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Image Transforms

Image Transforms. 主講人：虞台文. Content. Overview Convolution Edge Detection Gradients Sobel operator Canny edge detector Laplacian Hough Transforms Geometric Transforms Affine Transform Perspective Transform Histogram Equalization. Image Transforms. Overview. Image Transform Concept.

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Image Transforms

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  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:

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