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Multi-object Convexity Shape Prior for Segmentation

  • Lena GorelickEmail author
  • Olga Veksler
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10746)

Abstract

Convexity is known as an important cue in human vision and has been recently proposed as a shape prior for segmenting a single foreground object. We propose a mutli-object convexity shape prior for multilabel image segmentation. We formulate a novel multilabel discrete energy function. To optimize our energy, we extend the trust region optimization framework recently proposed in the context of binary optimization. To that end we develop a novel graph construction. In addition to convexity constraints, our model includes \(L^1\) color separation term between the background and the foreground objects. It can also incorporate any other multilabel submodular energy term. Our formulation can be used to segment multiple convex objects sharing the same appearance model, or objects consisting of multiple convex parts. Our experiments demonstrate general usefulness of the proposed convexity constraint on real image segmentation examples.

Keywords

Image segmentation Convexity shape prior High-order functionals Trust region Graph cuts 

References

  1. 1.
    Boykov, Y., Kolmogorov, V.: Computing geodesics and minimal surfaces via graph cuts. In: International Conference on Computer Vision, pp. 26–33 (2003)Google Scholar
  2. 2.
    Boykov, Y., Jolly, M.P.: Interactive graph cuts for optimal boundary and region segmentation of objects in N-D images. In: IEEE International Conference on Computer Vision (ICCV) (2001)Google Scholar
  3. 3.
    Boykov, Y., Kolmogorov, V., Cremers, D., Delong, A.: An integral solution to surface evolution pdes via geo-cuts. In: Leonardis, A., Bischof, H., Pinz, A. (eds.) ECCV 2006. LNCS, vol. 3953, pp. 409–422. Springer, Heidelberg (2006).  https://doi.org/10.1007/11744078_32 CrossRefGoogle Scholar
  4. 4.
    Boykov, Y., Veksler, O., Zabih, R.: Fast approximate energy minimization via graph cuts. IEEE Trans. Pattern Anal. Mach. Intell. 23(11), 1222–1239 (2001)CrossRefGoogle Scholar
  5. 5.
    Gorelick, L., Boykov, Y., Veksler, O., Ben Ayed, I., Delong, A.: Submodularization for binary pairwise energies. In: IEEE Conference on Computer Vision and Pattern Recognition (CVPR), pp. 1154–1161, June 2014Google Scholar
  6. 6.
    Gorelick, L., Schmidt, F.R., Boykov, Y.: Fast trust region for segmentation. In: IEEE Conference on Computer Vision and Pattern Recognition (CVPR), Portland, Oregon, pp. 1714–1721, June 2013Google Scholar
  7. 7.
    Gorelick, L., Veksler, O., Boykov, Y., Nieuwenhuis, C.: Convexity shape prior for segmentation. In: Fleet, D., Pajdla, T., Schiele, B., Tuytelaars, T. (eds.) ECCV 2014. LNCS, vol. 8693, pp. 675–690. Springer, Cham (2014).  https://doi.org/10.1007/978-3-319-10602-1_44 Google Scholar
  8. 8.
    Gorelick, L., Veksler, O., Boykov, Y., Nieuwenhuis, C.: Convexity shape prior for binary segmentation. Trans. Pattern Anal. Mach. Intell. 39(2), 258–271 (2017)CrossRefGoogle Scholar
  9. 9.
    Ishikawa, H.: Exact optimization for markov random fields with convex priors. IEEE Trans. Pattern Anal. Mach. Intell. 25(10), 1333–1336 (2003)CrossRefGoogle Scholar
  10. 10.
    Liu, Z., Jacobs, D., Basri, R.: The role of convexity in perceptual completion: beyond good continuation. Vis. Res. 39, 4244–4257 (1999)CrossRefGoogle Scholar
  11. 11.
    Mamassian, P., Landy, M.: Observer biases in the 3D interpretation of line drawings. Vis. Res. 38, 2817–2832 (1998)CrossRefGoogle Scholar
  12. 12.
    Nieuwenhuis, C., Töppe, E., Gorelick, L., Veksler, O., Boykov, Y.: Efficient regularization of squared curvature. In: IEEE Conference on Computer Vision and Pattern Recognition (CVPR), pp. 4098–4105, June 2014Google Scholar
  13. 13.
    Royer, L.A., Richmond, D.L., Rother, C., Andres, B., Kainmueller, D.: Convexity shape constraints for image segmentation. In: 2016 IEEE Conference on Computer Vision and Pattern Recognition, CVPR 2016, Las Vegas, NV, USA, 27–30 June 2016, pp. 402–410 (2016)Google Scholar
  14. 14.
    Schlesinger, D.: Exact solution of permuted submodular minsum problems. In: Yuille, A.L., Zhu, S.-C., Cremers, D., Wang, Y. (eds.) EMMCVPR 2007. LNCS, vol. 4679, pp. 28–38. Springer, Heidelberg (2007).  https://doi.org/10.1007/978-3-540-74198-5_3 CrossRefGoogle Scholar
  15. 15.
    Strekalovskiy, E., Cremers, D.: Generalized ordering constraints for multilabel optimization. In: International Conference on Computer Vision (ICCV) (2011)Google Scholar
  16. 16.
    Tang, M., Gorelick, L., Veksler, O., Boykov, Y.: Grabcut in one cut. In: International Conference on Computer Vision (2013)Google Scholar
  17. 17.
    Yuan, Y.: A review of trust region algorithms for optimization. In: The Fourth International Congress on Industrial and Applied Mathematics (ICIAM) (1999)Google Scholar

Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  1. 1.University of Western OntarioLondonCanada

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