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Sejong University, DMS Lab.
Digital Image Processing8. Image Compression
grkim@sju.ac.kr
Sejong University, DMS Lab.
What is image compression?
Image compression• Reducing the amount of data needed to represent the image• Removing duplicate data existing in the image
Applications• Digital TV broadcasting• Televideo-conferencing• Medical imaging• Facsimile transmission• Multi-media environment
Transport and storage
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Sejong University, DMS Lab.
Fundamentals
Compression and Restoration• Lossless compression Precisely reproducing original information when restored after compression
• Lossy compression Loss occurs when you restore the original information after compression
Duplicate characteristics of the image data• Coding redundancy• Interpixel redundancy• Psychovisual redundancy
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Sejong University, DMS Lab.
Fundamentals _ coding redundancy
Removing coding redundancy• Generating a short code assigned to the high frequency value• Generating a long code assigned to the low frequency value• The length of the code change• Reducing the total amount of data• Low bit for this histogram assign a higher value
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Sejong University, DMS Lab.
Fundamentals _ coding redundancy
The amount of data required• Show the pixel value range of [0,1] of random variable rk
• pr(rk) = rk of probability of occurrence
• L is total pixels and l(rk) is represented bits amounts of rk
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n
nrp kkr )(
1
0
)()(L
kkrkavg rprlL
Sejong University, DMS Lab.
Fundamentals_ coding redundancy
Removing coding redundancy
5
bits
rprlLk
krkavg
7.2
)02.0(6)03.0(6)06.0(5)08.0(4
)16.0(3)21.0(2)25.0(2)19.0(2
)()(7
02
code 1 code 2
bits
rprlLk
krkavg
0.3
)02.0(3)03.0(3)06.0(3)08.0(3
)16.0(3)21.0(3)25.0(3)19.0(3
)()(7
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Sejong University, DMS Lab.
Fundamentals _ Interpixel redundancy
Removing interpixel redundancy• Using the similarity between neighboring pixels• Using the similarity between neighboring fields• Data represented by the difference between the neighboring pixels• Using Run-length encoding, DPCM, ADPCM• Spatial redundancy
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Sejong University, DMS Lab.
Fundamentals _ Interpixel redundancy
Removing of interpixel redundancy
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Sejong University, DMS Lab.
Fundamentals _ Psychovisual redundancy
Removing of psychovisual redundancy• HVS It doesn’t respond accurately to the image information• Certain image information is ignored by eye of human• The removal of this information Doesn’t difference in perception• Relate to Sampling and Quantization
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Sejong University, DMS Lab.
Fundamentals _ Fidelity
Standard of fidelity• Building evaluation means define the Characteristics information and
amount of lost HVS Objective fidelity criteria
– Root-mean-square error of input image and output image– are each input image, output image.– The total amount of error between two images of MxN
– root-mean-square of two images erms
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),(ˆ),,( yxfyxf
1
0
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)],(),(ˆ[M
x
N
y
yxfyxf
2/11
0
1
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2)],(),(ˆ[1
M
x
N
yrms yxfyxf
MNe
Sejong University, DMS Lab.
Fundamentals _ Fidelity
Examples of objective fidelity criteria• Mean-square signal-to-noise ratio of the output image
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1
0
1
0
2
1
0
1
0
2
)],(),(ˆ[
),(ˆ
M
x
N
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yms
yxfyxf
yxf
SNR
Sejong University, DMS Lab.
Image compression model
Image compression system• Composed of the encoder and decoder• Source encoder : removing redundancy of input data• Channel encoder : reinforced immune to noise
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Source encoder
Channel encoder Channel Channel
decoderSource decoder
Encoder Decoder
),( yxf ),(ˆ yxf
Sejong University, DMS Lab.
Image compression model _ Source encoding
Step of source encoding• Mapper
Converting the data types in input image to reduce interpixel redundancy ex) run-length coding
• Quantizer Reducing the accuracy of the mapper output Reducing the Psychovisual redundancy
• Symbol encoder Reducing the Coding redundancy Outputting the fixed length or variable length code
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Mapper Quantizer Symbol encoder Channel
<Source Encoder>
),( yxf
Sejong University, DMS Lab.
Image compression model _ Source decoding Source Decoder
• Reconstruction original image in reverse process of source encoding• When encoding time, if the quantization process is not fully
recoverable
Process of Source Decoding
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Symbol Decoder
Inverse Mapper
Channel
<Source Decoder>
),(ˆ yxf
Sejong University, DMS Lab.
Lossless compression
Lossless compression• Removing interpixel, coding redundancy• The compression method used in the case does not allow the loss
Application• Medical or business documents• Satellite images• Digital radiography
Compression techniques • Variable-length coding• Arithmetic coding• Run-length coding• Lossless predictive coding
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Sejong University, DMS Lab.
Lossless compression _ variable length coding
Variable-length coding• The simplest compression technique • Removing coding redundancy• Specify the shortest codes to the most appeared to value
Category• Huffman coding• Truncated Huffman coding• Shift coding• Huffman shift coding
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variable length coding _ Huffman coding
Huffman coding• Allocate fewer bits to frequently used code
Process of Huffman coding• 1. Sort the probability of symbol• 2. Continuously reducing the number of exit symbol by combining the
symbol with the lowest probability of a single symbol• 3. Assigned to each code symbol in the smallest number• 4. Exit to allocate an additional code symbol is reduced to inverse
process
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Sejong University, DMS Lab.
variable length coding _ Huffman coding
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<Reducing the number of symbol>
<Assign code>
Sejong University, DMS Lab.
variable length coding _ Huffman coding
Advantages• Generating 1 code at a time Optimized code• It can be encoded as a look-up table method• Source symbol is mapped to a code symbol of a certain length
Disadvantages• If the symbol is difficult to configure a large number of code tables
Ex) The code assignment
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a b c d e
0.4 0.3 0.2 0.06 0.04
a b c d e
1 00 010 0110 0111
Sejong University, DMS Lab.
Lossless compression _ Arithmetic coding
Arithmetic coding• Generating nonblock code Several of the source symbols are gathered Create one arithmetic code
• Code word has a real number between 0 and 1
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Source symbol
Probability Initial subinterval
a1 0.2 [0.0,0.2)
a2 0.2 [0.2,0.4)
a3 0.4 [0.4,0.8)
a4 0.2 [0.8,1.0)
Sejong University, DMS Lab.
Lossless compression _ LZW coding
LZW coding ( Lempel-Ziv-Welch coding)• Source symbol of variable length Assign a code word of fixed
length• Using Gif, tiff, pdf file• Creating a basic codebook ( assignment 0~255 in image )• If source symbols in codebook are replaced with a code word in the
codebook• No prior knowledge required
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Sejong University, DMS Lab.
Lossless compression _ Bit-plane coding
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Bit-plane coding• After decomposing the image into a series of binary tone image,
compressing the data by using the coding method of binary image• Technology to increase the compression ratio for each bit-plane
Sejong University, DMS Lab.
Lossless compression _ Bit-plane coding
Reconstruction of bit-plane• The change of the data is very large in the low bit• Using m-bit gray code reducing bit changing
In the case of pixels adjacent to each other with similar characteristics using value
10진수 BCD 코드 그레이코드
0 0000 0000 1 0001 0001 2 0010 0011 3 0011 0010 4 0100 0110 5 0101 0111 6 0110 0101 7 0111 0100 8 1000 1100 9 1001 1101
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Sejong University, DMS Lab.
Lossless compression
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original image
original gray coded original gray coded
Sejong University, DMS Lab.
Lossless compression _ run-length coding
Run-length coding• Removing interpixel redundancy technique• Binary image compression• Applied to each bit-plane of the tone image• Representing the image of a continuous length (black, white)• FAX transmission• Tone image of 1,2,4 bit
• Input : 0000011110000000000• Output : 5b4w10b• BMP file
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Sejong University, DMS Lab.
Lossless predictive coding
Lossless predictive coding• Removing interpixel redundancy• Using the information obtained from previous pixel Only extract new information from neighboring pixels Encoding
• New information : (previous pixel – predictive value)
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Sejong University, DMS Lab.
Lossy compression
Lossy coding• Allowing the loss to increase the compression ratio• Removing interpixel, coding redundancy, psychovisual redundancy• Presence of Quantization step
Application• Digital TV : MPEG-2, image conference• Still image : JPEG
Coding technique• Lossy predictive coding• Transform coding• Hierarchical coding• Hybrid coding, wavelet coding
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Predictive coding
Lossy predictive coding
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Sejong University, DMS Lab.
Predictive coding _ DM
DM (Delta Modulation)• Assigning one bit to the representation of a pixel• Code assignment method
Comparing the input signal value and the current value If input value >= current value assignment ‘1’ Otherwise, ‘0’
• Implementation Define regular amplitude, encoding residual signal ‘1’ = + delta, ‘0’ = - delta
• Granular noise No change occurs in the part of the input image ( Amplitude )
• Slope overload The change in the input image generated in large part ( Amplitude )
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Sejong University, DMS Lab.
Predictive coding
ADM (Adaptive Delta Modulation)• Process the amplitude to a variable
DPCM (Differential Pulse Code Modulation)• Techniques to minimize the prediction error encoding unit
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}]ˆ{[}{ 22nnn ffEeE
Sejong University, DMS Lab.
Ex) lossy coding about DPCM
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1 bits/pixel 1.25 bits/pixel
2 bits/pixel
2.125 bits/pixel
3 bits/pixel3.125 bits/pixel
Sejong University, DMS Lab.
Ex) DPCM Error
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1.25 bits/pixel
2.125 bits/pixel
3.125 bits/pixel
1 bits/pixel
2 bits/pixel
3 bits/pixel
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