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10 July 2020
Image Compression
Dr. C. Seldev Christopher,
Professor , CSE Deparment,
St.Xavier,s Catholic College of Engineering,
Nagercoil.
10 July 2020
Contents
Why do we need to compress images?
Image types
Basic concept of compression
Classification of Compression Methods
Compression Methods
Conclusion
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Image Compression
Everyday an enormous amount of information is
stored, processed, and transmitted
Financial data
Reports
Inventory
Cable TV
Online Ordering and tracking
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What is Image Compression?
Image compression is the art and science of representing information in a compact form. It plays an important role in Video Conferencing, remote
sensing, satellite TV, FAX, document and medical
imaging.
The goal of image compression is to reduce the amount of data required to represent a digital image.
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Why do we need Image Compression?
1) Storage 2) Processes 3) Communication 2000-2020
Disc capacities : 20 GB -> 2 TB (100 times!) but seek time : 10 milliseconds 05 milliseconds
and transfer rate : 2MB/sec ->200 MB/sec. Compression improves overall response time in some applications.
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What is Image Compression? Still image data, that is a collection of 2-D arrays (one for each color plane) of values representing intensity (color) of the point in corresponding spatial location (pixel).
•Data and information are not synonymous terms!
•Data is the means by which information is conveyed.
•Data compression aims to reduce the amount of data
required to represent a given quantity of information while
preserving as much information as possible.
.
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Why do we need Image Compression? Data vs Information
The same amount of information can be
represented by various amount of data,
e.g.:
Your wife, Helen, will meet you at Logan Airport in Boston at
5 minutes past 6:00 pm tomorrow night
Your wife will meet you at Logan Airport at 5 minutes past
6:00 pm tomorrow night
Helen will meet you at Logan at 6:00 pm tomorrow night
Ex1:
Ex2:
Ex3:
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Source of images
•Image scanner
•Digital camera
•Video camera,
•Ultra-sound (US), Computer Tomography (CT),
Magnetic resonance image (MRI), digital X-ray (XR),
Infrared. etc.
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Image types
Why do we need special algorithms for images?
Basic concept of compression
Data might contain elements that provide
no relevant information : data redundancy
Data redundancy is a central issue in
image compression. It is not an abstract
concept but mathematically quantifiable
entity
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Data redundancy
Data redundancy occurs when the same
piece of data exists in multiple places,
whereas data inconsistency is when the
same data exists in different formats in
multiple tables.
Unfortunately, data redundancy can cause
data inconsistency, which can provide a
company with unreliable and/or meaningless
information.
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Data redundancy
Spatial redundancy
Temporal redundancy
Psycho-visual redundancy
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Spatial redundancy
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Spatial Redundancy
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Temporal redundancy
Next frame
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Temporal redundancy
• Consecutive images
of a video stream do
not vary much.
– Some areas don’t
change at all
(background).
– Others only
change
their spatial location
(moving objects).
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Psycho-visual redundancy
more detail in section “human visual system”
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Psycho visual redundancy
• Human visual system
– Different sensitivity to different information.
• Human processing
– We only see some
parts of the image.
– Our brain completes
the rest.
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Psycho visual redundancy
• We notice errors in
homogenous regions.
– Low frequencies.
• We notice errors in
edges.
– High frequencies.
• We don’t notice noise
in textured areas.
– Medium frequencies.
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Fidelity Criteria
How close is to ?
Measured in terms of the “closeness” of an image to an original source
Criteria
Subjective: based on human observers
Objective: mathematically defined criteria
Fidelity Criteria
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Rate measures
Bitrate:
Compression ratio:
N
C
image in the pixels
file compressed theof size
C
kN
file compressed theof size
file original theof size
bits/pel
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Distortion measures
Mean average error (MAE):
N
i
ii xyN 1
1MAE
Mean square error (MSE):
N
i
ii xyN 1
21MSE
MSElog10PSNR 2
10 APulse-signal-to-noise ratio (PSNR):
(decibels)
A is amplitude of the signal: A = 28-1=255 for 8-bits signal.
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Other issues
Coder and decoder computation complexity
Memory requirements
Fixed rate or variable rate
Error resilience
Symmetric or asymmetric
Decompress at multiple resolutions
Decompress at various bit rates
Standard or proprietary
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Human visual system
Human eye is less sensitive to chrominance
than to luminance.
Less sensitive to high and low spatial
frequency than to mid-spatial frequency.
Sensitivity to quantizing distortion decreases
with increasing luminance levels. (noise
masking property).
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Compression method
Classification 1
Lossy
Lossless
Classification 2
Spatial methods
Transform methods
Hybrid methods
There are more classifications in other survey
paper
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Loss-less Compression Methods
LZW
Huffman coding
Run-length coding
Arithmetic coding
Predictive coding
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LZW Coding
Works by coding short strings of data
Used in GIF, TIFF, and PDF file formats
Creates a “dictionary” of code words For an 8-bit image, the first 256 words are
assigned to the gray values 0,1,2, … , 255
As sequences are discovered, new code words are assigned to represent them
Eg: The sequence 126-126 may be assigned to code word 256
Huffman Coding
(coding redundancy)
A variable-length coding technique.
Symbols are encoded one at a time! There is a one-to-one correspondence between
source symbols and code words
Optimal code (i.e., minimizes code word length per source symbol).
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Arithmetic Coding
A sequence of values is assigned a single
arithmetic code word
The code word is a fractional number
between 0 and 1
Each symbol is assigned an interval based
on its probability of occurrence
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Run-length coding (RLC)
(interpixel redundancy)
Used to reduce the size of a repeating string of
symbols (i.e., runs):
1 1 1 1 1 0 0 0 0 0 0 1 (1,5) (0, 6) (1, 1)
a a a b b b b b b c c (a,3) (b, 6) (c, 2)
Encodes a run of symbols into two bytes: (symbol,
count)
Can compress any type of data but cannot achieve
high compression ratios compared to other
compression methods.
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Lossless Compression method
Predictive coding (DPCM)
Also called “differential pulse-coded modulation”
Prediction error = true value － prediction value
Only prediction error are coded
Prediction error’s dynamic range is smaller than
true value’s
Sensitivity to transmission and statistic error
Temporal predictive coding is difficult to random
accessing
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Predictive coding
Lossy Compression Methods
Transform coding
Lossy Predictive Coding
Hybrid coding
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Compression method
Transform coding
To compact the energy of image in a few
coefficients
To decorrelate the image pixels
Block size matter! (block size is 8x8 in JPEG)
Compact
energy Decorrelate
pixels
compromise
complexity Decorrelation
ability compromise
transform
Block size
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Transform Coding
Operates on the transform of an image,
rather than the original pixels
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DCT
Concentrate energy into a smaller number of coefficients
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Discrete Cosine Transform (DCT)
Most popular transform (used in JPEG)
Kernels:
1,...,2,1for2
0for1
)(
where
2
)12(cos
2
)12(cos)()(
),,,(),,,(
NuN
uNu
N
vy
N
uxvu
vuyxhvuyxg
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Quantization
Lossy Process!
Give higher importance to low spatial frequencies
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Zig-Zag scanning
Create long sequences of zeros – Huffman Coding
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Considerations
• We can control compression via a quantization
factor.
• The higher the factor, the higher the number of zeros
in the DCT > Better Huffman coding.
• Problem: High quantization factors produce
compression artifacts.
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Lossy Predictive Coding
Error values are quantized
Predictions by encoder and decoder must be same to prevent
error buildup
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Compression method
Hybrid coding
Combine transform and predictive coding
techniques
Ex: In video coding, DCT in the spatial plane
while DPCM in the temporal direction
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Other Compression methods
Vector quantization
X is set of values which will be coded
Y is output of “vector quantizer” Q
C is the codebook
Transmit the index of Y in the codebook
NwithiRYYC
yyyyXQY
xxxxX
k
ii
k
k
,....,2,1 ,|
,...,,)(
,...,,
321
321
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Other Compression methods
Vector quantization
Better performance can always be achieved by coding vectors instead of scalars. (Shannon’s rate-distortion theory)
Relatively high compression ratio
Computational demanding at encoding process
Major problem of VQ: how to design a good codebook
Fast search algorithms are being developed ( in 1993)
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Other Compression methods
Fractal image coding
Extract self similarity in the image
Describe an image region with a simple
transformation of another region
Transmit only the sequence of transformation
Relatively high compression ratios (about 70~80)
Encoding process is complex
Complexity of decoding process is relatively reasonable
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Other Compression methods
Model/knowledge-based coding
Transmitter and receiver agree on the basic
model for the image
Transmit the parameters to manipulate this model
Application example: teleconferencing system
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Other Compression methods
Sub-band coding
A set of band-pass filters divide the image into
different sub-band (spectral component)
Then code each component
Progressive coding
Example: wavelet coding
Image
LPF
HPF
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Wavelet Coding
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Other Compression methods
Contour-texture oriented techniques
Segment the image into texture and contour,
coded separately
Whole picture = texture + contour
How to extract Contour?
Region growing
Edge detection
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Other Compression methods
Other technique
Adaptive coding
Coding parameters are adjusted according to the data
statistics
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Applications
Videoconferencing and videophone
Speed
Compression ratio
progressive
Multimedia electronic mail
Compression ratio
Picture archiving and information distribution
Reliability
Compression ratio
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Conclusion
We had review many compression methods
Cost of
compression
Cost of
Transmission and
storage
compromise
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