1. Hough Transform Omri Zorea and Alon LipnikGroup #11

2.  Technique to find imperfect instances of object within a certain class of shapes.  (i.e. lines, cycles, ellipses, parabolas etc.).  Use in image analysis, computer vision and digital image processing.  Was invented by Richard Duda and Peter Hart in 1972 (patent of Paul Hough, 1962). Introduction Hough Transform 1. Aerial photo 2. X-Y plane 3. Hough plane detecting transform

3. Hough Transform  Find lines in picture (y = -mx + b).  Match dots on the picture to lines and match line to a dot.  The slope (m) can goes to infinity (unbounded domain)  polar coordinates.

4. Hough Transform  Detect arbitrary shapes in picture.  Each point in Image space is now a sinusoid: ρ = x cosθ + y sinθ  For each edge point on image it compute his gradient and know which shape is it.

5. Hough Transform  Detect arbitrary shapes in picture.  Accumulator matrix - find lines with maximum points.  determines Threshold values in matrix.  the values are the points-density of shape.

6. Parallel Algorithm Hough Transform  The image is divided into rows with the same number of columns.  PVM is a programming tool used for the message routing, data conversion and task scheduling.  Complexity of O(m*n^2). m – different theta values. nxn – image size (* Algorithm LARPBS – linear array reconfigurable pipeline bus system)

7. Parallel Algorithm Hough Transform Speed Up:  Check on 4, 8, 16 and 32 processors.  Two different algorithms.  Image density range 5% - 15%.

8. Parallel Algorithm Hough Transform Efficiency:  Image density range from 5% to 25%.  Check on 4, 8, 12, 16 and 32 processors (process 0 is the master).  Trade-Off (processors and image density).

9.  Parallel algorithms for Hough Transform, Fevzi Oktay Ozbek : http://preserve.lehigh.edu/cgi/viewcontent.cgi?article=1073&context=etd http://preserve.lehigh.edu/cgi/viewcontent.cgi?article=1073&context=etd  A fast efficient parallel HT algorithm on LARPBS: http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.99.8684&rep=rep1&type=pdf  Guillermo Sapiro of Duke university : https://www.youtube.com/watch?v=kMK8DjdGtZo References