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Geodesic Minimal Paths

Geodesic Minimal Paths. Vida Movahedi Elder Lab, January 2010. Contents. What is the goal? Minimal Path Algorithm Challenges How can Elderlab help? Results. Goal. Finding boundary of salient objects in images of natural scenes. Minimal Path. Inputs: Two key points

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Geodesic Minimal Paths

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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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