1. 240-373 Image Processing, Leture #16
Image Compression
Purposes
To minimize storage space
To maximize transfer speed
To minimize hardware costs
Requirements
Speedy operation (compression and unpacking)
Significantly reduction in required memory
No significant loss of quality
Format of output suitable for transfer and storage
Types
Statistical compression--based on pixels in whole image
Spatial compression--based on the spatial relationship of pixels of similar type
Quantizing compression--reducing number of gray levels and resolution
Fractal compression--based on fractal generating functions
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Image Processing, Leture #16

2. Statistical Compression
The Huffman Coding
Based on the assumption that the histogram is not normally flat
If 4 of 16 colors are used 60% of the time, 4 more for a further 30% and the rest for 10%, then we could use the following scheme:
frequently used four colors
000
001
010
011
next most frequently used colors
1000
1001
1010
1011
the rest
11000
11001
11010
11011
11100
11101
11110
11111
This means that the length (for an 640x480 image=150K) is reduced to
[(0.6*3)+(0.3*4)+(0.1*5)] * 640 * 480 = K
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Image Processing, Leture #16

3. 240-373 Image Processing, Leture #16
The average length has been reduced from 4 bits to 3.5 bits
It can be shown that with M gray levels, each with probability of P0, P1, .. PM-1 , The number of bits required to code them is at least
Technique 1: The Huffman Code
USE: To reduce the space that an image uses on disk or in transit
OPERATION:
Order the gray levels according to their frequency of use, most occurrence first
Combine the two least used gray levels into one group, combine their frequencies and reorder the gray levels
Continue to do this until only two gray levels are left
Now allocate a 0 to one of these gray-level groups and a 1 to the other
Work back through the groupings so that where two groups have been combined to form a new, larger, group which is currently coded as ‘ccc’
Code one of the smaller groups as ccc0 and the other as ccc1
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Image Processing, Leture #16

4. Huffman coding example
Example: For a nine-color system, we obtain the following coding:
5 11
Storage has improved from 19000*3 bits = bits to bits.
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Image Processing, Leture #16

5. 240-373 Image Processing, Leture #16
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Image Processing, Leture #16

6. 240-373 Image Processing, Leture #16
Spatial Compression
Technique 2: Run length encoding
USE: To reduce the space required by an image
OPERATION:
The run is encoded by creating pairs of values: the first representing the gray level and the second how many of them are in the run
Example: image
giving a sequence:
(24 values)
with run length encoding
(1,1) (2,1) (1,5) (3,1) (4,4) (1,2) (3,3) (5,1) (1,4) (3,2)
this would give:
(20 values)
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Image Processing, Leture #16

7. Spatial Compression: Cont’d
Notes
Huffman coding can be performed after Run length encoding
It might be possible to implement the Huffman code only on the run lengths
Contour Coding
Reducing the areas of pixels of the same gray levels to a set of contours that bound those areas
Consider the following image
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Image Processing, Leture #16

8. 240-373 Image Processing, Leture #16
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Image Processing, Leture #16

9. 240-373 Image Processing, Leture #16
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Image Processing, Leture #16

10. 240-373 Image Processing, Leture #16
Changing the Domain
Technique 3: Compression using the frequency domain
USE: To reduce space required for an image
OPERATION:
Convert the image to the frequency domain using FFT or FHT
Threshold this new image removing all values less than k
If what is left is significantly less than the original image, using one of the spatial region techniques, store the rest of the image
If it is not significantly less, increase k-- more information will be lost
08/12/61
Image Processing, Leture #16