Computer Vision – Compression(2) Hanyang University Jong-Il Park

Department of Computer Science and Engineering, Hanyang University Topics in this lecture Practical techniques  Lossless coding  Lossy coding  Optimum quantization  Predictive coding  Transform coding

Department of Computer Science and Engineering, Hanyang University Lossless coding =Error-free compression =information-preserving coding General steps 1. Devising an alternative representation of the image in which its interpixel redundancies are reduced 2. Coding the representation to eliminate coding redundancies

Department of Computer Science and Engineering, Hanyang University Huffman coding Most popular coding (Huffman[1952]) Two step approach 1. To create a series of source reduction by ordering the probabilities of the symbols and combining the lowest probability symbols into a single symbol that replaces them in the next source reduction 2. To code each reduced source, starting with the smallest source and working back to the original source Instantaneous uniquely decodable block code  Optimal code for a set of symbols and probabilities subject to the constraint that the symbols be coded one at a time.

Department of Computer Science and Engineering, Hanyang University Eg. Huffman coding

Department of Computer Science and Engineering, Hanyang University Arithmetic coding Non-block code One-to-one correspondence between source symbols and code words does not exist.  an entire sequence of source symbols is assigned a single arithmetic code word. As the length of the sequence increases, the resulting arithmetic code approaches the bound established by the noiseless coding theorem. Practical limiting factors  The addition of the end-of-message indicator  The use of finite precision arithmetic

Department of Computer Science and Engineering, Hanyang University Eg. Arithmetic code 0.068

Department of Computer Science and Engineering, Hanyang University LZW coding Lempel-Ziv-Welch coding Assigning fixed-length code words to variable length sequences of source symbols but requires no a priori knowledge of the probability of occurrence of the symbols to be encoded Generating a dictionary(=codebook) as the encoding proceeds. The size of the dictionary is an important parameter. => trade-off Applied to GIF, TIFF, PDF format and many zip algorithm

Department of Computer Science and Engineering, Hanyang University Eg. LZW coding

Department of Computer Science and Engineering, Hanyang University 2D Run-length coding Relative address coding(RAC)

Department of Computer Science and Engineering, Hanyang University Lossless predictive coding Principle: De-correlating data by prediction = entropy reduction

Department of Computer Science and Engineering, Hanyang University Eg. Lossless predictive coding Histogram

Department of Computer Science and Engineering, Hanyang University Lossy compression Approaches  Predictive coding  Transform coding  Vector quantization  Etc. Significant data reduction compared with lossless compression at the expense of quality degradation

Department of Computer Science and Engineering, Hanyang University Lossy predictive coding Prevent error accumulation

Department of Computer Science and Engineering, Hanyang University Delta modulation(DM)

Department of Computer Science and Engineering, Hanyang University DPCM (Differential pulse code modulation) Optimal predictor: Try to minimize the mean-square of the prediction error subject to the constraint that and

Department of Computer Science and Engineering, Hanyang University Practical prediction Prediction for 2D Markov source Reduction of accumulated transmission error Typical predictors

Department of Computer Science and Engineering, Hanyang University Eg. Predictor AB CD

Department of Computer Science and Engineering, Hanyang University Optimal quantization Minimization of the mean-square quantization error:

Department of Computer Science and Engineering, Hanyang University Lloyd-Max quantizer Optimal quantizer in the mean-square sense Method  Reconstruction level: centroid  Decision level: halfway No explicit closed-form solutions for most pdfs An iterative design procedure is applied in many cases Optimum uniform quantizer  (uniform q.+VLC) outperforms (non-uniform q.+FLC)

Department of Computer Science and Engineering, Hanyang University Adaptive quantization Different quantization for each subimage(eg.block)  improved performance  increased complexity Eg. Four different quantizers: Scaled version of the same quantizer Notice: Substantial decrease in error BUT small improvement in compression ratio

Department of Computer Science and Engineering, Hanyang University Eg. DPCM vs. Adaptive DPCM DPCM Adaptive DPCM Substantial decrease in perceived error

Department of Computer Science and Engineering, Hanyang University Transform coding A reversible, linear transform is used Goal:  to decorrelate the pixels of each subimage, or  to pack as much information as possible into the smallest number of transform coefficients

Department of Computer Science and Engineering, Hanyang University Basis images: WHT

Department of Computer Science and Engineering, Hanyang University Basis images: DCT

Department of Computer Science and Engineering, Hanyang University Comparison: Energy compaction DFT WHT DCT Best performance KLT is optimal BUT it is image dependent! DCT is a good compromise!

Department of Computer Science and Engineering, Hanyang University DFT vs. DCT Less blocking artifact 2n-point periodicity

Department of Computer Science and Engineering, Hanyang University Effect of subimage size Complexity increases Performance enhances

Department of Computer Science and Engineering, Hanyang University Eg. Block size 2x2 8x8 4x4 Org. 25% reduction Error(8x8)

Department of Computer Science and Engineering, Hanyang University Bit allocation Zonal coding  Allocation of appropriate bits for each coefficient according to the statistics  Rate-distortion theory  Eg. Gaussian pdf Threshold coding  Global threshold  Local threshold  Fixed (N-largest coding)  constant rate  Variable  variable rate. Good performance

Department of Computer Science and Engineering, Hanyang University Zonal vs. Threshold

Department of Computer Science and Engineering, Hanyang University Eg. Zonal vs. Threshold Threshold  better zonal

Department of Computer Science and Engineering, Hanyang University Quantization table Different scaling for each coefficient. The same quantization curve for all coefficients. Z

Department of Computer Science and Engineering, Hanyang University Eg. Quality control by scaling Z 34:167:1

Department of Computer Science and Engineering, Hanyang University Wavelet coding New technique in 1990s Computationally efficient No subdivision  no blocking artifact Good performance!

Department of Computer Science and Engineering, Hanyang University Eg. Wavelet transform