Circle Recognition Using The ‘folding’ method

1. Circle Recognition Using The ‘folding’ method Guy Ben-Yosef July 2005

2. A Folding of an image • We can part the image into two sub image identical on its size, • An AND operation between these two sub image is folding of an image around the given axis. • Regard non-zero as 1 • reduce the amount of information leaving only the information relevant for identify the symmetry. • As a circle being an all around symmetric shape, we can use folding around its diameter as much as we want without losing valuable information for detecting it.

3. The Hough Transform • Search and Score method • Voting for all possible structure • Using The gradient normal for voting a circle • Advantages: Accurate, missing parts and distortion shapes • Disadvantages: Depend no the gradient, noisy edge image can lead to false detection

4. The Use of Folding for circle detection • The double fold over X axis and Y axis • Such double fold would be unique for an origin of a circle

5. A Voting process on the double fold image • The voting process on the double fold image. • Examining each distance votes • How many votes for a circle declaration? • Using the condition • Noise can be confused with small radiuses • Using the T threshold:

6. Complexity • The Fold operation takes O(N^2) • Total complexity:

7. Performance Synthetic Images

8. Performance (2) Noisy Images Additive noise: Noisy Images Salt and Paper noise:

9. Performance (3) Real image:

10. Performance – My Magnum Opus Computer, Computer Where is the Ball?

11. Performance - My Magnum Opus Here is the ball!!!

12. The main advantages • Accurate origin, Accurate radius. • The ability to deal and recognize fat edges contour . • Low chance for false circles. • Folding makes the algorithm robust to noise on any kind.

13. The main disadvantages • Time complexity • The inability to detect distortion and missing parts circles. • Detection of small circles • Can not detect two different circle with the same origin

14. The Fold and Vote Vs. Hough • Complexity: HT (Hough transform) takes O(N3) while Fold&Vote algorithm takes (N4). • Dealing with noise image: The folding method gives for the Fold&Vote algorithm a small benefit upon HT. • Dealing with noisy edge-detection: The HT is heavily dependant on a good clear edge detection, both in edges and gradients. • Fold&Vote algorithm is capable of handing noisy edge detection, as long as the circle edge stays as a whole. • Robustness to shape distortions and to occlusions/missing parts of an object: The HT iscapable of finding such circles while the Fold&Vote algorithm is not. • False detection: HT algorithm can fall into phantom circles , while the strict and simple voting process on The Fold&Vote algorithm minimize false detections

15. Conclusions and Further work • The problem of circle detection on an image is a tough problem. • The algorithm presented has its disadvantages, and the major of it , the way I see it is it’s time complexity. For example, it takes about 3-4 hours for it to detect a 260x355 image. • It seems that smaller time complexity algorithm would take its price on the performances. • I kept compare my algorithm to the Hough transform base algorithm, and to the naïve circle detection algorithm. I guess my algorithm is somewhere between. • I do think now, that progress on solving the problem ,need the use of other tools then image manipulation, such as inference, for example. • The algorithm, of course can use for detection of all kinds of symmetric shapes, after making few changes on the voting process.