1 / 30

Edge detection

Edge detection. Winter in Kraków photographed by Marcin Ryczek. Edge detection. Goal: Identify sudden changes (discontinuities) in an image Intuitively, most semantic and shape information from the image can be encoded in the edges More compact than pixels

finley
Télécharger la présentation

Edge detection

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Edge detection Winter in Kraków photographed by MarcinRyczek

  2. Edge detection • Goal: Identify sudden changes (discontinuities) in an image • Intuitively, most semantic and shape information from the image can be encoded in the edges • More compact than pixels • Ideal: artist’s line drawing (but artist is also using object-level knowledge) Source: D. Lowe

  3. Origin of edges • Edges are caused by a variety of factors: surface normal discontinuity depth discontinuity surface color discontinuity illumination discontinuity Source: Steve Seitz

  4. Review: Linear filtering • Image blurring • Separability • Median filtering

  5. intensity function(along horizontal scanline) first derivative edges correspond toextrema of derivative Edge detection • An edge is a place of rapid change in the image intensity function image

  6. Derivatives with convolution For 2D function f(x,y), the partial derivative is: For discrete data, we can approximate using finite differences: To implement the above as convolution, what would be the associated filter? Source: K. Grauman

  7. Partial derivatives of an image -1 1 1 -1 -1 1 or Which shows changes with respect to x?

  8. Finite difference filters • Other approximations of derivative filters exist: Source: K. Grauman

  9. Image gradient • The gradient of an image: The gradient points in the direction of most rapid increase in intensity • How does this direction relate to the direction of the edge? The gradient direction is given by The edge strength is given by the gradient magnitude Source: Steve Seitz

  10. Application: Gradient-domain image editing • Goal: solve for pixel values in the target region to match gradients of the source region while keeping background pixels the same P. Perez, M. Gangnet, A. Blake, Poisson Image Editing, SIGGRAPH 2003

  11. Where is the edge? Effects of noise • Consider a single row or column of the image Source: S. Seitz

  12. g f * g • To find edges, look for peaks in Solution: smooth first f Source: S. Seitz

  13. f Derivative theorem of convolution • Differentiation is convolution, and convolution is associative: • This saves us one operation: Source: S. Seitz

  14. Derivative of Gaussian filters • Which one finds horizontal/vertical edges? y-direction x-direction

  15. Derivative of Gaussian filters • Are these filters separable? y-direction x-direction

  16. Recall: Separability of the Gaussian filter Source: D. Lowe

  17. Scale of Gaussian derivative filter • Smoothed derivative removes noise, but blurs edge. Also finds edges at different “scales” 1 pixel 3 pixels 7 pixels Source: D. Forsyth

  18. Review: Smoothing vs. derivative filters • Smoothing filters • Gaussian: remove “high-frequency” components; “low-pass” filter • Can the values of a smoothing filter be negative? • What should the values sum to? • One: constant regions are not affected by the filter • Derivative filters • Derivatives of Gaussian • Can the values of a derivative filter be negative? • What should the values sum to? • Zero: no response in constant regions • High absolute value at points of high contrast

  19. The Canny edge detector • Filter image with derivative of Gaussian • Find magnitude and orientation of gradient • Non-maximum suppression: • Thin wide “ridges” down to single pixel width • Linking and thresholding(hysteresis): • Define two thresholds: low and high • Use the high threshold to start edge curves and the low threshold to continue them • MATLAB: edge(image, ‘canny’); J. Canny, A Computational Approach To Edge Detection, IEEE Trans. Pattern Analysis and Machine Intelligence, 8:679-714, 1986.

  20. The Canny edge detector original image Slide credit: Steve Seitz

  21. The Canny edge detector norm of the gradient

  22. The Canny edge detector thresholding

  23. The Canny edge detector How to turn these thick regions of the gradient into curves? thresholding

  24. Non-maximum suppression Check if pixel is local maximum along gradient direction, select single max across width of the edge requires checking interpolated pixels p and r

  25. The Canny edge detector Problem: pixels along this edge didn’t survive the thresholding thinning (non-maximum suppression)

  26. Hysteresis thresholding • Use a high threshold to start edge curves, and a low threshold to continue them. Source: Steve Seitz

  27. high threshold (strong edges) low threshold (weak edges) hysteresis threshold Hysteresis thresholding original image Source: L. Fei-Fei

  28. Recap: Canny edge detector • Compute x and y gradient images • Find magnitude and orientation of gradient • Non-maximum suppression: • Thin wide “ridges” down to single pixel width • Linking and thresholding(hysteresis): • Define two thresholds: low and high • Use the high threshold to start edge curves and the low threshold to continue them • MATLAB: edge(image, ‘canny’); J. Canny, A Computational Approach To Edge Detection, IEEE Trans. Pattern Analysis and Machine Intelligence, 8:679-714, 1986.

  29. Image gradients vs. meaningful contours • Berkeley segmentation database:http://www.eecs.berkeley.edu/Research/Projects/CS/vision/grouping/segbench/ human segmentation image gradient magnitude

  30. Data-driven edge detection Input images Training data Ground truth Output P. Dollar and L. Zitnick, Structured forests for fast edge detection, ICCV 2013

More Related