Efficient Closed-Form Solution to Generalized Boundary Detection

  • Marius Leordeanu
  • Rahul Sukthankar
  • Cristian Sminchisescu
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7575)


Boundary detection is essential for a variety of computer vision tasks such as segmentation and recognition. We propose a unified formulation for boundary detection, with closed-form solution, which is applicable to the localization of different types of boundaries, such as intensity edges and occlusion boundaries from video and RGB-D cameras. Our algorithm simultaneously combines low- and mid-level image representations, in a single eigenvalue problem, and we solve over an infinite set of putative boundary orientations. Moreover, our method achieves state of the art results at a significantly lower computational cost than current methods. We also propose a novel method for soft-segmentation that can be used in conjunction with our boundary detection algorithm and improve its accuracy at a negligible extra computational cost.


Window Size Boundary Detection Image Channel Window Center Occlusion Boundary 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


  1. 1.
    Roberts, L.: Machine perception of three-dimensional solids. In: Optical and Electro-Optical Information Processing, pp. 159–197. MIT Press (1965)Google Scholar
  2. 2.
    Prewitt, J.: Object enhancement and extraction. In: Picture Processing and Psychopictorics, pp. 75–149. Academic Press, New York (1970)Google Scholar
  3. 3.
    Marr, D., Hildtreth, E.: Theory of edge detection. Proc. Royal Society (1980)Google Scholar
  4. 4.
    Canny, J.: A computational approach to edge detection. PAMI 8, 679–698 (1986)CrossRefGoogle Scholar
  5. 5.
    Ruzon, M., Tomasi, C.: Edge, junction, and corner detection using color distributions. PAMI 23 (2001)Google Scholar
  6. 6.
    Stein, A., Hebert, M.: Occlusion boundaries from motion: Low-level detection and mid-level reasoning. IJCV 82 (2009)Google Scholar
  7. 7.
    Sundberg, P., Brox, T., Maire, M., Arbelaez, P., Malik, J.: Occlusion boundary detection and figure/ground assignment from optical flow. In: CVPR (2011)Google Scholar
  8. 8.
    He, X., Yuille, A.: Occlusion Boundary Detection Using Pseudo-depth. In: Daniilidis, K., Maragos, P., Paragios, N. (eds.) ECCV 2010, Part IV. LNCS, vol. 6314, pp. 539–552. Springer, Heidelberg (2010)CrossRefGoogle Scholar
  9. 9.
    Arbelaez, P., Maire, M., Fowlkes, C., Malik, J.: Contour detection and hierarchical image segmentation. PAMI 33 (2011)Google Scholar
  10. 10.
    Mairal, J., Leordeanu, M., Bach, F., Hebert, M., Ponce, J.: Discriminative Sparse Image Models for Class-Specific Edge Detection and Image Interpretation. In: Forsyth, D., Torr, P., Zisserman, A. (eds.) ECCV 2008, Part III. LNCS, vol. 5304, pp. 43–56. Springer, Heidelberg (2008)CrossRefGoogle Scholar
  11. 11.
    Hariharan, B., Arbelaez, P., Bourdev, L., Maji, S., Malik, J.: Semantic contours from inverse detectors. In: ICCV (2011)Google Scholar
  12. 12.
    Kanade, T.: Image understanding research at CMU. In: DARPA IUW (1987)Google Scholar
  13. 13.
    Di Senzo, S.: A note on the gradient of a multi-image. CVGIP 33 (1986)Google Scholar
  14. 14.
    Cumani, A.: Edge detection in multispectral images. CVGIP 53 (1991)Google Scholar
  15. 15.
    Koschan, M., Abidi, M.: Detection and classification of edges in color images. Signal Processing Magazine, Special Issue on Color Image Processing 22 (2005)Google Scholar
  16. 16.
    Martin, D., Fawlkes, C., Malik, J.: Learning to detect natural image boundaries using local brightness, color, and texture cues. PAMI 26 (2004)Google Scholar
  17. 17.
    Ren, X.: Multi-scale Improves Boundary Detection in Natural Images. In: Forsyth, D., Torr, P., Zisserman, A. (eds.) ECCV 2008, Part III. LNCS, vol. 5304, pp. 533–545. Springer, Heidelberg (2008)CrossRefGoogle Scholar
  18. 18.
    Meer, P., Georgescu, B.: Edge detection with embedded confidence. PAMI 23 (2001)Google Scholar
  19. 19.
    Baker, S., Nayar, S.K., Murase, H.: Parametric feature detection. In: DARPA Image Understanding Workshop (1997)Google Scholar
  20. 20.
    Petrou, M., Kittler, J.: Optimal edge detectors for ramp edges. PAMI 13 (1991)Google Scholar
  21. 21.
    Lagarias, J., Reeds, J.A., Wright, M.H., Wright, P.E.: Convergence properties of the Nelder-Mead simplex method in low dimensions. SIAM Optimization 9 (1998)Google Scholar
  22. 22.
    Catanzaro, B., Su, B.Y., Sundaram, N., Lee, Y., Murphy, M., Keutzer, K.: Efficient, high-quality image contour detection. In: ICCV (2009)Google Scholar
  23. 23.
    Shi, J., Malik, J.: Normalized cuts and image segmentation. PAMI 22 (2000)Google Scholar
  24. 24.
    Sargin, M., Bertelli, L., Manjunath, B., Rose, K.: Probabilistic occlusion boundary detection on spatio-temporal lattices. In: ICCV (2009)Google Scholar
  25. 25.
    Carreira, J., Sminchisescu, C.: Constrained parametric min-cuts for automatic object segmentation. In: CVPR (2010)Google Scholar
  26. 26.
    Leordeanu, M., Sukthankar, R., Sminchisescu, C.: Generalized boundaries from multiple image interpretations. Techincal Report, Institute of Mathematics of the Romanian Academy (August 2012)Google Scholar
  27. 27.
    Sun, D., Roth, S., Black, M.: Secrets of optical flow estimation and their principles. In: CVPR (2010)Google Scholar
  28. 28.
    Brox, T., Bregler, C., Malik, J.: Large displacement optical flow. In: CVPR (2009)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Marius Leordeanu
    • 1
  • Rahul Sukthankar
    • 3
    • 4
  • Cristian Sminchisescu
    • 2
    • 1
  1. 1.Institute of Mathematics of the Romanian AcademyRomania
  2. 2.Faculty of Mathematics and Natural ScienceUniversity of BonnGermany
  3. 3.Google ResearchUSA
  4. 4.Carnegie Mellon UniversityUSA

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