CS 414 – Multimedia Systems Design Lecture 8 – JPEG Compression (Part 3) Administrative Outline Hybrid Coding (Usage of RLE/Huffman, Arithmetic Coding) Image Compression and FormatsUbiquitous use of digital imagesJPEG (Joint Photographic Experts Group)Slide Number 8JPEG Compression1. Image PreparationDivision of Source Image into PlanesComponents and their ResolutionsColor Transformation (optional)Image Preparation (Pixel Allocation)Image Preparation - BlocksData Unit OrderingExample of Interleaved Ordering2. Image Processing Forward DCT1D Forward DCTUnderstanding DCT1D DCT Basic FunctionsVisualization of 1D DCT Basic Functions1D Inverse DCTExtend DCT from 1D to 2DEquations for 2D DCTVisualization of 2D DCT Basis FunctionsCoefficient Differentiation 3. QuantizationDe facto Quantization Table4. Entropy EncodingDC EncodingDifference Coding applied to DC CoefficientsAC EncodingHuffman EncodingInterchange Format of JPEGExample - One Everyday PhotoExample - One Everyday PhotoExample - One Everyday PhotoExample - One Everyday PhotoExample - One Everyday PhotoExample - One Everyday PhotoDiscussionCS 414 - Spring 2011CS 414 – Multimedia Systems DesignLecture 8 – JPEG Compression (Part 3)Klara NahrstedtSpring 2011CS 414 - Spring 2011Administrative MP1 is posted Extended Deadline of MP1 is February 18 Friday midnight – submit via compass Help-session for MP1 – Wednesday, February 9, 7pm , Room: 1111 SCOutline Hybrid Coding: JPEG Coding Reading: Section 7.5 out of “Media Coding and Content Processing”, Steinmetz & Nahrstedt, Prentice Hall 2002CS 414 - Spring 2011Hybrid Coding (Usage of RLE/Huffman, Arithmetic Coding) CS 414 - Spring 2011RLE, HuffmanArithmeticCodingImage Compression and Formats RLE Huffman LZW GIF JPEG / JPEG-2000 (Hybrid Coding) Fractals TIFF, PICT, BMP, etc.CS 414 - Spring 2011Ubiquitous use of digital imagesCS 414 - Spring 2011JPEG (Joint Photographic Experts Group) Requirements: Very good compression ratio and good quality image Independent of image size Applicable to any image and pixel aspect ratio Applicable to any complexity (with any statistical characteristics)CS 414 - Spring 2011CS 414 - Spring 2011JPEG CompressionFDCTSourceImageQuantizerEntropyEncoderTableTableCompressedimage dataDCT-based encoding8x8 blocksRBGCS 414 - Spring 2011Image Preparation1. Image Preparation The image preparation is NOT BASED on 9-bit YUV encoding Fixed number of lines and columns Mapping of encoded chrominance Source image consists of components (Ci) and to each component we assign YUV, RGB or TIQ signals. CS 414 - Spring 2011Division of Source Image into PlanesCS 414 - Spring 2011Components and their ResolutionsCS 414 - Spring 2011Color Transformation (optional) Down-sample chrominance components compress without loss of quality (color space) e.g., YUV 4:2:2 or 4:1:1 Example: 640 x 480 RGB to YUV 4:1:1 Y is 640x480 U is 160x120 V is 160x120CS 414 - Spring 2011Image Preparation (Pixel Allocation) Each pixel is presented by ‘p’ bits, value is in range of (0,2p-1) All pixels of all components within the same image are coded with the same number of bits Lossy modes use precision 8 or 12 bits per pixel Lossless mode uses precision 2 up to 12 bits per pixelCS 414 - Spring 2011Image Preparation - Blocks Images are divided into data units, called blocks – definition comes from DCT transformation since DCT operates on blocks Lossy mode – blocks of 8x8 pixels; lossless mode – data unit 1 pixelCS 414 - Spring 2011Data Unit Ordering Non-interleaved: scan from left to right, top to bottom for each color component Interleaved: compute one “unit” from each color component, then repeat full color pixels after each step of decoding but components may have different resolutionCS 414 - Spring 2011Example of Interleaved Ordering[Wallace, 1991]CS 414 - Spring 2011MCU: Minimum Coding Unit2. Image Processing Shift values [0, 2P- 1] to [-2P-1, 2P-1- 1] e.g. if (P=8), shift [0, 255] to [-127, 127] DCT requires range be centered around 0 Values in 8x8 pixel blocks are spatial values and there are 64 samples values in each block CS 414 - Spring 2011Forward DCT Convert from spatial to frequency domain convert intensity function into weighted sum of periodic basis (cosine) functions identify bands of spectral information that can be thrown away without loss of quality Intensity values in each color plane often change slowlyCS 414 - Spring 20111D Forward DCT Given a list of n intensity values I(x),where x = 0, …, n-1 Compute the n DCT coefficients:1...0,2)12(cos)()(2)(10−=+=∑−=nunxxIuCnuFnxµπ==otherwiseuforuCwhere1,021)(CS 414 - Spring 2011Understanding DCT For example, in R3, we can write (5, 2, 9) as the sum of a set of basis vectors Basic functions in R3: [(1,0,0), (0,1,0), (0,0,1)] (5,2,9) = 5*(1,0,0) + 2*(0,1,0) + 9*(0,0,1) DCT is can be also composed as sum of set of basic functions CS 414 - Spring 20111D DCT Basic Functions Decompose the intensity function into a weighted sum of cosine basis functionsCS 414 - Spring 2011Visualization of 1D DCT Basic FunctionsCS 414 - Spring 2011F(0) F(1) F(2) F(3) F(4) F(5) F(6) F(7)1D Inverse DCT Given a list of n DCT coefficients F(u),where u = 0, …, n-1 Compute the n intensity values:==otherwiseuforuCwhere1,021)(1...0,2)12(cos)()(2)(10−=+=∑−=nxnxuCuFnxInuµπCS 414 - Spring 2011Extend DCT from 1D to 2D Perform 1D DCT on each row of the block Again for each column of 1D coefficients alternatively, transpose the matrix and perform DCT on the rowsXYEquations for 2D DCT Forward DCT: Inverse DCT:++=∑∑−=−=mvynuxyxIvCuCnmvuFmynx2)12(cos*2)12(cos*),()()(2),(1010ππ++=∑∑−=−=mvynuxvCuCuvFnmxyImvnu2)12(cos*2)12(cos)()(),(2),(1010ππVisualization of 2D DCT Basis FunctionsIncreasing frequencyIncreasing frequencyCS 414 - Spring 2011Coefficient Differentiation F(0,0) includes the lowest frequency in both directions is called DC coefficient Determines fundamental color of the block F(0,1) …. F(7,7) are called AC coefficients Their frequency is non-zero in one or both directionsCS 414 - Spring 20113. Quantization Throw out bits Consider example: 1011012= 45 (6
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