1. Image Compression
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Image Compression

2. Reference [1] Gonzalez and Woods, Digital Image Processing. 9/20/2018
Image Compression

3. Objective
Reduce the number of bytes required to represent a digital image
Redundant data reduction
Remove patterns
Uncorrelated data confirms redundant data elimination
Auto correlation?
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Image Compression

4. Enabling Technology Compressions is used in FAX RPV Teleconference
REMOTE DEMO
etc
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Image Compression

5. Review What and how to exploit data redundancy
Model based approach to compression
Information theory principles
Types of compression
Lossless, lossy
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Image Compression

6. Information recovery
Processing
Data
Information
We want to recover the information, with reduced data volumes.
Reduce data redundancy.
How to measure the data redundancy.
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Image Compression

7. Relative Data Redundancy
Assume that we have two data sets D1 and D2.
Both on processing yield the same information.
Let n1 and n2 be the info – carrying units of the respective data sets.
Relative data redundancy is defined on comparing the relative dataset sizes
RD = 1 – 1/CR
where CR is the compression ratio
CR = n1 / n2
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Image Compression

8. Examples RD = 1 – 1/CR CR = n1 / n2
D1 is the original and D2 is compressed.
When CR = 1, i.e. n1 = n2 then RD=0; no data redundancy relative to D1 .
When CR = 10, i.e. n1 = 10 n2 then RD=0.9; implies that 90% of the data in D1 is redundant.
What does it mean if n1 << n2 ?
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Image Compression

9. Types of data redundancy
Coding
Interpixel
Psychovisual
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Image Compression

10. Coding Redundancy How to assign codes to alphabet
In digital image processing
Code = gray level value or color value
Alphabet is used conceptually
General approach
Find the more frequently used alphabet
Use fewer bits to represent the more frequently used alphabet, and use more bits for the less frequently used alphabet
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Image Compression

11. Coding Redundancy 2 Focus on gray value images
Histogram shows the frequency of occurrence of a particular gray level
Normalize the histogram and convert to a pdf representation – let rk be the random variable
pr(rk) = nk/n ; k = 0, 1,2 …., L-1, where L is the number of gray level values
l(rk) = number of bits to represent rk
Lavg = k=0 to L-1 l(rk) pr(rk) = average number of bits to encode one pixel. For M x N image, bits required is MN Lavg
For an image using an 8 bit code, l(rk) = 8, Lavg = 8.
Fixed length codes.
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Image Compression

12. Fixed vs Variable Length Codes
From [1]
Lavg = 2.7
CR= 3/2.7 = 1.11
RD = 1 – 1/1.11 = 0.099
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Image Compression

13. Code assignment view
From [1]
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Image Compression

14. Interpixel Redundancy
From [1]
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Image Compression

15. Run Length Coding From [1] CR=1024*343/12166*11 = 2.63
RD = 1-1/2.63 = 0.62
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Image Compression

16. Psychovisual Redundancy
Some visual characteristics are less important than others.
In general observers seeks out certain characteristics – edges, textures, etc – and the mentally combine them to recognize the scene.
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Image Compression

17. From [1]
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Image Compression

18. From [1]
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Image Compression

19. Fidelity Criteria Subjective Objective Sum of the absolute error
RMS value of the error
Signal to Noise Ratio
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Image Compression

20. Subjective scale
From [1]
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Image Compression

21. Image Compression Model
From [1]
Run length JPEG Huffman
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Image Compression