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Exploring Geodesic Minimal Paths for Boundary Detection in Natural Images

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  1. Geodesic Minimal Paths Vida Movahedi Elder Lab, January 2010

  2. Contents • What is the goal? • Minimal Path Algorithm • Challenges • How can Elderlab help? • Results

  3. Goal • Finding boundary of salient objects in images of natural scenes

  4. Minimal Path • Inputs: • Two key points • A potential function to be minimized along the path • Output: • The minimal path

  5. Minimal Path- problem formulation • Global minimum of the active contour energy: C(s): curve, s: arclength, L: length of curve • Surface of minimal action U: minimal energy integrated along a path between p0 and p Ap0,p : set of all paths between p0 and p

  6. Fast Marching Algorithm • Computing U by frontpropagation: evolving a front starting from an infinitesimal circle around p0 until each point in image is reached

  7. Challenges • Can the minimal path algorithm solve the boundary detection problem? • Key points? • Potential Function? • Idea: Use York’s multi-scale algorithm (MS)

  8. MS Algorithm • We have a set of contour hypotheses at each scale • These contours can be used to find good candidates for key points • These contours (and some other cues) can also be used to build potential functions. • Multi-scale model (coarse to fine) can also help

  9. Key Points • Simplest approach: 3 key points, equally spaced on the MS contour (prior) • Maximize product of probabilities (MS unary cue)

  10. Rotating Key Points • Consider multiple hypothesis for key points • Obtain multiple contours • Next step: Find which contour is the best • Distribution model for contour lengths • Distribution model for average Pb value • Improve method to find simple contours only

  11. Rotating Key Points

  12. Potential Function • Ideas: • The Sobel edge map • Distance transform of MS contour (prior) • Distance transform of several overlapped MS contours • Berkeley’s Pb map • Likelihood based on Pb and distance to prior contour

  13. Sobel Edge Map

  14. Sobel Edge Map • Can use the MS prior to emphasize or de-emphasize map

  15. Distance Transform

  16. Distance transform • Too much emphasis on MS prior

  17. Distance transform of 10 overlapped MS contours

  18. Challenge: If MS contours are not good

  19. Challenge: If MS contours are not good

  20. Berkeley’s Pb map

  21. Combining Pb and Distance Next step: learning models

  22. Summary • The MP algorithm provides global minimal paths • The MS algorithm provides contour hypothesis • The MS contours can be used to obtain key points and potential functions for MP algorithm • Next steps: • Learning models for better potential functions • Obtaining simple contours • Ranking contours • Evaluate multi-scale model

  23. References Laurent D. Cohen (2001), “Multiple Contour Finding and Perceptual Grouping using Minimal Paths”, Journal of Mathematical Imaging and Vision, vol. 14, pp. 225-236. Estrada, F.J. and Elder, J.H. (2006) “Multi-scale contour extraction based on natural image statistics”, Proc. IEEE Workshop on Perceptual Organization in Computer Vision, pp. 134-141. J. H. Elder, A. Krupnik and L. A. Johnston (2003), "Contour grouping with prior models," IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 25, pp. 661-674.

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