1. Image Transforms 主講人：虞台文

2. Content • Overview • Convolution • Edge Detection • Gradients • Sobel operator • Canny edge detector • Laplacian • Hough Transforms • Geometric Transforms • Affine Transform • Perspective Transform • Histogram Equalization

3. Image Transforms Overview

4. Image Transform Concept T[]

5. Image Transform Concept T[]

6. Image Transforms Convolution

7. g(x,y)is known as convolution kernel. Image Convolution

8. g(x,y)is known as convolution kernel. Image Convolution height2h + 1 width2w + 1

9. g(x,y)is known as convolution kernel. Image Convolution height2h + 1 width2w + 1

10. Some Convolution Kernels

11. OpenCV Implementation  Image Filter void cvFilter2D( const CvArr* src, CvArr* dst, const CvMat* kernel, CvPoint anchor=cvPoint(-1, -1) );

12. Deal with Convolution Boundaries void cvCopyMakeBorder( const CvArr* src, CvArr* dst, CvPoint offset, int bordertype, CvScalar value=cvScalarAll(0) );

13. Image Transforms Edge Detection

14. Edge Detection • Convert a 2D image into a set of curves • Extracts salient features of the scene • More compact than pixels

15. Origin of Edges surface normal discontinuity depth discontinuity surface color discontinuity illumination discontinuity Edges are caused by a variety of factors

16. How can you tell that a pixel is on an edge? Edge Detection

17. Step Edges Line Edges Roof Edge Edge Types

18. I x Real Edges • We want an Edge Operator that produces: • Edge Magnitude • Edge Orientation • High Detection Rate and Good Localization Noisy and Discrete!

19. Derivatives of Image in 1D • Edges can be characterized as either: • local extrema of I(x) • zero-crossings of 2I(x)  1D image  gradient  Laplacian

20. 2D-Image Gradient

21. 2D-Image Gradient • Gives the direction of most rapid change in intensity • Gradient direction: • Edge strength:

22. To precisely locate the edge, we need to thin. Ideally, edges should be only one point thick. T Non-zero edge width Classification of Points

23. The Sobel Operators Good Localization Noise Sensitive Poor Detection Sobel (3 x 3): Sobel (5 x 5): Poor Localization Less Noise Sensitive Good Detection

24. OpenCV Implementation  The Sobel Operators void cvSobel( const CvArr* src, CvArr* dst, int xorder, int yorder, int aperture_size = 3 );

25. OpenCV Implementation  The Scnarr Operator void cvSobel( const CvArr* src, CvArr* dst, int xorder, int yorder, int aperture_size = 3 ); aperture_size CV_SCHARR

26. Demonstration

27. Exercise Download Test Program

28. Effects of Noise Consider a single row or column of the image Where is the edge?

29. Solution: Smooth First

30. Solution: Smooth First Where is the edge?

31. Gaussian: Derivative Theorem of Convolution

32. Derivative Theorem of Convolution saves us one operation.

33. Optimal Edge Detection: Canny • Assume: • Linear filtering • Additive iidGaussian noise • An "optimal" edgedetector should have: • Good Detection Filter responds to edge, not noise. • Good Localization detected edge near true edge. • Single Response one per edge.

34. Optimal Edge Detection: Canny • Based on the first derivative of a Gaussian • Detection/Localization trade-off • More smoothing improves detection • And hurts localization.

35. Stages of the Canny algorithm • Noise reduction Size of Gaussian filter • Finding the intensity gradient of the image • Non-maximum suppression • Tracing edges through the image and hysteresisthresholding High threshold Low threshold

36. Parameters of Canny algorithm • Noise reduction • Size of Gaussian filter • Finding the intensity gradient of the image • Non-maximum suppression • Tracing edges through the image and hysteresis thresholding • High threshold • Low threshold

37. OpenCV Implementation  The Canny Operator void cvCanny( const CvArr* img, CvArr* edges, double lowThresh, double highThresh, int apertureSize = 3 );

38. Example: Canny Edge Detector Download Test Program

39. Review:Derivatives of Image in 1D • Edges can be characterized as either: • local extrema of I(x) • zero-crossings of 2I(x)  1D image  gradient  Laplacian

40. Laplacian • A scalar isotropic. • Edge detection: Find all points for which 2I(x, y) = 0 • Nothinning is necessary. • Tends to produce closed edge contours.

41. Laplacian

42. Discrete Laplacian Operators

43. OpenCV Implementation The Discrete Laplacian Operators void cvLaplace( const CvArr* src, CvArr* dst, int apertureSize = 3 );

44. Example

45. Laplician for Edge Detection Find zero-crossing on the Laplacian image.

46. Zero Crossing Detection There is a little bug in the above algorithm. Try to design your own zero-crossing detection algorithm.

47. Example:Laplician for Edge Detection Download Test Program

48. Laplacian for Image Sharpening

49. Example:Laplacian for Image Sharpening Sharpened Image

50. Laplacian of Gaussian (LoG) Gaussian: