Image Compression

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Image Compression

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Image Compression

• Reducing the size of image data files
• While retaining necessary information

Original Image
Compressed Image file
extracted Image file
compress
decompress
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Terminology

• refer relation between original image and
• the compressed file

1. Compression Ratio
2. Bits per Pixel

A larger number implies a better compression
A smaller number implies a better compression
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Compression Ratio
(1)

• Ex Image 256X256 pixels, 256 level grayscale can
  be compressed file size 6554 byte.
• Original Image Size 256X256(pixels) X
  1(byte/pixel)
• 65536 bytes

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Bits per Pixel

• Ex Image 256X256 pixels, 256 level grayscale can
  be compressed file size 6554 byte.
• Original Image Size 256X256(pixels) X
  1(byte/pixel)
• 65536 bytes
• Compressed file 6554(bytes)X8(bits/pixel)
• 52432 bits

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Why we want to compress?

• To transmit an RGB 512X512, 24 bit image
• via modem 28.2 kbaud(kilobits/second)

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Key of compression

• Reducing Data but Retaining Information

DATA are used to convey information.
Various amounts of data can be used to represent
the same amount of information. Its Data
redundancy
Relative data redundancy
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Entropy

• Average information in an image.

• Average number of bits per pixel

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Redundancy

• Coding Redundancy
• Interpixel Redundancy
• Psychovisual Redundancy

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Coding Redundancy

• Occurred when data used to represent image are
  not utilized in an optimal manner

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Coding Redundancy(cont)

• An 8 gray-level image distribution shown in Table

rk p(rk) code1 l1(rk) code2 l2(rk)
r00 0.19 000 3 11 2
r11/7 0.25 001 3 01 2
r22/7 0.21 010 3 10 2
r33/7 0.16 011 3 001 3
r44/7 0.08 100 3 0001 4
r55/7 0.06 101 3 00001 5
r66/7 0.03 110 3 000001 6
r71 0.02 111 3 000000 6
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Coding Redundancy(cont)

• Original Image 8 possible gray level 23

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Interpixel Redundancy

• Adjacent pixel values tend to be highly correlated

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Psychovisual Redundancy

• Some information is more important to the human
  visual system than other types of information

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Compression System Model

• Compression

• Decompression

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Types of Compression

• There are 2 types of Compression
• Loseless Compression
• Lossy Compression

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Loseless Compression

• No data are lost
• Can recreated exactly original image
• Often the achievable compression is mush less

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Huffman Coding

• Using Histogram probability
• 5 Steps
• Find the histogram probabilities
• Order the input probabilities(small?large)
• Addition the 2 smallest
• Repeat step 23, until 2 probability are left
• Backward along the tree assign 0 and 1

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Huffman Coding(cont)

• Step 1 Histogram Probability

p0 20/100 0.2 p1 30/100 0.3 p2 10/100
0.1 p3 40/100 0.4

• Step 2 Order

p3 ? 0.4 p1 ? 0.3 p0 ? 0.2 p2 ? 0.1
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Huffman Coding(cont)

• Step 3 Add 2 smallest

Natural Code Probability Huffman Code
00 0.2 010
01 0.3 00
10 0.1 011
11 0.4 1
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Huffman Coding(cont)

• The original Image average 2 bits/pixel
• The Huffman Codeaverage

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Run-Length Coding

• Counting the number of adjacent pixels with the
  same gray-level value
• Used primarily for binary image
• Mostly use horizontal RLC

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Run-Length Coding(cont)

• Binary Image 8X8

horizontal
1st Row 8
2nd Row 0,4,4
3rd Row 1,2,5
4th Row 1,5,2
5th Row 1,3,2,1,1
6th Row 2,1,2,2,1
7th Row 0,4,1,1,2
8th Row 8
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Run-Length Coding(cont)

• Extending basic RLC to gray-level image by using
  bit-plane coding
• It will better if change the natural code into
  gray code

00 01 10 11
00 01 11 10
Natural
Gray Code
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Lempel-Ziv-Weich Coding(LZW)
CRS PBP Encoded O/P Dictionary Location Dictionary Entry
39 39 39 256 39-39
39 120 39 257 39-120
120 39 120 259 120-39
39-39 120 256 260 39-39-126

• Assign fixed-length code words to variable
• GIF,TIFF,PDF

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Lossy Compression

• Allow a loss in the actual image data
• Can not recreated exactly original image
• Commonly the achievable compression is mush more
• JPEG

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Fidelity Criteria

• Objective fidelity criteria
• RMS Error
• RMS Signal-To-Noise Ratio
• Subjective fidelity criteria

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JPEG