Image Compression

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Lecture 4

• Image Compression

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Stochastic Processes and Lmsee

• Lineal Predictive Coding

• Delta Modulation

• Bit Plane Encoding

• 2-D Transform Coding

• Other Approaches

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Introduction ToStochastic Processes
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Ensemble of Random Processes
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(No Transcript)
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EXAMPLE 1
Not Ergodic
But Stationary
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EXAMPLE 2
NON Stationary
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EXAMPLE 3
STATIONARY
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Stationary Case-Spectral Densities
H(?)
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Stationary Case-Spectral Densities
Cross Density
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Orthogonality Uncorrelated and Independence
Exy Ex Ey
Exy 0
f(x,y)f(x)f(y)f(y/x)f(x)
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Mean Squared Error Estimation

• Index of Performance

• Nonlinear

ESTIMATE y BY g(x)

• Linear

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GAUSSIAN PROCESSES
BEST MSE ESTIMATE IS LINEAR!
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ORTHOGONALITY PRINCIPLE
Error is Orthogonal to Each
Piece of Data X
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EXAMPLE
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(Bandwidth compression, bit rate reduction)
Image Compression

• Reduction of the number of bits needed to
• represent a given image or its information

• Image compression
• exploits the fact that all images are not
• equally likely

• Exploits energy gaps in signal

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Information vs Data
REDUNDANTDATA
INFORMATION
DATA INFORMATION REDUNDANT DATA
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An Image Model-Ref J.B.ONeal
Picture size is one unit wide X one unit high
MNumber of Sample DSpacing Between Samples
Correlation Between Adjacent Samples
Width 1 Unit
1/2
Height 1 Unit
M
D
1/2
M
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Compression As It Relates To Image Content
-1
Picture Correlation Distance Portrait
6.3 (Fills 1/2 Frame) Typical
16.7 (Moderate Detail) 100
People 50 2000 People 150
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INTERFRAME and INTRAFRAME PROCESSING
Intraframe Processing
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BIT RATE NQF
N NUMBER OF PIXELS
Q QUANTIZATION BITS/PIXEL
F FRAME RATE
Channel Bit Rate N Q F
Compression Ratio 10 LOG
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• REDUCING

• CREATES

We need More Sophisticated Approches
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Selected Representative

• Compression Methods

• Linear Predictive Coding

• Delta Modulation

• Bit Plane Encoding

• Transform Encoding

• Variable Scan, Speed, Contour Encoding

• Hybrid

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PREDICTIVE CODING
Predictive Coding transmit the difference
between estimate of future sample
the sample itself.
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BIT PLANE ENCODING
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SIMPLE DELTA MODULATION
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SIMPLE DELTA MODULATION
t
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TRANSFORM CODING
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USEFUL TRANSFORMS
Fourier (DFT,FFT) - (u,v) plane is spatial
frequency plane Cosine Sine
Hadamard(Walsh)- basis values 1, -1 (
clipped Fourier )
HAAR -basis values 0,1, -1
Areas of (u,v) planegtdifferential energy
concentration
SLANT - Designed for efficient implementation
high energy compaction
KL(HOTELLING) - used in coding produces
maximally uncorrelated coefficients is
contextual- uses covariance matrix of image or
image class
WAVELET - Transient NOT WAVES
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Transform Processing and Encoding
Objective
(a) Redistribute Variance to Decorrelate
Transform Coefficients
(b) Transform Variance of each Pixel into
Low Order Coefficients of Transform
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Transform Processing and Encoding
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Potential Bit Rate Reduction for 525 Line Video
Imagery
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TYPE
COMMENTS
OPERATIONS
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COMPRESSION/COST RATIO RANKING
Compression/ Cost Ratio
Compression/ Vs. 6-Bit PCM
RANK
Technique
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THIS LECTURE IS CONDUCTED AT256,000 BPSA
REDUCTION OF HUNDREDS TO ONE FROM PCM.