1. See Through Fog Imaging Project: P06441
Fog is a natural occurring phenomenon which inhibits visibility. Fog has effects on all facets of transportation whether it be flying over or through it in an airplane, or driving through it with a car. It also affects the visibility of images through the use of cameras in aerial photography.
By eliminating the fog from these images, a number of exciting applications become possible. Using video cameras in transportation will allow the vehicle operator to have a clear view of the surrounding terrain through the use of video sampling and a LCD screen. Using a similar process in aerial photography will allow video reconnaissance of foggy areas.
Two algorithms have been developed to successfully remove fog from images. Each algorithm uses the same basic equation to defog the image:
Equation:
Algorithm One
Algorithm Two
Algorithm One uses the above equation to defog the images by making an initial guess as to the values of the two main variables, B and C0, and scales the pixels within the image to be between zero and one. It then runs the algorithm using the initial guesses and searches for the smallest pixel. Once this is found, it then varies B until this pixel value reaches zero. It then locates the largest pixel and varies C0 until the pixel value becomes one. It then checks to see if the difference between the new and old B and C0 values are less then a threshold value, a very small number somewhere around 1E10^-15. If it is, then the B and C0 values have been found and the image can be defogged, if not, then repeats the process using the calculated B and C0 values. Examples can be seen below.
The images below are an example of how the defogging algorithm was applied to an image. The first image is a common picture of a baboon and the graph below is its histogram. The middle image is the same image after fog was induced artificially induced upon, using greater “distance” for pixels that are nearer the top of the image. The histogram below this image shows a histogram that is substantially different from the original histogram. The third image is the image after the second defogging algorithm has been applied to it. It is visually identical to the original image. The histogram is also nearly identical to the original histogram, however, its right side has been stretched to the right (toward one) a small, but noticeable, amount (by ).
Original Image
Fog Induced Image
Defogged Image
Original Histogram
Fogged Histogram
Defogged Histogram
Algorithm Comparison
The Algorithms were compared in order to get a better understanding of how they may be used, be it for surveillance or traveling purposes.
Algorithm Two defogs faster then Algorithm One in most cases
Algorithm Two has a smaller Root Mean Square Error (the resulting image is clearer)
Algorithm Two tends to determine a B and C0 which is closer to the actual B and C0
It can be concluded that Algorithm Two is the better of the two algorithms
Future Work
Design a system to retrieve distance information
Devise a method to apply these techniques to color images
Implement a video system capable of removing fog in real-time
Find a way to apply the algorithm to images where B is not constant
Team Members
Philip Edwards, Computer Engineering William Parsons, Computer Engineering
Acknowledgments
Project Sponsor: Dr. Raghuveer Rao Project Mentor: Professor George Slack