Edges and Contours– Chapter 7

1. Edges and Contours– Chapter 7 continued

2. Edge detection • All of the previously studied edge detection filters worked on finding local gradients (1st derivative) • As such, all had to make decisions regarding the actual existence of an edge based on local information

3. Sobel edges – threshold on magnitude

4. Sobel edges – threshold on magnitude • The preceding images were edge-detected with a Sobel operator then binarized with various thresholds • The overall trend is predictable but the individual results are not • This threshold dependency is the curse of image processing • Difficult to isolate “real” edges • Difficult to find accurate edge location • We need smarter algorithms

5. Scale space processing • One method of dealing with the threshold dependency is through scale-space processing • An image is processed at various scales (sizes/resolution) revealing different sets of features at each scale • Features common to all [or many] sets are deemed “important”

6. The Gaussian Pyramid • Select a set of Gaussian filter parameters (sigma and width) and blur the image • Save the image • Reduce it’s size by subsampling (eliminating every other row/column) • Do it again

7. The Gaussian Pyramid • You end up with a series of images (a pyramid) each exposing different features • Coarse features at the top of the pyramid • Fine features at the bottom • You can now use the coarse features to select where to concentrate your processing of the fine features

8. Better (different) algorithms • Another method of dealing with the threshold dependency is through more complex algorithms

9. A better kernel • The Sobel mask is a derivative mask (computes the weighted difference of neighborhood pixels) • So is the Laplacian (negative in the middle, positive around the rest) • From calculus: the 2nd derivative of a signal is zero when the derivative magnitude is extremal

10. A better kernel • Combining these observations we can derive the Laplacian-Gaussian filter due to Marr and Hildreth • Also known as a DoG (Difference of Gaussians) because it can be approximated by subtracting two Gaussian kernels of same width and differing sigmas

11. The Gaussian kernel • Sigma 1.6, Filter Width 15

12. The Laplacian-Gaussian kernel • Bypassing the math and jumping to the results of applying the rules of calculus… • Similar in form to the Gaussian kernel

13. The Laplacian-Gaussian kernel • In 1 dimension… • Can be approximated by difference of two Gaussians

14. The Laplacian-Gaussian kernel • Convolution with this kernel results in edge magnitudes of both positive and negative values • We’re interested in where the sign changes occur (the zero crossing) • These are where the edges are (recall the calculus result)

15. Sobel vs. Laplacian-Gaussian • L-G does not detect as much “noise” as Sobel – why not?

16. Still something missing… • What are we ignoring in the following edge detection processes? • Gaussian filter • Sobel edge detection • Threshold based binarization of Sobel magnitude And • Laplacian-Gaussian filter • Zero crossing detection

17. We need a smarter algorithm • We merely selected each edge based on its magnitude and zero-crossing • We completely ignored its immediate surroundings • Why is this bad? • Detects edges we don’t want • Prone to noise • Prone to clutter • Doesn’t detect edges we do want • Weak magnitude edges are thresholded (thresheld?) away • We need a smarter algorithm!

18. The Canny edge detector • John Canny – MIT 1986 • Developed a process (series of steps) for identifying edges in an image • Gaussian smoothing of input image • Local derivative operator to detect edge candidates • Removal of edges that are clustered around a single location • Adaptive thresholding algorithm for final edge selection

19. Concepts • Gaussian smooth original image • Reduce the effects of noise • Local derivative operator • Simple neighbor pixel subtraction to detect gradients (1st derivative) • Non-maximal suppression • Thin out the edges around a given point • Threshold • Use two thresholds combined with spatial continuity

20. Spatial continuity • aka contour following • Apply the high threshold to get “obvious” edges • Search for a neighboring edge above the low threshold in the direction of the strong edge • We’re using a strong edge as an anchor point for a contour of weak and strong edges – known as Hysteresis

21. Canny results • With very conservative high/low thresholds

22. Results All edges Weak edges Contours Strong edges

23. Summary • Through more complex processing we arrive at a set of edges in which we have confidence • Minimal reliance on thresholds • The cost is complex (slow, memory intensive) processing • We must trade resources for accuracy!

24. ImageJ • Download/install plugins for • Sobel, Prewitt, Roberts, Kirsch, Nevatia-Babu • Plugins->FeatureJ->Edges • Canny implementation

25. Edge Sharpening • An process for making an image look “better” • In this case “better” means “sharper” • The general approach is to amplify the high-frequency components (the edges) to create a “perceived” sharpness

26. Method 1 – subtract 2nd derivative • This causes a step edge to undershoot at the bottom and overshoot at the top • The Laplacian works well for the 2nd derivative

27. ImageJ • Note that this is difficult to do in ImageJ since the convolution operation clamps negative pixel values to 0

28. Unsharp mask • Steps • Subtract a Gaussian-smoothed version of the image from the original creating a mask • Add a weighted version of the mask to the original image

29. ImageJ • Plugins->Chapter07->Filter UnsharpMask