1. Research Institute for Future Media Computing
未来媒体技术与计算研究所
Research Institute for Future Media Computing
7. DCT-based Research Topics
江健民，国家千人计划特聘教授
深圳大学未来媒体技术与计算研究所所长
Office Room: 409

2. Research Road Map Input Information or Data
Visualization to convert the data into 2D or other multi-dimensional sets
Data transform via Fourier, DCT, etc.
Feature extraction and analysis in transform domain

3. 7.1 Image extraction in DCT domain
Jiang J. and Weng Y. (2004) “Video Extraction for Fast Content Access to MPEG Compressed Videos” IEEE Transactions on Circuits, Systems and Video Technology, Vol 14, No 5, 2004,pp ;
Jiang J. and Feng G.C. (2002): "The spatial relationship of DCT coefficients between a block and its sub-blocks" IEEE Transactions on Signal Processing, IEEE, 50 (5):
Jiang J., Qiu K. and G. Xiao (2008) “An edge block content descriptor for MPEG compressed videos”, IEEE Transactions on Circuits, Systems and Video Tech. Vol 18, No 7, pp ;

4. DCT Simplifications

5. Introduction of Taylor series

6. Taylor series expansion of discrete cosine transform
When v=1, we have:

7. DCT simplifications for v=1

8. DCT simplification for v=0
Consider：

9. DCT simplification for variable u
For variable u, we can make similar arrangement as given below：
Consider the simplification derived for variable v：
Observations：
The constant coefficient is 4 for v=0，and for v=1;
When v=0，the corresponding two terms indexed by j are added together, and when v=1, the corresponding two terms indexed by j are subtracted together.

10. Inference on DCT simplifications for variable u
For b00 ：
For b01 ：
For b10 ：
For b11 ：

11. DCT simplification results

12. Summary of DCT Simplifications

13. Approximated image extraction in DCT domain
Solving the above equations，we have:
Observations:
The approximated image has ¼ of the original width and height；
The extracted pixel aij is constructed from the first four DCT coefficients, b00, b01, b10, b11, which contain the majority of energy inside the block;

14. Implementation of the image extraction algorithm
b11
b00
b01
b10
a00
a10
a01
a11 - +
1/8
Observation of the implementation cost:
As seen above, the extraction of 2x2 pixel block only needs 8 additions；
The multiplication with 1/8 can be implemented via shifting 3 bits to the right.