Edges and Contours– Chapter 7

1. Edges and Contours– Chapter 7

2. Visual perception • We don’t need to see all the color detail to recognize the scene content of an image • That is, some data provides critical information for recognition, other data provides information that just makes things look “good”

3. Visual perception • Sometimes we see things that are not really there!!! Kanizsa Triangle (and variants)

4. Edges • Edges (single points) and contours (chains of edges) play a dominant role in (various) biological vision systems • Edges are spatial positions in the image where the intensity changes along some orientation (direction) • The larger the change in intensity, the stronger the edge • Basis of edge detection is the first derivative of the image intensity “function”

5. First derivative – continuous f(x) • Slope of the line at a point tangent to the function

6. First derivative – discrete f(u) • Slope of the line joining two adjacent (to the selected point) point u-1 u u+1

7. Discrete edge detection • Formulated as two partial derivatives • Horizontal gradients yield vertical edges • Vertical gradients yield horizontal edges • Upon detection we can learn the magnitude (strength) and orientation of the edge • More in a minute…

8. NOTE • In the following images, only the positive magnitude edges are shown • This is an artifact of ImageJ Process->Filters->Convolve… command • Implemented as an edge operator, the code would have to compensate for this

9. Detecting edges – sharp image Image Vertical Edges Horizontal Edges

10. Detecting edges – blurry image Image Vertical Edges Horizontal Edges

11. The problem… • Localized (small neighborhood) detectors are susceptible to noise

12. The solution • Extend the neighborhood covered by the filter • Make the filter 2 dimensional • Perform a smoothing step prior to the derivative • Since the operators are linear filters, we can combine the smoothing and derivative operations into a single convolution

13. Edge operator • The following edge operators produce two results • A “magnitude” edge map (image) • An “orientation” edge map (image)

14. Prewitt operator • 3x3 neighborhood • Equivalent to averaging followed by derivative • Note that these are convolutions, not matrix multiplications

15. Prewitt – sharp image

16. Prewitt – blurry image

17. Prewitt – noisy image • Clearly this is not a good solution…what went wrong? • The smoothing just smeared out the noise • How could you fix it? • Perform non-linear noise removal first

18. Prewitt magnitude and direction

19. Prewitt magnitude and direction

20. Sobel operator • 3x3 neighborhood • Equivalent to averaging followed by derivative • Note that these are convolutions, not matrix multiplications • Same as Prewitt but the center row/column is weighted heavier

21. Sobel – sharp image

22. Sobel – blurry image

23. Sobel – noisy image • Clearly this is not a good solution…what went wrong? • The smoothing just smeared out the noise • How could you fix it? • Perform non-linear noise removal first

24. Sobel magnitude and direction

25. Sobel magnitude and direction

26. Sobel magnitude and direction • Still not good…how could we fix this now? • Using the information of the direction (lots of randomly oriented, non-homogeneous directions) can help to eliminate edged due to noise • This is a “higher level” (intelligent) function

27. Roberts operator • Looks for diagonal gradients rather than horizontal/vertical • Everything else is similar to Prewitt and Sobel operators

28. Roberts magnitude and direction

29. Roberts magnitude and direction

30. Roberts magnitude and direction

31. Compass operators • An alternative to computing edge orientation as an estimate derived from two oriented filters (horizontal and vertical) • Compass operators employ multiple oriented filters • To most famous are • Kirsch • Nevatia-Babu

32. Kirsch Filter • Eight 3x3 kernel • Theoretically must perform eight convolutions • Realistically, only compute four convolutions, the other four are merely sign changes • The kernel that produces the maximum response is deemed the winner • Choose its magnitude • Choose its direction

33. Kirsch filter kernels Vertical edges L-R diagonal edges Horizontal edges R-L diagonal edges

34. Kirsch filter

35. Nevatia-Babu Filter • Twelve 5x5 kernel • Theoretically must perform twelve convolutions • Increments of approximately 30° • Realistically, only compute six convolutions, the other six are merely sign changes • The kernel that produces the maximum response is deemed the winner • Choose its magnitude • Choose its direction

36. Nevatia-Babu filter