representation of the original samples. Yao Wang, NYU-Poly EL5123: Transform Coding and JPEG 4 Quantization (Review) • General description • Uniform quantizer 3 Yao Wang, NYU-Poly EL5123: Transform Coding and JPEG 5 General Description of Quantization Quantizer f Q(f) f Q(f) r r 1 r 5 t 1 t 2 t 5 Decision Levels {t k , k = 0, …, L} Reconstruction Levels {r k , k = 0, …, L-1} If ) , [ 1 + ∈ k k t t f Then Q(f) = r k t 6 Quantizer error L levels need bits L R 2 log = t 3 t 7 r 2 r 3 t 4 r 4 r 6 r 7 x returns the smallest integer that is bigger than or equal to x f t 1 t 2 t 3 t 4 t 5 t 6 t 7 r 1 r 2 r 3 r 4 r 5 r 6 r 7 r t =- ∞ t 8 = ∞ Yao Wang, NYU-Poly EL5123: Transform Coding and JPEG 6 Uniform Quantization • Equal distances between adjacent decision levels and between adjacent reconstruction levels – t l – t l-1 = r l – r l-1 = q • Parameters of Uniform Quantization – L: levels (L = 2 R ) – B: dynamic range B = f max – f min – q: quantization interval (step size) – q = B/L = B2-R 4 Yao Wang, NYU-Poly EL5123: Transform Coding and JPEG 7 Uniform Quantization: Functional Representation min min 2 ) ( f q q q f f f Q + + * - = f Q(f) t t 1 t 2 t 3 t 4 t 5 t 6 t 7 t 8 f min f max r =f min +q/2 r 1 r 2 r 3 r 4 r 5 r 6 r 7 =f max-q/2 stepsize q=(f max-f min )/L x returns the biggest integer that is smaller than or equal to x . for used is level tion reconstruc which indicates which index, level tion reconstruc the called is ) ( min f q f f f I - = Yao Wang, NYU-Poly EL5123: Transform Coding and JPEG 8 Uniform Quantization on Images Original, L=256 q=8, L=32 q=16, L=16 q=64, L=4 5 Yao Wang, NYU-Poly EL5123: Transform Coding and JPEG 9 Implementation • Setup the quantization function Q(f) for all possible input level into a look-up table first. Actual quantization can be implemented as a table look-up....
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This note was uploaded on 01/22/2012 for the course EL 5123 taught by Professor Yaowang during the Fall '07 term at NYU Poly.

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lecture10_TransformCoding_JPEG - 1 Lossy Image Compression...

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