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

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

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

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

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

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

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

Algorithm One

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

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

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

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

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

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

Algorithm Two: Introduction

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

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

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

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

Algorithm Two: Real Images continued The calculated B * R for Pixels at the bottom of this image was 0.1386. 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.

Questions & Demonstration 3 iterations

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

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

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

Questions 4 iterations