computer vision – compression(2)
DESCRIPTION
Computer Vision – Compression(2). Hanyang University Jong-Il Park. Topics in this lecture. Practical techniques Lossless coding Lossy coding Optimum quantization Predictive coding Transform coding. Lossless coding. =Error-free compression =information-preserving coding General steps - PowerPoint PPT PresentationTRANSCRIPT
Computer Vision – Computer Vision – Compression(2)Compression(2)
Hanyang University
Jong-Il Park
Department of Computer Science and Engineering, Hanyang University
Topics in this lectureTopics in this lecture Practical techniques
Lossless coding Lossy coding
Optimum quantization Predictive coding Transform coding
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Lossless codingLossless coding=Error-free compression=information-preserving coding
General steps1. Devising an alternative representation of the image in
which its interpixel redundancies are reduced2. Coding the representation to eliminate coding
redundancies
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Huffman codingHuffman 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.
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Eg. Huffman codingEg. Huffman coding
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Arithmetic codingArithmetic 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
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Eg. Arithmetic codeEg. Arithmetic code
0.068
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LZW codingLZW 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
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Eg. LZW codingEg. LZW coding
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22D Run-length codingD Run-length coding
• Relative address coding(RAC)
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Lossless predictive codingLossless predictive coding
Principle: De-correlating data by prediction = entropy reduction
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Eg. Lossless predictive codingEg. Lossless predictive coding
Histogram
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Lossy compressionLossy compression Approaches
Predictive coding Transform coding Vector quantization Etc.
Significant data reduction compared with lossless compression at the expense of quality degradation
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Lossy predictive codingLossy predictive coding
Prevent error accumulation
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Delta modulation(DM)Delta modulation(DM)
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DPCMDPCM(Differential pulse code modulation)(Differential pulse code modulation)
Optimal predictor: Try to minimize the mean-square of the prediction error
subject to the constraint that
and
}]ˆ{[}{ 22nnn ffEeE
nnnnnn ffefef ˆˆ
in
m
iin ff
1
ˆ
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Practical predictionPractical prediction Prediction for 2D Markov source
Reduction of accumulated transmission error
Typical predictors
jh
ivjyixfyxfE 2)},(),({
m
ii
1
1
otherwise ),1(97.0 if )1,(97.0
),(ˆ)
)1,1(5.0),1(75.0)1,(75.0),(ˆ)
),1(5.0)1,(5.0),(ˆ)
)1,(97.0),(ˆ)
yxfΔvΔhyxf
yxfD
yxfyxfyxfyxfC
yxfyxfyxfB
yxfyxfA
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Eg. PredictorEg. Predictor
A B
C D
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Optimal quantizationOptimal quantization Minimization of the mean-square quantization error:
}){( 2itsE
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Lloyd-Max quantizerLloyd-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)
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Adaptive quantizationAdaptive 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
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Eg. DPCM vs. Adaptive DPCMEg. DPCM vs. Adaptive DPCM
DPCM AdaptiveDPCM
Substantial decreasein perceived error
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Transform codingTransform 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
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Basis images: WHTBasis images: WHT
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Basis images: DCTBasis images: DCT
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Comparison: Energy compactionComparison: Energy compaction
DFT
WHT
DCT
Best performance
• KLT is optimal BUT it is image dependent!
•DCT is a good compromise!
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DFT vs. DCT DFT vs. DCT
Less blocking artifact
2n-pointperiodicity
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Effect of subimage sizeEffect of subimage size
•Complexity increases•Performance enhances
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Eg. Block sizeEg. Block size
2x2
8x84x4
Org.
25% reductionError(8x8)
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Bit allocationBit 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
DR
2
2log21
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Zonal vs. ThresholdZonal vs. Threshold
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Eg. Zonal vs. ThresholdEg. Zonal vs. Threshold
Threshold better
zonal
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Quantization tableQuantization table
•Different scaling for each coefficient.•The same quantization curve for all coefficients.
Z
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Eg. Quality control by scaling ZEg. Quality control by scaling Z
34:1 67:1
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Wavelet codingWavelet coding
• New technique in 1990s• Computationally efficient• No subdivision no blocking artifact• Good performance!
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Eg. Wavelet transformEg. Wavelet transform