1. Parallel Processing – Final Project Performed by:Nitsan Mane Jonathan Distler PP9

2. Overview Main Goal Main Goal Hough Transform – Definition Hough Transform – Definition Straight Lines Recognition Straight Lines Recognition Circles Recognition Circles Recognition Parallel Implementation Parallel Implementation

3. Main Goal Learning the algorithm and its applications Learning the algorithm and its applications Implementation on line detection and circle detection with constant radius Implementation on line detection and circle detection with constant radius Translating critical serial code to parallel code Translating critical serial code to parallel code Comparison on cost and speed up between the serial and parallel version Comparison on cost and speed up between the serial and parallel version

4. Hough Transform (Definition) Shape detection in a picture Shape detection in a picture Standard Method – simple equations (algebraic and parametric) Standard Method – simple equations (algebraic and parametric) Generalized Method – high order equations, complex shapes recognition Generalized Method – high order equations, complex shapes recognition

5. Hough Transform (Definition) The algorithm is based on axis transformation Straight Lines: Circles:

6. Line Recognition X Y φ r 0 π Given a radius and an angle we find the solution to the equation by choosing a point on the (X,Y) plain The equation:

7. Line Recognition (Detection) 1.Intersection on the polar plain gives the point on the ( x,y ) axis 2.An infinite line 90º left-right to this point, gives the detected line

8. Line Recognition (Example) The (x,y) points are the edges of the figure

9. Line Recognition (Under noise)

10. Circle Recognition r X Y Cx Cy 0 The equation:

11. Circle Recognition (Example)

12. Parallel Implementation Line Recognition Line Recognition –Send a picture to all the processors –Angle computing at the beginning of the program using a lookup table - sin() and cos() are calculated only once –All the angles are sorted in groups and every processor handles a different group 1111 2222 3333 4444 5555… nnnn n Processors

13. Parallel Implementation Circle Recognition Circle Recognition –Send the picture to all the processors –Divide Cx in order to generate the same number of Cy points between the processors Cx n Processors

14. Questions?