1. Stockman MSU/CSE Fall 2009 Finding region boundaries

2. Stockman MSU/CSE Fall 2009 Object boundaries How to detect? How to represent? Problems relative to region/area segmentation

3. Stockman MSU/CSE Fall 2009 advantages Contrast often more reliable under varying lighting Boundaries give precise location Boundaries have useful shape information Boundary representation is sparse Humans use edge information

4. Stockman MSU/CSE Fall 2009 problems Detection weakens at boundary corners Topology of result is imperfect

5. Stockman MSU/CSE Fall 2009 topics Aggregating chains of boundary pixels Line and curve fitting Angles, sides, vertices Ribbons Imperfect graphs

6. Stockman MSU/CSE Fall 2009 Canny edge detector/tracker Detect, then follow high gradient boundary pixels Track along a “thin” edge Bridge across weaker contrast

7. Stockman MSU/CSE Fall 2009 Canny algorithm data

8. Stockman MSU/CSE Fall 2009 Overall Canny algorithm

9. Stockman MSU/CSE Fall 2009 Create thin edge response by suppressing weaker neighbors Find neighbors in direction of the gradient (across the edge) If neighbor response is weaker, delete it. Recall thick edges from 5x5 Sobel or Prewitt

10. Stockman MSU/CSE Fall 2009 Begin tracking only at high gradient points

11. Stockman MSU/CSE Fall 2009 Results with two spreads

12. Stockman MSU/CSE Fall 2009 Notes/Variations Very few parameters needed Can use multiple spreads and correlate the results in multiple edge images Can carefully manage the use of low and high thresholds, perhaps depending on size and quality of the current track Canny edge tracker is very popular

13. Stockman MSU/CSE Fall 2009 Aggregating pixels into curves Producing a discrete data structure with meaningful parts.

14. Stockman MSU/CSE Fall 2009 Tracking tasks Canny algorithm does some of these.

15. Stockman MSU/CSE Fall 2009 Possible output from tracker

16. Stockman MSU/CSE Fall 2009 The Hough Transform Detecting a straight line segment as a cluster in rho-theta space. (Can do circles or ellipses too.)

17. Stockman MSU/CSE Fall 2009 Voting evidence in cluster space

18. Stockman MSU/CSE Fall 2009 Pixels with distinct (r,c) coordinates map to same (d, Θ) X Y Θ d Detected set of edge points Textbook coordinate system vs Cartesian system

19. Stockman MSU/CSE Fall 2009 Mapping pixels (r, c) to polar parmameters (d, Θ) Row-column system Cartesian coordinate system d = x cos Θ + y sin Θ

20. Stockman MSU/CSE Fall 2009 Simple algorithm overview

21. Stockman MSU/CSE Fall 2009 Possible implementation

22. Stockman MSU/CSE Fall 2009 Binning evidence: note that original pixels [R, C] are saved in the bins.

23. Stockman MSU/CSE Fall 2009 Real world considerations The gradient direction Θ is bound to have error (due to what?) Since d is computed from Θ, d will also have error Thus, evidence is spread in parameter space and may frustrate binning methods (2D histogram)

24. Stockman MSU/CSE Fall 2009 Solutions Bins for (d, Θ) can be smoothed to aggregate neighbors. Multiple evidence can be put into the bins by adding deltas to Θ and computing variations of (d, Θ) Clustering can be done in real space; e.g. do not use binning Busy images should be handled using a grid of (overlapping) windows to avoid a cluttered transform space

25. Stockman MSU/CSE Fall 2009 What is the space of d and Θ ? Many apps range Θ from 0 to π only However, gradient direction can be detected from 0 to 2 π. Imagine a checkerboard – there are 4 prominent directions, not 2. Using full range of direction requires negative values of d – consider checkerboard with origin in the center.

26. Stockman MSU/CSE Fall 2009 Additional material Plastic slides from Stockman Plastic slides from Kasturi

27. Stockman MSU/CSE Fall 2009 Image to map work of Kasturi

28. Stockman MSU/CSE Fall 2009 Circular Hough Transform There are 3 parameters for a circle

29. Stockman MSU/CSE Fall 2009 Possible implementation

30. Stockman MSU/CSE Fall 2009 Some notes Circular and elliptical Hough Transforms are interesting, but of dubious value by themselves Smarter tracking methods, such as Snakes, balloons, etc. might be needed along with region features There are weak publications that will not help in real applications.

31. Stockman MSU/CSE Fall 2009 Fitting models to edge data Can use straight line segments for data compression, or parametric curves for shape detection.

32. Stockman MSU/CSE Fall 2009 Fitting curves

33. Stockman MSU/CSE Fall 2009 An unlimited number of models

34. Stockman MSU/CSE Fall 2009 Least squares fitting

35. Stockman MSU/CSE Fall 2009 Best fit minimizes sum of squared errors

36. Stockman MSU/CSE Fall 2009

37. Axis of least inertia better?

38. Stockman MSU/CSE Fall 2009 Ramer’s alg: perimeter to polygon

39. Stockman MSU/CSE Fall 2009 Angles, corners, ribbons

40. Stockman MSU/CSE Fall 2009 The downspout as a ribbon

41. Stockman MSU/CSE Fall 2009 Road and canal as ribbons

42. Stockman MSU/CSE Fall 2009 More boundary detection later Will investigate “physics-based models” Can fit to 2D (snakes) or 3D data (balloons) Models do not allow the object topology to break Models enforce object smoothness