EE465: Introduction to Digital Image Processing1 Data Compression Techniques Text: WinZIP, WinRAR...

EE465: Introduction to Digital Image Processing 1

Data Compression Techniques

Text: WinZIP, WinRAR (Lempel-Ziv compression’1977)

Image: JPEG (DCT-based), BMP (run-length coding)

Video: VCD/DVD (MPEG), Real Player/Windows Media Player (H.263/H.264), BluRay

Audio and Speech: MP3, G.728 (CELP)


Lossless vs. Lossy Compression

One is original and the other is compressed, which one is original?

Mathematical lossy can still be visually lossless


Engineering is About Design and Implementation

cost

performance

Product A

Product B


A Tour of JPEG Coding Algorithm

Flow-chart diagram of DCT-based coding algorithm specified by Joint Photographic Expert Group (JPEG)

T Q C


First Building Block: 8-by-8 DCT

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Transform Coding of Images

Why not transform the whole image together? Require a large memory to store transform

matrix It is not a good idea for compression due to

spatially varying statistics within an imageIdea of partitioning an image into blocks

Each block is viewed as a smaller-image and processed independently

It is not a magic, but a compromise


Block Processing under MATLAB

Type “help blkproc” to learn the usage of this function B = BLKPROC(A,[M N],FUN) processes the

image A by applying the function FUN to each distinct M-by-N block of A, padding A with zeros if necessary.

ExampleI = imread('cameraman.tif'); fun = @dct2; J = blkproc(I,[8 8],fun);


Block-based DCT Example

JI

note that white lines are artificially added to the border of each 8-by-8 block to denote that each block is processed independently


Boundary Padding

padded regions

Example

1213141516171819

1213141516171819

1213141516171819

1213141516171819

When the width/height of an image is not the multiple of 8, the boundary isartificially padded with repeated columns/rows to make them multiple of 8


Work with a Toy Example

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Any 8-by-8 block in an image is processed in a similar fashion


Encoding Stage I: Transform

• Step 1: DC level shifting

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• Step 2: 8-by-8 DCT

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Encoding Step 1: Transform (Con’t)

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Second Building Block: Quantization

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Q-table

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ˆ:

:

1

ji

Qsxf

Q

xsf

ijijij

ij

ijij

: specifies quantization stepsize (see slide #28)

Notes: Q-table can be specified by customerQ-table is scaled up/down by a chosen quality factor Quantization stepsize Qij is dependent on the coordinates (i,j) within the 8-by-8 block Quantization stepsize Qij increases from top-left to bottom-right


Encoding Stage II: Quantization (Con’t)

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Example

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The Third Building Block: Entropy Coding

Zigzag Scan

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(20,5,-3,-1,-2,-3,1,1,-1,-1,0,0,1,2,3,-2,1,1,0,0,0,0,0,0,1,1,0,1,EOB)

zigzag scan

End Of the Block:All following coefficients are zero


Run-length Coding

(20,5,-3,-1,-2,-3,1,1,-1,-1,0,0,1,2,3,-2,1,1,0,0,0,0,0,0,1,1,0,1,EOB)

DCcoefficient

ACcoefficient

- DC coefficient : DPCM coding- AC coefficient : run-length coding (run, level)

(5,-3,-1,-2,-3,1,1,-1,-1,0,0,1,2,3,-2,1,1,0,0,0,0,0,0,1,1,0,1,EOB)

(0,5),(0,-3),(0,-1),(0,-2),(0,-3),(0,1),(0,1),(0,-1),(0,-1),(2,0),(0,1),(0,2),(0,3),(0,-2),(0,1),(0,1),(6,0),(0,1),(0,1),(1,0),(0,1),EOB

Huffman codingencoded bit stream

encoded bit stream


JPEG Decoding Stage I: Entropy Decoding

(20,5,-3,-1,-2,-3,1,1,-1,-1,0,0,1,2,3,-2,1,1,0,0,0,0,0,0,1,1,0,1,EOB)

Huffman decodingencoded bit stream

AC coefficients

DC coefficient

DPCM decoding

(0,5),(0,-3),(0,-1),(0,-2),(0,-3),(0,1),(0,1),(0,-1),(0,-1),(2,0),(0,1),(0,2),(0,3),(0,-2),(0,1),(0,1),(6,0),(0,1),(0,1),(1,0),(0,1),EOB

encoded bit stream


JPEG Decoding Stage II: Inverse Quantization

(20,5,-3,-1,-2,-3,1,1,-1,-1,0,0,1,2,3,-2,1,1,0,0,0,0,0,0,1,1,0,1,EOB)

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JPEG Decoding Stage III: Inverse Transform

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Quantization Noise

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MSE=||X-X||2^Distortion calculation:

Rate calculation: Rate=length of encoded bit stream/number of pixels (bps)


JPEG Examples

1000

90 (58k bytes)50 (21k bytes)10 (8k bytes)

best quality,

lowest compression

worst quality,

highest compression


Rate-Distortion Tradeoff


Block artifacts of JPEG when the bit rate is low (0.25bpp)


JPEG Coding Algorithm Summary


Lossy Compression of Color Images

Color-space transformation

B

G

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C

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1.06.03.0luminance

chrominance

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inverse transform

forward transform

Luminance channel can be treated just like a gray-scale image


Compression of Chrominance Channels

Human eye is relatively insensitive to the high-frequencycontent of the chrominance channels.

Down-sampling

2

Cr/Cb

Q-Table

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Technology is About New Tools

The same design principle but each building block can be replaced by a more advanced technique Transform: DCT becomes Wavelet Transform Quantization: uniform quantization becomes

bitplane coding (to support scalability) Entropy coding: Huffman coding becomes

arithmetic coding (more flexible)

JPEG becomes JPEG2000


A Glimpse into Wavelet Transform*

Multi-Resolution Analysis in Vision

Human vision system is capable of interpretingthe visual information regardless of the resolution


Progressive Image Transmission

I hate to wait – show me a piece and see if I like it or not

Low-resolution (LR)

High-resolution (HR)


Haar Transform – the simplest wavelet transform

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Example

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Reordering Coefficients

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Apply Haar transformto each 2-by-2 block

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Y regrouping

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HHHL

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approximation horizontal details

diagonal detailsvertical details


Multi-level Wavelet Transform

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Apply one-level Haar transform

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Apply Haar transformto Low-Low band only

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Image Example


Wavelet Image Compression

WaveletTransform

ScalarQuantization

EntropyCodingimage

compressedbit stream

Major improvements

Wavelet transform instead of DCT

Arithmetic coding instead of Huffman coding

Modeling location instead of intensity

Those are the topics in EE565: Advanced Image Processing


FBI Wavelet Scalar Quantization (WSQ) Standard

Established by FBI in 1990s as the standard for fingerprint image compression

Wavelet-based: Daubechies’ wavelets were built just in time to win the race

Demonstrate better Rate-Distortion performance than DCT-based JPEG standard


JPEG2000 Standard

Developed by ISO in late 1990s to replace the DCT-based JPEG standard

Accumulative research progress on wavelet image compression has dramatically pushed the art of lossy image compression forward

Demonstrate much better Rate-Distortion performance than DCT-based JPEG standard for typical photographic images


Wavelet vs. DCT

JPEG (CR=64) JPEG2000 (CR=64)

discrete cosine transform based wavelet transform based


BIGGER Question

Why haven’t we seen JPEG being replaced by JPEG2000?

Technical superiority DO NOT always imply economical wins (think about Unix vs. Windows)

THE next image compression standard has to wait for the right timing

Anyone including you can be a part of that business

EE465: Introduction to Digital Image Processing1 Data Compression Techniques Text: WinZIP, WinRAR...

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Transcript of EE465: Introduction to Digital Image Processing1 Data Compression Techniques Text: WinZIP, WinRAR...