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Canny Edge Detector

Canny Edge Detector. Instructor: Guodong Guo. Detecting Edges in Image. Sobel Edge Detector. Edges. Threshold. Image I. Sobel Edge Detector. Sobel Edge Detector. Marr and Hildreth Edge Operator. Smooth by Gaussian Use Laplacian to find derivatives. Marr and Hildreth Edge Operator.

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Canny Edge Detector

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  1. Canny Edge Detector Instructor: Guodong Guo

  2. Detecting Edges in Image • Sobel Edge Detector Edges Threshold Image I

  3. Sobel Edge Detector

  4. Sobel Edge Detector

  5. Marr and Hildreth Edge Operator • Smooth by Gaussian • Use Laplacian to find derivatives

  6. Marr and Hildreth Edge Operator

  7. Marr and Hildreth Edge Operator Y X

  8. Marr and Hildreth Edge Operator Edge Image Zero Crossings Detection Zero Crossings

  9. Quality of an Edge Detector • Robustness to Noise • Localization • Too Many/Too less Responses True Edge Poor localization Too many responses Poor robustness to noise

  10. Canny Edge Detector • Criterion 1: Good Detection: The optimal detector must minimize the probability of false positives as well as false negatives. • Criterion 2: Good Localization: The edges detected must be as close as possible to the true edges. • Single Response Constraint: The detector must return one point only for each edge point.

  11. Canny Edge Detector • Difficult to find closed-form solutions.

  12. Canny Edge Detector • Convolution with derivative of Gaussian • Non-maximum Suppression • Hysteresis Thresholding

  13. Canny Edge Detector • Smooth by Gaussian • Compute x and y derivatives • Compute gradient magnitude and orientation

  14. Canny Edge Operator

  15. Canny Edge Detector

  16. Canny Edge Detector

  17. Non-Maximum Suppression We wish to mark points along the curve where the magnitude is biggest. We can do this by looking for a maximum along a slice normal to the curve (non-maximum suppression). These points should form a curve. There are then two algorithmic issues: at which point is the maximum, and where is the next one?

  18. Non-Maximum Suppression • Suppress the pixels in ‘Gradient Magnitude Image’ which are not local maximum

  19. Non-Maximum Suppression

  20. Non-Maximum Suppression

  21. Hysteresis Thresholding

  22. Hysteresis Thresholding • If the gradient at a pixel is above ‘High’, declare it an ‘edge pixel’ • If the gradient at a pixel is below ‘Low’, declare it a ‘non-edge-pixel’ • If the gradient at a pixel is between ‘Low’ and ‘High’ then declare it an ‘edge pixel’ if and only if it is connected to an ‘edge pixel’ directly or via pixels between ‘Low’ and ‘ High’

  23. Hysteresis Thresholding

  24. Finding Connected Components • Scan the binary image left to right top to bottom • If there is an unlabeled pixel p with a value of ‘1’ • Assign a new label to it • Recursively check the neighbors of pixel p and assign the same label if they are unlabeled with a value of ‘1’. • Stop when all the pixels with value ‘1’ have been labeled.

  25. Suggested Reading • Chapter 8, David A. Forsyth and Jean Ponce, "Computer Vision: A Modern Approach“ • Chapter 4, Emanuele Trucco, Alessandro Verri, "Introductory Techniques for 3-D Computer Vision"

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