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### 240-373 Image Processing

Montri Karnjanadecha

http://fivedots.coe.psu.ac.th/~montri

240-373: Chapter 12: Image Compression

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

240-373: Chapter 12: Image Compression

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

240-373: Chapter 12: Image Compression

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

240-373: Chapter 12: Image Compression

Statistical Compression

next most frequently used colors

1000

1001

1010

1011

the rest

11000

11001

11010

11011

11100

11101

11110

11111

240-373: Chapter 12: Image Compression

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

240-373: Chapter 12: Image Compression

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

240-373: Chapter 12: Image Compression

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

240-373: Chapter 12: Image Compression

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

240-373: Chapter 12: Image Compression

Huffman coding example

- Example: For a nine-color system, we obtain the following coding:

0 100000 5 01

1 10001 6 000

2 101 7 1001

3 001 8 100001

5 11

Storage has improved from 19000*3 bits (57000) to 51910 bits.

240-373: Chapter 12: Image Compression

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

240-373: Chapter 12: Image Compression

Run Length Encoding

Example: image

giving a sequence: 1 2 1 1 1 1 1 3 4 4 4 4 1 1 3 3 3 5 1 1 1 1 3 3

(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: 1 1 2 1 1 5 3 1 4 4 1 2 3 3 5 1 1 4 3 2

(20 values)

240-373: Chapter 12: Image Compression

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

240-373: Chapter 12: Image Compression

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

240-373: Chapter 12: Image Compression

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

240-373: Chapter 12: Image Compression

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

240-373: Chapter 12: Image Compression

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

240-373: Chapter 12: Image Compression

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

240-373: Chapter 12: Image Compression

Quantizing compression example

- Consider the following image

which is to be compressed to 2 bits/pixel, i.e. N = 4

240-373: Chapter 12: Image Compression

Quantizing compression example

histogram:

0 **

1 **

2 *********

3 ***********

4 *********

5 ****

6 *****

7 ********

8 *********

9 ******

240-373: Chapter 12: Image Compression

Quantizing compression example

65 pixels, down to 4 gray levels = 16.24 in each range. The best range are:

0 **

13 1 **

2 *********

3 ***********

20 4 *********

5 ****

17 6 *****

7 ********

8 *********

15 9 ******

240-373: Chapter 12: Image Compression

Example: Cont’d

With median gray levels 2,3,6 and 8, the new image become:

Note that this technique is similar to the histogram equalization technique.

240-373: Chapter 12: Image Compression

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

240-373: Chapter 12: Image Compression

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

240-373: Chapter 12: Image Compression

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
- Example

3 bits/pixel x 48 pixels = 144 bits/image

240-373: Chapter 12: Image Compression

Example (cont’d)

If the first frame is sent, then the differences (mod 8) are now:

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

240-373: Chapter 12: Image Compression

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

240-373: Chapter 12: Image Compression

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.

240-373: Chapter 12: Image Compression

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”

240-373: Chapter 12: Image Compression

Latest frame

m

Search area

n

p

p

One of many blocks

Motion Prediction240-373: Chapter 12: Image Compression

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

240-373: Chapter 12: Image Compression

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

2

1

2

1 2 1

- Image standard
- .BMP, .PIC, .PCX, .PIG, .TIFF, .GIF, .JPG, etc.

240-373: Chapter 12: Image Compression

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.

240-373: Chapter 12: Image Compression

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