1. Corners
Why are they important?

2. Corners
Why are they important?

3. Corners
Why are they important?

4. Corners
Why are they important?

5. Corners
Why are they important?

6. Corners
Why are they important?

7. Corners
Why are they important?

8. Corners
Why are they important?

9. Corners
Why are they important?

10. Corners
Why are they important?

11. Corners
Why are they important?

12. STOP

13. STOP

14. STOP

15. STOP

16. STOP

17. Corners
Why are they important?

18. Corners
Why are they important?

19. Corners
Why are they important?

20. Corners
Why are they important?

21. Corners
Why are they important?

22. Corners
Why are they important?

23. Corners
Why are they important?

24. Corners
Why are they important?

25. Corners
Why are they important?

26. Corners
Why are they important?

27. Corners
Why are they important?

28. Corners contain more edges than lines.
A point on a line is hard to match.

29. Corners contain more edges than lines.
A corner is easier

30. Edge Detectors Tend to Fail at Corners

31. Matlab

32. Finding Corners Intuition: Right at corner, gradient is ill defined.
Near corner, gradient has two different values.

33. Formula for Finding Corners
We look at matrix:
Gradient with respect to x, times gradient with respect to y
Sum over a small region, the hypothetical corner
WHY THIS?
Matrix is symmetric

34. First, consider case where:
This means all gradients in neighborhood are:
(k,0) or (0, c) or (0, 0) (or off-diagonals cancel).
What is region like if:
l1 = 0?
l2 = 0?
l1 = 0 and l2 = 0?
l1 > 0 and l2 > 0?

35. General Case:
From Linear Algebra we haven’t talked about it follows that since C is symmetric:
where R is a rotation matrix.
So every case is like one on last slide.

36. So, to detect corners Filter image.
Compute magnitude of the gradient everywhere.
We construct C in a window.
Use Linear Algebra to find l1 and l2.
If they are both big, we have a corner.