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

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


Lossless codingLossless coding

=Error-free compression

=information-preserving coding

General steps1. Devising an alternative representation of the image in

which its interpixel redundancies are reduced

2. Coding the representation to eliminate coding redundancies


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.


Eg. Huffman codingEg. Huffman coding


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


Eg. Arithmetic codeEg. Arithmetic code

0.068


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


Eg. LZW codingEg. LZW coding


22D Run-length codingD Run-length coding

• Relative address coding(RAC)


Lossless predictive codingLossless predictive coding

Principle: De-correlating data by prediction = entropy reduction


Eg. Lossless predictive codingEg. Lossless predictive coding

Histogram


Lossy compressionLossy compression

Approaches Predictive coding Transform coding Vector quantization Etc.

Significant data reduction compared with lossless compression at the expense of quality degradation


Lossy predictive codingLossy predictive coding

Prevent error accumulation


Delta modulation(DM)Delta modulation(DM)


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


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)

yxf

ΔvΔhyxfyxfD

yxfyxfyxfyxfC

yxfyxfyxfB

yxfyxfA


Eg. PredictorEg. Predictor

A B

C D


Optimal quantizationOptimal quantization

Minimization of the mean-square quantization error:

}){( 2itsE


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)


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


Eg. DPCM vs. Adaptive DPCMEg. DPCM vs. Adaptive DPCM

DPCMAdaptiveDPCM

Substantial decreasein perceived error


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


Basis images: WHTBasis images: WHT


Basis images: DCTBasis images: DCT


Comparison: Energy compactionComparison: Energy compaction

DFT

WHT

DCT

Best performance

• KLT is optimal BUT it is image dependent!

•DCT is a good compromise!


DFT vs. DCT DFT vs. DCT

Less blocking artifact

2n-pointperiodicity


Effect of subimage sizeEffect of subimage size

•Complexity increases•Performance enhances


Eg. Block sizeEg. Block size

2x2

8x84x4

Org.

25% reduction

Error(8x8)


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

2log2

1


Zonal vs. ThresholdZonal vs. Threshold


Eg. Zonal vs. ThresholdEg. Zonal vs. Threshold

Threshold better

zonal


Quantization tableQuantization table

•Different scaling for each coefficient.•The same quantization curve for all coefficients.

Z


Eg. Quality control by scaling ZEg. Quality control by scaling Z

34:1 67:1


Wavelet codingWavelet coding

• New technique in 1990s• Computationally efficient• No subdivision no blocking artifact• Good performance!


Eg. Wavelet transformEg. Wavelet transform

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