1. Project P06441: See Through Fog Imaging
November 10, 2006
Project Sponsor: Dr. Raghuveer Rao
Philip Edwards
William Parsons
Team Mentor: George Slack

2. Project Background
Paper by Raghuveer Rao and Seungsin Lee proposed 2 algorithms (intensity only)
Basic work to ensure current algorithms perform correctly
No characterization of parameters
Pixel values between zero and one

3. Sponsor Needs
Characterize and optimize two different algorithms for removing fog
Each algorithm uses the same basic equation:
F(k)=((I(k)/C0 – 1)*exp(B*dist(k))) + 1
Equation affects image at the pixel level
Characterize parameters used to defog
B guess, C0 guess, precision, Distance
Compare speed, quality, and overall performance of both algorithms
Apply Algorithms to actual foggy images

4. Process Overview Needs Assessment Concept Development Processing Speed
Quality of Image
Overall Performance
Concept Development
Color images
Hardware Realization
Analysis of Algorithms

5. Key Requirements High quality of defogged images Processing time B C0
Low distortion
Processing time
Must produce images reasonable quickly B
Crucial to removing fog from images C0
Also affects the amount of fog removed
Distance Matrix
Assigns a distance value to each pixel

6. F(k)=((I(k)/C0 – 1)*exp(B*dist(k))) + 1
Final Design
Analysis of the two algorithms
F(k)=((I(k)/C0 – 1)*exp(B*dist(k))) + 1
Using Matlab
Determine good initial values for B and C0
Characterize Distance Matrix
Determine reasonable threshold values
Apply to actual foggy images

7. Fog Induction Fog Induced in images for testing purposes
Known B
Known C0
Known Distance Matrix
Can control amount of fog in images

8. Algorithm One

9. Algorithm One: Distance Matrix Analysis
Found distance matrix does not need to be exact
Initial attempts on real world images have shown it can be estimated
B affected the most by changes in distance
Must be close to original distance to successfully remove fog
Otherwise fog is enhanced and fog becomes a brighter white

10. Algorithm One: β and C0 Analysis
B vs. distance
Initial guess
Iterations
Affect on each other

11. Algorithm One: Performance/Running Time
Average iterations to defog images
Performance vs. iterations
B calculations
C0 calculations
Root Mean Square Error

12. Iterations vs. Quality Fogged Image One Iteration Two Iterations
Three Iterations
Four Iterations
Five Iterations

13. Algorithm One: Real Images
Attempt to remove real fog from images:

14. Questions & Demonstration
Larger sky distance large ground distance
Small sky distance large ground distance
Original Image
Varied distance horizontally and vertically
Varied Distance vertically

15. Algorithm Two: Introduction

16. Algorithm Two: Distance Matrix Analysis
Change distances for fog/defog, observe image and record B
Distance affects fog pattern
Product Rij * B always comes out the same when R matrix is scaled

17. Algorithm Two: β Analysis
Ran algorithm using a wide variety of initial guesses for β
Number of iterations never went below 2 or above 5, except for images when iteration limit was reached

18. Algorithm Two: Performance vs. Running Time
Conducted by running algorithm for only a select number of iterations

19. Algorithm Two: Real Images
Distance matrix estimated
With actual distances, algorithm expected to perform better

20. Algorithm Two: Real Images continued
The calculated B * R for Pixels at the bottom of this image was It took 5 iterations to produce the defogged image.
The above images are an edge detection technique. Although the image on the right has slightly more and brighter edges, the difference is small.

21. Questions & Demonstration
3 iterations

22. Comparison of the Algorithms
Algorithms performance compared
B approximation
Mean square error
Number of iterations
Processing speed

23. Conclusions
Algorithms successfully applied to real-world images using estimated distances
Better algorithm has been determined through comparison
Run time Vs. performance analysis completed
Project was successful, pending approval from sponsor

24. Future Recommendations
Design a system to provide correct distance matrix
Apply these techniques to color images (perhaps through conversion to YCrCb)
Implement a video system to remove fog in real time
Devise a method to apply the algorithm to images where β isn’t constant

25. Questions
4 iterations