Finite Sample Bias of Robust Estimators in Segmentation of Closely Spaced Structures: A Comparative Study

  • Reza HoseinnezhadEmail author
  • Alireza Bab-Hadiashar
  • David Suter


This paper presents the design and implementation of a new comparative analytical framework for studying the usability of modern high breakdown robust estimators. The emphasis is on finding the intrinsic limits, in terms of size and relative spatial accuracy, of such techniques in solving the emerging challenges of the segmentation of fine structures. A minimum threshold for the distance between separable structures is shown to depend mainly on the scale estimation error. A scale invariant performance measure is introduced to quantify the finite sample bias of the scale estimate of a robust estimator and the measure is evaluated for some state-of-the-art high breakdown robust estimators using datasets containing at least two close but distinct structures with varying distances and inlier ratios. The results show that the new generation of density-based robust estimators (such as pbM-estimator and TSSE) have a poorer performance in problems with datasets containing only a small number of samples in each structure compared with ones based on direct processing of the residuals (such as MSSE). An important message of this paper is that an estimator that performs best in some circumstances, may not be competitive in others: particularly performance on data structures that are relatively large and/or well-separated vs closely spaced fine structures.


Segmentation Robust estimation Finite sample bias 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Bab-Hadiashar, A., Suter, D.: Robust optic flow computation. Int. J. Comput. Vis. 29(1), 59–77 (1998) CrossRefGoogle Scholar
  2. 2.
    Qian, G., Chellappa, R., Zheng, Q.: Bayesian algorithms for simultaneous structure from motion estimation of multiple independently moving objects. IEEE Trans. Image Process. 14(1), 94–109 (2005) CrossRefMathSciNetGoogle Scholar
  3. 3.
    Vidal, R., Ma, Y., Soatto, S., Sastry, S.: Two-view multibody structure from motion. Int. J. Comput. Vis. 68(1), 7–25 (2006) CrossRefGoogle Scholar
  4. 4.
    Bab-Hadiashar, A., Gheissari, N.: Range image segmentation using surface selection criterion. IEEE Trans. Image Process. 15(7), 2006–2018 (2006) CrossRefGoogle Scholar
  5. 5.
    Bab-Hadiashar, A., Suter, D.: Range and motion segmentation. In: Bab-Hadiashar, A., Suter, D. (eds.) Data Segmentation and Model Selection for Computer Vision, pp. 119–142. Springer, New York (2000). Chap. 5 Google Scholar
  6. 6.
    Meer, P.: Robust techniques for computer vision. In: Medioni, G., Kang, S. (eds.) Emerging Topics in Computer Vision, pp. 107–190. Prentice Hall, New York (2004). Chap. 3 Google Scholar
  7. 7.
    Chen, H., Meer, P.: Robust regression with projection based M-estimators. In: Proceedings of the Ninth IEEE International Conference on Computer Vision (ICCV’03), pp. 878–885, Nice, France (2003) Google Scholar
  8. 8.
    Subbarao, R., Meer, P.: Heteroscedastic projection based M-estimators. In: Workshop on Empirical Evaluation Methods in Computer Vision (in Conjunction with CVPR’05), pp. 38–44, San Diego, CA (2005) Google Scholar
  9. 9.
    Subbarao, R., Meer, P.: Beyond RANSAC: user independent robust regression. In: Workshop on 25 Years of RANSAC (in Conjunction with CVPR’06), pp. 101–108, New York, NY (2006) Google Scholar
  10. 10.
    Romanesque Churches of the Bourbonnais (France): Image and range data provided by Columbia University, Department of Art, History and Archeology.
  11. 11.
    Stewart, C.: Bias in robust estimation caused by discontinuities and multiple structures. IEEE Trans. Pattern Anal. Mach. Intell. 19(8), 818–833 (1997) CrossRefGoogle Scholar
  12. 12.
    Hoseinnezhad, R., Bab-Hadiashar, A.: Consistency of robust estimators in multi-structural visual data segmentation. Pattern Recognit. 40, 3677–3690 (2007) zbMATHCrossRefGoogle Scholar
  13. 13.
    Yu, X., Bui, T., Krzyzak, A.: Robust estimation for range image segmentation and reconstruction. IEEE Trans. Pattern Anal. Mach. Intell. 16(5), 530–538 (1994) CrossRefGoogle Scholar
  14. 14.
    Bab-Hadiashar, A., Suter, D.: Robust segmentation of visual data using ranked unbiased scale estimator. Robotica 17, 649–660 (1999) CrossRefGoogle Scholar
  15. 15.
    Lee, K., Meer, P., Park, R.: Robust adaptive segmentation of range images. IEEE Trans. Pattern Anal. Mach. Intell. 20(2), 200–205 (1998) CrossRefGoogle Scholar
  16. 16.
    Wang, H., Suter, D.: Robust adaptive-scale parametric model estimation for computer vision. IEEE Trans. Pattern Anal. Mach. Intell. 26(11), 1459–1474 (2004) CrossRefGoogle Scholar
  17. 17.
    Rousseeuw, P., Leroy, A.: Robust Regression and Outlier Detection, pp. 1–20. Wiley, New York (2003). Chap. 1 Google Scholar
  18. 18.
    Huber, P.: Robust Statistics. Wiley, New York (2004). Chap. 5 Google Scholar
  19. 19.
    Li, G.: Robust regression. In: Hoaglin, D., Mosteller, F., Tukey, J. (eds.) Exploring Data Tables, Trends and Shapes, pp. 281–343. Wiley, New York (1985) Google Scholar
  20. 20.
    Bab-Hadiashar, A., Suter, D.: Motion segmentation: a robust approach. In: Proceedings of IEEE International Workshop on the Interpretation of Visual Motion (IVM 98), pp. 3–9, Santa Barbara, California (1998) Google Scholar
  21. 21.
    Cheng, Y.: Mean shift, mode seeking, and clustering. IEEE Trans. Pattern Anal. Mach. Intell. 17(8), 790–799 (1995) CrossRefGoogle Scholar
  22. 22.
    Comaniciu, D., Meer, P.: Mean shift: a robust approach toward feature space analysis. IEEE Trans. Pattern Anal. Mach. Intell. 24(5), 603–619 (2002) CrossRefGoogle Scholar
  23. 23.
    Fashing, M., Tomasi, C.: Mean shift is a bound optimization. IEEE Trans. Pattern Anal. Mach. Intell. 27(3), 471–474 (2005) CrossRefGoogle Scholar
  24. 24.
    Fischler, M., Bolles, R.: Random sample consensus: a paradigm for model fitting with applications to image analysis and automated cartography. Commun. Assoc. Comput. Mach. 24(6), 381–395 (1981) MathSciNetGoogle Scholar
  25. 25.
    Gander, W., Gautschi, W.: Adaptive quadrature—revisited. BIT Numer. Math. 40, 84–101 (2000) CrossRefMathSciNetGoogle Scholar
  26. 26.
    Subbarao, R., Meer, P.: Subspace estimation using projection based M-estimators over Grassman manifolds. In: Ales Leonardis, A.P. (ed.) 9th European Conference on Computer Vision–ECCV’06, Graz, Austria, May 2006, pp. 301–312. Springer, Berlin (2006) Google Scholar
  27. 27.
    Ronchetti, E.: Robust regression methods and model selection. In: Bab-Hadiashar, A., Suter, D. (eds.) Data Segmentation and Model Selection for Computer Vision, pp. 31–40. Springer, New York (2000). Chap. 2 Google Scholar

Copyright information

© Springer Science+Business Media, LLC 2010

Authors and Affiliations

  • Reza Hoseinnezhad
    • 1
    Email author
  • Alireza Bab-Hadiashar
    • 2
  • David Suter
    • 3
  1. 1.Melbourne School of EngineeringThe University of MelbourneMelbourneAustralia
  2. 2.Faculty of Engineering and Industrial SciencesSwinburne University of TechnologyMelbourneAustralia
  3. 3.School of Computer ScienceThe University of AdelaideAdelaideAustralia

Personalised recommendations