1. Hough Transform Procedure to find a shape in an image Shape can be described in parametric form Shapes in image correspond to a family of parametric solutions A voting scheme is used to determine the correct parameters

2. Hough Transform for Lines

3. Quantize space Each bin represents a line defined by Accumulate values in bin according to edge points Each bin contains the amount of points in image that would form a line defined by

4. Hough Transform for Lines Problem with vertical lines Normal form

5. Hough Transform for Lines -3-2123 -2 1 2

6. Hough Transform for Lines -3-2123 -4 -2 2 4

7. Pick in the parametric space that corresponds to the line

8. Hough Transform for Lines Domain of the parametric space: and image resolution M and N image resolution Not just lines, any parametric curve! However increase of dimensions of the parametric space

9. Hough Transform of Circles Circle is define by its center and radius -3D Hough parametric space

10. Hough Transform of Circles

12. Hough Transform Find parametric shapes in an image Slow but robust to noise and occlusion Quantization of the parameters controls accuracy and speed