International Journal of Computer Vision

, Volume 126, Issue 1, pp 111–139 | Cite as

On the Beneficial Effect of Noise in Vertex Localization

  • Konstantinos A. RaftopoulosEmail author
  • Stefanos D. Kollias
  • Dionysios D. Sourlas
  • Marin Ferecatu


A theoretical and experimental analysis related to the effect of noise in the task of vertex identification in unknown shapes is presented. Shapes are seen as real functions of their closed boundary. An alternative global perspective of curvature is examined providing insight into the process of noise-enabled vertex localization. The analysis reveals that noise facilitates in the localization of certain vertices. The concept of noising is thus considered and a relevant global method for localizing Global Vertices is investigated in relation to local methods under the presence of increasing noise. Theoretical analysis reveals that induced noise can indeed help localizing certain vertices if combined with global descriptors. Experiments with noise and a comparison to localized methods validate the theoretical results.


Noising Global vertices Global curvature Shape representation Object recognition Shape modeling Incremental noising Vertex localization 


  1. Raftopoulos, K., & Kollias, S. (2011). The Global-local transformation for noise resistant shape representation. Computer Vision and Image Understanding, 115(8), 1170.CrossRefGoogle Scholar
  2. Bennett, J. R., & Mac, J. S. (1975). Donald, on the measurement of curvature in a quantized environment. IEEE Transactions on Computers, 24(8), 803.CrossRefzbMATHGoogle Scholar
  3. Rosin, P., & Zunic, J. (2008). Algorithms for measuring shapes with applications in computer vision. In A. Nayak & I. Stojmenovic (Eds.), Handbook of applied algorithms: Solving scientific, engineering, and practical problems (pp. 347–372). Hoboken: Wiley.CrossRefGoogle Scholar
  4. Flusser, J., Zitova, B., & Suk, T. (2006). Rotation moment invariants for recognition of symmetric object. Pattern Recognition, 15(12), 3784.MathSciNetGoogle Scholar
  5. Xu, D., & Li, H. (2008). Geometric moment invariants. Pattern Recognition (PR), 41(1), 240.CrossRefzbMATHGoogle Scholar
  6. Zunic, J. D., Rosin, P. L., & Kopanja, L. (2006). On the orientability of shapes. IEEE Transactions on Image Processing, 15(11), 3478.CrossRefGoogle Scholar
  7. Stojmenovic, M., & Zunic, J. (2008). Measuring elongation from shape boundary. Journal of Mathematical Imaging and Vision, 30(1), 73.Google Scholar
  8. Zunic, J. D., Hirota, K., & Rosin, P. L. (2010). A Hu moment invariant as a shape circularity measure. Pattern Recognition, 43(1), 47.CrossRefzbMATHGoogle Scholar
  9. Abbasi, S., Mokhtarian, F., & Kittler, J. (1999). Curvature scale space image in shape similarity retrieval. Multimedia Systems, 7(6), 467.CrossRefGoogle Scholar
  10. Zhang, D., & Lu, G. (2003). A comparative study of curvature scale space and Fourier descriptors for shape-based image retrieval. Journal of Visual Communication and Image Representation, 14(1), 39.CrossRefGoogle Scholar
  11. Belongie, S., Malik, J., & Puzicha, J. (2002). Shape matching and object recognition using shape contexts. IEEE Transactions on Pattern Analysis and Machine Intelligence, 24(4), 509.CrossRefGoogle Scholar
  12. Sladoje, N., & Lindblad, J. (2009). High-precision boundary length estimation by utilizing gray-level information. IEEE Transaction on Pattern Analysis and Machine Intelligence, 31(2), 357–363.CrossRefGoogle Scholar
  13. Biasotti, S., Floriani, L. D., Falcidieno, B., Frosini, P., Giorgi, D., Landi, C., et al. (2008). Describing shapes by geometrical-topological properties of real functions. ACM Computing Surveys, 40(4), 12:1.CrossRefGoogle Scholar
  14. Porteous, I. (2001). Geometric Differentiation. Cambridge: Cambridge University Press.zbMATHGoogle Scholar
  15. Goldfeather, J., & Interrante, V. (2004). A novel cubic-order algorithm for approximating principal direction vectors. ACM Transactions on Graphics, 23(1), 45.CrossRefGoogle Scholar
  16. Razdan, A., & Bae, M. (2005). Curvature estimation scheme for triangle meshes using biquadratic BéZier patches. Computer-Aided Design, 37(14), 1481.CrossRefzbMATHGoogle Scholar
  17. Nguyen, T., & Debled-Rennesson, I. (2007). Curvature estimationin noisy curves. In W. Kropatsch, M. Kampel, & A. Hanbury (Eds.), Computer analysis of images and patterns (Vol. 4673, pp. 474–481)., Lecture notes in computer science Berlin: Springer.CrossRefGoogle Scholar
  18. Bajaj, C. L., & Xu, G. (2003). Anisotropic diffusion of surfaces and functions on surfaces. ACM Transactions on Graphics, 22(1), 4.CrossRefGoogle Scholar
  19. Pottmann, H., Wallner, J., Huang, Q. X., & Yang, Y. L. (2009). Integral invariants for robust geometry processing. Computer Aided Geometric Design, 26(1), 37.MathSciNetCrossRefzbMATHGoogle Scholar
  20. Tward, D. J., Ma, J., Miller, M. I., & Younes, L. (2013). Robust diffeomorphic mapping via geodesically controlled active shapes. Journal of Biomedical Imaging, 2013, 205494.Google Scholar
  21. Coeurjolly D., Lachaud, J., & Levallois, J. (2013). Integral based curvature estimators in digital geometry. In 17th IAPR International Conference, DGCI (pp. 215–227).Google Scholar
  22. He, X., & Yung, N. H. C. (2004). Curvature scale space corner detector with adaptive threshold and dynamic region of support. In Proceedings of the 17th International Conference on Pattern Recognition, 2004. ICPR 2004 (vol. 2, pp. 791–794).Google Scholar
  23. Kerautret, B., & Lachaud, J. O. (2009). Curvature estimation along noisy digital contours by approximate global optimization. Pattern Recognition, 42(10), 2265.CrossRefzbMATHGoogle Scholar
  24. Nguyen, T. P., & Debled-Rennesson, I. (2011). A discrete geometry approach for dominant point detection. Pattern Recognition, 44(1), 32.CrossRefzbMATHGoogle Scholar
  25. Raftopoulos, K., & Ferecatu, M. (2014). Noising versus smoothing for vertex identification in unknown shapes. In 2014 IEEE Conference on Computer Vision and Pattern Recognition (CVPR) (pp. 4162–4168).Google Scholar
  26. Manay, S., Cremers, D., Hong, B. W., Yezzi, A., & Soatto, S. (2006). Integral invariant signatures for shape matching. IEEE Transactions on Pattern Analysis and Machine Intelligence, 27(11), 1602.CrossRefzbMATHGoogle Scholar
  27. Sebastian, T. B., Klein, P. N., & Kimia, B. B. (2004). Recognition of shapes by editing their shock graphs. IEEE Transactions on Pattern Analysis and Machine Intelligence, 26(5), 550.CrossRefGoogle Scholar
  28. Manning, C. D., Raghavan, P., & Schutze, H. (2008). Introduction to information retrieval. New York: Cambridge University Press.CrossRefzbMATHGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC 2017

Authors and Affiliations

  1. 1.CEDRIC-CNAMParis Cedex 03France
  2. 2.University of LincolnLincolnUK
  3. 3.Elais Unilever Hellas SAA.I. Rentis, AthensGreece
  4. 4.IVML-NTUAAthensGreece

Personalised recommendations