1). We can represent the equation of a circle parametrically by :

               x= a+ rcosϑ

               y= b + rsinϑ

               0 ≤ ϑ ≤ 2π

How you could implement a Hough Transform to detect circles using this form of equation? Comment on this methods relative merits / drawbacks.

2). How would you use the Hough transform to detect three-dimensional shapes? In particular how would you detect two and three - dimensional straight lines?

3). Write a Matlab code type procedure to detect straight lines only in  any given image using the Hough transform algorithm.

4). Enhance the algorithm you will use and the written code in order to attain more accuracy.

Your report should consists of

• Problem Statement - formulate the problem.
• Analysis - determine the inputs, outputs, relevant formulas, etc.
• Design - define the list of steps (the Hough Transform algorithm) needed to solve the problem.
• Implementation - list here the name of the functions used in the program, indicating for each function which algorithm steps are going to be implemented by each function.
• Use comments in your code and explain every step wherever needed.
• Write down how you can further improve the existing code and algorithm for stronger accuracy and results?