IMAGE COMPRESSION

1
IMAGE COMPRESSION

• By ARCHANA MEKA

2
OVERVIEW

• Introduction
• Lossless Compression techniques
• Lossy Image coding techniques
• Image Compression standards

3
INTRODUCTION

• Digital Image processing creates significant
  numbers of large files containing digital image
  data
• Why Compression ???
• Often these must be exchanged between different
  users and systems

4
PRIME TARGET

• Redundant and Irrelevant Information
• Compression techniques exploit inherent
  redundancy and irrelevancy by transforming a data
  file into a smaller file

5
Classification

• Lossless compression
• lossless compression for legal and medical
  documents, computer programs
• exploit only data redundancy
• Lossy compression
• digital audio, image, video where some errors or
  loss can be tolerated
• exploit both data redundancy and irrelevant data

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Performance Measure

• Compression efficiency
• Complexity
• Distortion Measurement ( lossy algorithm)

7
Lossless Compression Techniques

• Image can be recovered exactly upon decompression
• These algorithms fall into two broad categories
• Dictionary-based techniques
• Statistical methods

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DictionaryBased Techniques

• Generates a compressed file containing
  fixed-length codes, representing a particular
  sequence of bytes in the original file
• Run-Length Encoding
• Simplest particularly for few gray levels
• In an image stored line by line, a series of
  pixels having the same gray-level value is called
  a run

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• Code can be stored specifying the value followed
  by length of the run, rather than simply storing
  the value many times over
• WWWWWWWWWWWWBWWWWWWWWWWWWBBB
• 12WB12W3B

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• LZW (Lemple Ziv Welch) Encoding
• Like RLE, it effects compression by encoding
  strings of characters
• Unlike RLE, it builds up a table of strings and
  their corresponding codes as it encodes the file

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LZW Example
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Statistical Encoding Methods

• Generates a compressed file using variable length
  codes, representing a particular sequence of
  bytes in the original file
• Huffman Coding
• It uses Binary encoding tree representing
  commonly occurring values in few bits and less
  commonly occurring values in more bits

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Lossy Compression algorithm

• Eliminates redundant as well as irrelevant
  information
• only an approximate reconstruction of the
  original image is possible
• Achieves higher compression ratios

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Vector Quantization

• Composed of two operations
• Encoder
• takes an input vector and outputs the index of
  the codeword that offers the lowest distortion
• Once the closest codeword is found, the index of
  that codeword is sent
• Decoder
• The decoder receives the index of the codeword,
  and outputs the codeword

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Codebook Design

• The algorithm
• Determine the number of code words, N,  or the
  size of the codebook
• Select N code words at random, and let that be
  the initial codebook (randomly chosen from the
  set of input vectors)
• Using the Euclidean distance measure, cluster the
  vectors around each codeword ( by finding the
  Euclidean distance between it and each
  codeword, The input vector belongs to the cluster
  of the codeword that yields the minimum distance

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• Compute the new set of code words.  This is done
  by obtaining the average of each cluster.  Add
  the component of each vector and divide by the
  number of vectors in the cluster.
• Repeat steps 3 and 4 until either the code words
  don't change or the change in the code words is
  small.

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Digital Image Compression Standards
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JPEG

• Joint Photographic Experts Group

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JPEG cont.

• Work commenced in 1986
• International standard ISO/IEC 10918-1 and CCITT
  Rec. T.81 in 1992 Widely used for image exchange,
  WWW, and digital photography
• Motion-JPEG is de facto standard for digital
  video editing

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JPEG Modes

• Sequential DCT based mode
• Sequential lossless mode
• Progressive DCT based mode
• Hierarchical mode

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Steps in JPEG Baseline
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• The picture is divided in blocks of 8 x 8 pixels
• Each block is transformed into coordinates of the
  discrete-cosine space, so each block of pixels is
  represented by the amplitudes of 2D-Cosine waves
  with different frequencies, with these amplitudes
  forming a new block

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Discrete Cosine Transformation

• DCT converts the information from spatial domain
  to frequency domain
• Consider an unsorted list of 12 numbers between
  0 and 3 -gt (2, 3, 1, 2, 2, 0, 1, 1, 0, 1, 0, 0).
  Consider a transformation of the list involving
  two steps
• sort the list
• Count the frequency of occurrence of each of the
  numbers
• (4,4,3,1 ) spatial info lost, captured freq. info

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Quantization

• To reduce number of bits per sample
• F(u,v) round(F(u,v)/q(u,v))
• Example 101101 45 (6 bits)
• Truncate to 4 bits 1011 11 ( 11 x 4 44)
  3 bits 101 5 (8 x 5 40)
  more bits we truncate the more precision
  we lose
• Quantization error is the main source of the
  Lossy Compression
• Uniform Quantization
• q(u,v) is a constant
• Non-uniform Quantization -- Quantization Tables
• Custom quantization tables can be put in
  image/scan header
• JPEG Standard defines two default quantization
  tables, one each for luminance and chrominance

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Quantization cont

• These coefficients are weighted by a matrix, each
  coefficient is divided by a number (weight)
  specific for the coefficients position in the
  block and then rounded to integer numbers (higher
  frequencies are divided by a larger number)

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Zig-Zag Scan

• why?-To group low frequency coefficients in top
  of vector and high frequency coefficients at the
  bottom
• Maps 8 x 8 matrix to a 1 x 64 vector

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Zig-Zag Scan
8x8
. . .
1x64
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DPCM on DC Components

• The DC component value in each 8x8 block is large
  and varies across blocks, but is often close to
  that in the previous block.
• Differential Pulse Code Modulation (DPCM) Encode
  the difference between the current and previous
  8x8 block. Remember, smaller number -gt fewer bits

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45
45
1x64
1x64
54
9
1x64
1x64
48
-6
1x64
1x64
. . .
. . .
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12
1x64
1x64
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4
1x64
1x64
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Entropy Coding DC Components

• DC components are differentially coded as
  (SIZE,Value)
• The code for a Value is derived from the
  following table

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Example If a DC component is 40 and the previous
DC component is 48. The difference is -8.
Therefore it is coded as 1010111 0111 The
value for representing 8 (see Size_and_Value
table) 101 The size from the same table reads
4. The corresponding code from the table at left
is 101.
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RLE on AC Components

• The 1x64 vectors have a lot of zeros in them,
  more so towards the end of the vector
• Higher entries in the vector capture higher
  frequency (DCT) components which tend to capture
  less of the content.
• Could have been as a result of using a
  quantization table
• Encode a series of 0s as a (skip,value) pair,
  where skip is the number of zeros and value is
  the next non-zero component
• Send (0,0) as end-of-block sentinel value

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Entropy Coding AC Components

• AC components (range 1023..1023) are coded as
  (S1,S2 pairs)
• S1 (RunLength/SIZE)
• RunLength The length of the consecutive zero
  values 0..15
• SIZE The number of bits needed to code the next
  nonzero AC components value. 0-A
• (0,0) is the End_Of_Block for the 8x8 block.
• S1 is Huffman coded (see AC code table below)
• S2 (Value)
• Value Is the value of the AC component.(refer to
  size_and_value table)

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Huffman Table for AC components
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Entropy Coding Example
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12
0
0
0
0
0
0

• Consider encoding the AC components by arranging
  them in a zig-zag order -gt 12,10, 1, -7 2 0s, -4,
  56 zeros
• 12 read as zero 0s,12 (0/4)12 ? 10111100
• 1011 The code for (0/4 from AC code table)
• 1100 The code for 12 from the Size_and_Value
  table.
• 10 (0/4)10 ? 10111010
• 1 (0/1)1 ? 001
• -7 (0/3)-7 ? 100000
• 2 0s, -4 (2/3)-4 ? 1111110111011
• 1111110111 The 10-bit code for 2/3
• 011 representation of 4 from Size_and_Value
  table.
• 56 0s (0,0) ? 1010 (Rest of the components are
  zeros therefore we simply put the EOB to signify
  this fact)

10
-7
-4
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
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JPEG Modes

• Sequential Mode
• Each image is encoded in a single left-to-right,
  top-to-bottom scan.
• The technique we have been discussing so far is
  an example of such a mode, also referred to as
  the Baseline Sequential Mode.
• It supports only 8-bit images as opposed to
  12-bit images as described before

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JPEG Modes

• Lossless Mode
• Truly lossless
• It is a predictive coding mechanism as opposed to
  the baseline mechanism which is based on DCT and
  quantization (the source of the loss).

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• Simple block diagram of the technique

Predictive Difference
Huffman EnCoder
Lossless Coding
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• Predictive Difference
• For each pixel a predictor (one of 7 possible) is
  used that best predicts the value contained in
  the pixel as a combination of up to 3 neighboring
  pixels.
• The difference between the predicted value and
  the actual value (X)contained in the pixel is
  used as the predictive difference to represent
  the pixel.
• The predictor along with the predictive
  difference are encoded as the pixels content.
• The series of pixel values are encoded using
  huffman coding

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• The very first pixel in location (0, 0) will
  always use itself
• Pixels at the first row always use P1
• Pixels at the first column always use P2
• The best (of the 7) predictions is always chosen
  for any pixel

C
B
A
X
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JPEG Modes

• Progressive Mode
• It allows a coarse version of an image to be
  transmitted at a low rate, which is then
  progressively improved over subsequent
  transmissions.

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Progressive mode cont.

• Spectral Selection Sends DC component and first
  few AC coefficients first, then gradually some
  more ACs

Spectral Selection
First Scan
Second Scan
Third Scan
. .
Nth Scan
Image Pixels
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Progressive mode cont.

• Successive Approximation All the DCT components
  are sent few bits at a time

Pixels ordered (zig-zag-wise)
LSB
MSB
7
6
5
4
0
3
2
1
. . .
One Pixel
First Scan
. . .
Second Scan
. . .
Third Scan
. .
. .
. . .
5th Scan
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Progressive mode cont..

• example send n1 (say 4) bits (starting with
  MSB) of all pixels in the first scan, the next
  n2(say 1) bits of all pixels in the second and so
  on

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Hierarchical Mode

• Used primarily to support multiple resolutions of
  the same image which can be chosen from depending
  on the targets capabilities

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3-level Hierarchical Encoder
L4
I4
4x4
Encode
Decode
I4
Decode
2x2
-
L2
I2

2x2
Decode
Encode

Decode


L1
-
I

I

Encode
Decode
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JPEG 2000

• Features
• Improved compression efficiency (vs. JPEG)
• Highly scalable embedded data streams
• Progressive lossy to lossless compression
  within a single data stream
• Arbitrarily crop images in the compressed domain
• Selectively enhance quality of spatial regions
  of interest
• Support for very large images

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JPEG 2000 Compression
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Comparision JPEG vs JPEG 2000
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Comparision JPEG vs JPEG 2000
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HD PHOTO

• Gives a high-dynamic-range image encoding while
  requiring only integer operations (with no
  divides)
• Preferred image format for MS xps and vista
• Microsoft claims that HD Photo offers a
  perceptible image quality comparable to JPEG 2000
• computational and memory performance closely
  comparable to JPEG
• delivers a lossy compressed image of better
  perceptive quality than JPEG at less than half
  the file size
• lossless compression compresses images 2.5
  times.

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Motion JPEG

• It is a video codec where each video field
  (frame) is separately compressed into a JPEG
  image
• resulting quality of video compression is
  independent from the motion in the image (which
  differs from MPEG video where quality often
  decreases when footage contains lots of movement)

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• Characteristics of M-JPEG
• At low bandwidth availability, priority is given
  to image resolution (i.e. transmitted images
  would maintain their quality, however some images
  would be dropped)
• Images have a consistent file size
• Still the most widespread picture compression
  format used today

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MPEG

• "Moving Picture Coding Experts Group", standards
  body for delivery of video and audio.
• MPEG-1 Target VHS quality on a CD-ROM or Video
  CD (VCD) (352 x 240 CD audio _at_ 1.5 Mbits/sec)
• MPEG-2 allows different levels and profiles
• Both standards have four parts
• Video Defines the video compression decoder
• Audio Defines the audio compression decoder
• System Describes how various streams(video,
  audio or generic data) are multiplexed and
  synchronized.
• Conformance Defines a set of tests designed to
  aid in establishing that particular
  implementations conform to the design.

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MPEG cont..

• Each picture is divided into macroblocks of 16 X
  16 pixels.
• Macroblocks are intracoded for I frames and
  predictive coded or intracoded for P and B frames
• Macroblocks are divided into six blocks of 8 X 8
  pixels (4 luminance and 2 chrominance) and DCT is
  applied to each block and transform coefficients
  are quantized and zig-zag scanned and
  variable-length coded.

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MPEG cont.

• Some macroblocks need information that is not
  present in the previous reference frame.
• Maybe, such information is available in a
  succeeding frame!
• Add a third frame type (B-frame) To form a
  B-frame, search for matching macroblocks in both
  past and future frames
• Typical pattern is IBBPBBPBB IBBPBBPBB IBBPBBPBB
  Actual pattern is up to encoder, and need not be
  regular

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Bitstream Order Vs Display Order

• Bitstream (Transmit) order 1(I), 4(P), 2(B),
  3(B), 7(P), 5(B), 6(B), 10(I), 8(B), 9(B)

I
P
B
B
P
B
B
I
B
B
B
B
P
B
1
4
2
3
7
5
6
10
8
9
-2
-1
-3
11
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Frame and Macroblock Prediction Types

• Anchor frame A frame that can be used for
  prediction
• We now discuss the various frame types and
  Macroblock types

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MPEG Notation

• Though the standard does not dictate this, the
  pattern (order) of frames are commonly referred
  by the following notation (N,M) where
• N is the number of frames from one
  I-frame(inclusive) to the next (exclusive).
• M is the number of frames from one
  anchor(inclusive) to the next(exclusive).

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MPEG2

• MPEG-2 is a standard for digital TV. It meets
  the requirements for HDTV and DVD (Digital
  Video/Versatile Disc)
• MPEG2 Supports the following levels

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MPEG4

• Originally targeted at very low bit-rate
  communication (4.8 to 64 Kb/sec), it now aims at
  the following ranges of bit-rates
• video -- 5 Kb to 5 Mb per second
• audio -- 2 Kb to 64 Kb per second
• It emphasizes the concept of Visual Objects --gt
  Video Object Plane (VOP)
• Objects can be of arbitrary shape, VOPs can be
  non-overlapped or overlapped
• Supports content-based scalability
• Supports object-based interactivity
• Individual audio channels can be associated with
  objects
• Good for video composition, segmentation, and
  compression networked VRML, audiovisual
  communication systems (e.g., text-to-speech
  interface, facial animation), etc.
• Standards being developed for shape coding,
  motion coding, texture coding, etc.

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CONCLUSION

• Why compression
• Performance issues
• Lossless compression techniques
• Run Length Encoding, LZW Encoding
• Lossy compression techniques
• Vector Quantization
• Compression standards
• JPEG, MPEG

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READING

• Digital Image Compression Algorithms and
  Standards By Weidong Kou
• Digital Image processing- By Kenneth Castleman
• Gregory K Wallace The JPEG still picture
  compression standard 1991
• http//www.onssi.com/downloads/OnSSI_WP_compressio
  n_techniques.pdf