240-373
Image Processing
Montri Karnjanadecha
montri@coe.psu.ac.th
http://fivedots.coe.psu.ac.th/~montri
240-373: Chapter 12: Image Compression
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Chapter 12
Image Compression
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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
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Image Compression
• 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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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:
four frequently used colors
000
001
010
011
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Statistical Compression
next most frequently used colors
1000
1001
1010
1011
the rest
11000
11001
11010
11011
11100
11101
11110
11111
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Statistical Compression
This means that the length (for an 640x480 image
=150K) is reduced to
[(0.6*3)+(0.3*4)+(0.1*5)] * 640 * 480 = 131.25K
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– 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
M 1
  pi log 2 pi
i 0
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Huffman Coding
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
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Huffman Coding
OPERATION: (cont’d)
– 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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Huffman coding example
• Example: For a nine-color system, we obtain
the following coding:
0
1
2
3
5
100000
10001
101
001
11
5
6
7
8
01
000
1001
100001
Storage has improved from 19000*3 bits (57000) to
51910 bits.
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Run Length Encoding
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
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Run Length Encoding
Example:
image
1
1
1
1
2
3
1
1
1
4
3
1
1
4
3
1
1
4
3
3
1
4
5
3
giving a sequence:
121111134444113335111133
(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:
11211531441233511432
(20 values)
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Run Length Encoding
• Notes
– Huffman coding can be performed after Run
length encoding
– It might be possible to implement the Huffman
code only on the run lengths
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Run Length Encoding
• 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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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
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Changing the Domain
OPERATION: (cont’d)
– 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
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Quantizing Compression
• Involves reducing number of gray levels
• The easiest way is to divide all the gray levels
by a factor
Technique 4: Quantizing compression
USE: To reduce storage space by limiting
number of colors or gray levels
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Quantizing Compression
OPERATION:
– Let P be the number of pixels in an original image to be
compressed to N gray levels
– Create a histogram of the gray level in the original image
– Identify N ranges in the histogram such that approximately
P/N lie in each range
– Identify the median (the gray level with 50% of the pixels in
the range on one side of it and 50% on the other) gray level
in each range. These will be the N gray levels used to
quantize the image
– Store the N gray levels and allocate to each pixel a group (0
to n -1) according to which range it lies in
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Quantizing compression example
• Consider the following image
2 9 6 4 8 2 6 3 8 5 9 3 7
3 8 5 4 7 6 3 8 2 8 4 7 3
3 8 4 7 4 9 2 3 8 2 7 4 9
3 9 4 7 2 7 6 2 1 6 5 3 0
2 0 4 3 8 9 5 4 7 1 2 8 3
which is to be compressed to 2 bits/pixel, i.e. N = 4
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Quantizing compression example
histogram:
0
1
2
3
4
5
6
7
8
9
**
**
*********
***********
*********
****
*****
********
*********
******
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Quantizing compression example
65 pixels, down to 4 gray levels = 16.24 in
each range. The best range are:
13
20
17
15
0
1
2
**
**
*********
3
4
***********
*********
5
6
7
****
*****
********
8
9
*********
******
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Example: Cont’d
With median gray levels 2,3,6 and 8, the new image
become:
0 3 2 1 3 0 2 1 3 2 3 1 2
1 3 2 1 2 2 1 3 0 3 1 2 1
1 3 1 2 1 3 0 1 3 0 2 1 3
1 3 1 2 0 2 2 0 0 2 2 1 0
0 0 1 1 3 3 2 1 2 0 0 3 0
Note that this technique is similar to the histogram
equalization technique.
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Fractal Compression
• Fractal Compression
– Yields 10000:1 compression ratio
– Can also yield 1000000:1 compression ration with
conventional algorithm added
– Based on very simple functions to generate (in
multi-dimensional space) highly complex and
totally predictable pattern
– Fractal graphics workstations: a 640x480 VGA
image requires 5800 bytes of storage
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Real-Time Image Transmission
• Compressing and sending a sequence of
images in real-time
• Most of real-time vision systems send many
images of the same type before changing the
image to a new scene
• For example, most television program will
dwell on a scene for at least 5 seconds
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Real-Time Image Transmission
• Approach: the full first frame is sent, then
only the differences of the next frames will be
sent
• Run length encoding or simple vector
encoding can be used for data reduction
1 1 2 2 1 2 2 1
1 1 2 2 1 2 2 1
• Example
1 2 2 1 1 2 1 1
1 1 4 4 4 1 1 1
1 2 2 1 1 2 1 1
1 1 2 4 4 4 1 1
2 1 4 4 4 1 1 1
1 2 4 4 4 2 1 1
2 1 1 4 4 4 1 1
1 2 1 4 4 4 1 1
1 1 2 2 2 1 1 1
1 1 2 2 2 1 1 1
3 bits/pixel x 48 pixels = 144 bits/image
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Example (cont’d)
If the first frame is sent, then the differences (mod
8) are now:
0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0
0 0 2 0 0 5 0 0
0 0 3 0 0 5 0 0
0 0 3 0 0 6 0 0
0 0 0 0 0 0 0 0
vector encoded:
(2,2)=2, (2,5)=5, (3,2)=3, (3,5)=5, (4,2)=3, (4,5)=6
6 vectors, 6 bits/position, 4 bits/difference = 60 bits
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Example (cont’d)
Modified run length encoded:
18 2 2 2 5 4 3 2 5 4 3 2 6 10
6 bits/0 count, 4 bits/difference = 66 bits
• Difficulties arise when the scene does change, then
the information may be too much to be transmitted
in one frame time
• Solution: The receiver has a series of buffers for
images to be displayed. The differences image must
take less than the minimum ‘uncompressed’ frame
time
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Motion Prediction
• The image may still have the same
constituent parts but they may have all
shifted in one direction
Technique 5: Block matching for motion
prediction
USE: Saving space by estimating what motion
has occurred between past and present
images, then only saving the changes.
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Motion Prediction
OPERATION:
1.Tile off the latest frame into blocks
2.Each of these blocks is then compared with blocks
of the same size from the previous frame that are
near in position to the block on the latest frame.
3.This has to be done for all blocks in the latest
frame. Then the best match (and the
corresponding predicted movement vector) is
determined. This is called “ full-search block
matching”
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Motion Prediction
Previous frame
Latest frame
m
Search area
n
p
One of many blocks
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Quadtrees
• A quadtree is a recursive segmenting of an
image into four parts
• A suitable compression method for an image
that has large area of the same colored pixels
and rectangular in character
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Quadtrees
• Operation:
– the original image is cut into 4 equal quarter
images and theses are cut into four, and so on…
– consider each quarter image, break the image that
has more than one color (non-homogeneous) and
combine similar quarter
– build a tree structure to store sub-images
relationship
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Quadtrees
2
1
2
1
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Standard Image File Format
–
–
–
–
–
–
–
–
.BMP
.PIC
.PCX
.PIG
.TIFF
.GIF
.JPG
etc.
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Image Compression Exercise
• Compare the compression of the following image
using (a) Huffman coding (b) run length coding. The
image has a gray level range of 0-7.
1 1 1 1 5 5 5 5 2 2 2 2
1 1 1 5 5 5 5 5 5 2 2 3
1 1 5 5 5 5 5 2 2 3 3 2
1 1 1 1 5 5 5 2 2 2 2 2
1 1 1 1 1 1 5 2 2 2 3 2
1 1 1 1 1 1 1 1 1 1 1 1
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