Pattern Analysis and Applications

, Volume 17, Issue 1, pp 141–152 | Cite as

A new set distance and its application to shape registration

  • Vladimir Ćurić
  • Joakim Lindblad
  • Nataša Sladoje
  • Hamid Sarve
  • Gunilla Borgefors
Short Paper

Abstract

We propose a new distance measure, called Complement weighted sum of minimal distances, between finite sets in \({\mathbb Z }^n\) and evaluate its usefulness for shape registration and matching. In this set distance the contribution of each point of each set is weighted according to its distance to the complement of the set. In this way, outliers and noise contribute less to the new similarity measure. We evaluate the performance of the new set distance for registration of shapes in binary images and compare it to a number of often used set distances found in the literature. The most extensive evaluation uses a set of synthetic 2D images. We also show three examples of real problems: registering a set of 2D images extracted from synchrotron radiation micro-computed tomography (SR\(\upmu \)CT) volumes depicting bone implants; the difficult multi-modal registration task of finding the exact location of a 2D slice of a bone implant, as imaged by a light microscope, within a 3D SR\(\upmu \)CT volume of the same implant; and finally recognition of handwritten characters. The evaluation shows that our new set distance performs well for all tasks and outperforms the other observed distance measures in most cases. It is therefore useful in many image registration and shape comparison tasks.

Keywords

Set distance Distance measure Image registration Multi-modal registration Shape matching 

References

  1. 1.
    Audette MA, Siddiqi K, Ferrie FP, Peters TM (2003) An integrated range-sensing, segmentation and registration framework for the characterization of intra-surgical brain deformations in image-guided surgery. Comput Vis Image Underst 89(2–3):226–251CrossRefGoogle Scholar
  2. 2.
    Barrow HG, Tenenbaum JM, Bolles RC, Wolf HC (1977) Parametric correspondence and chamfer matching: two new techniques for image matching. In: Proceedings of the 5th joint conference on artificial intelligence, Cambridge, MA, USA, pp 659–663.Google Scholar
  3. 3.
    Birsan T, Tiba D (2006) One hundred years since the introduction of the set distance by Dimitrie Pompeiu. In: 22nd IFIP conference on system modeling and optimization. Turin, Italy, pp 35–39Google Scholar
  4. 4.
    Borgefors G (1988) Hierarchical Chamfer matching: a parametric edge matching. IEEE Trans Pattern Anal Mach Intell 10(6):849–865CrossRefGoogle Scholar
  5. 5.
    Borgefors G, Olsson H (1992) Localizing and identifying objects: a method for distinguishing noise, occlusion, and other disturbances. In: Proceedings of the 2nd Nordic workshop on industrial machine vision, Kuusamo, Finland, 4 p, ISBN 951-42-3316-6.Google Scholar
  6. 6.
    Cai J, Chu JC, Recine D, Sharma M, Nguyen C, Rodebaugh R, Saxena VA, Ali A (1999) CT and PET lung image registration and fusion in radiotherapy treatment planning using the chamfer-matching method. Int J Radiat Oncol 43:883–891CrossRefGoogle Scholar
  7. 7.
    de Campos TE, Babu BR, Varma M (2009) Character recognition in natural images. In: Proceedings of the international conference on computer vision theory and applications, Lisbon, Portugal, pp 273–289. http://www.ee.surrey.ac.uk/CVSSP/demos/chars74k/
  8. 8.
    Dubuisson MP, Jain AK (1994) A modified Hausdorff distance for object matching. In: Proceedings of international conference on pattern recognition, Jerusalem, Israel, pp 566–568Google Scholar
  9. 9.
    Eiter T, Mannila H (1997) Distance measures for point sets and their computation. Acta Inform 34(2):103–133CrossRefMathSciNetGoogle Scholar
  10. 10.
    Hajdu A, Kormos B, Nagy B, Zörgó Z (2004) Choosing appropriate distance measurement in digital image segmentation. Annales Univ Sci Budapest Sect Comp 24:193–208MATHGoogle Scholar
  11. 11.
    Huttenlocher DP, Klanderman GA, Rucklidge WA (1993) Comparing images using the Hausdorff distance. IEEE Trans Pattern Anal Mach Intell 15(9):850–863CrossRefGoogle Scholar
  12. 12.
    Kirkpatrick S, Gelatt CD, Vecchi MP (1983) Optimization by simulated annealing. Science 220(4598):671–680CrossRefMATHMathSciNetGoogle Scholar
  13. 13.
    Kimia B (2002) A large binary image database, the LEMS Vision Group at Brown University. http://www.lems.brown.edu/dmc/
  14. 14.
    Klette R, Rosenfeld A (2004) Digital Geometry. Morgan Kaufmann, San FranciscoMATHGoogle Scholar
  15. 15.
    Klette R, Zamperoni P (1989) Measure of correspondence between binary image patterns. Image Vis Comput 5(4):287–295CrossRefGoogle Scholar
  16. 16.
    Lindblad J, Ćurić V, Sladoje N (2009) On set distances and their application to image registration. In: Proceedings of 6th international symposium on image and signal processing and analysis (IEEE), Salzburg, Austria, pp 449–454.Google Scholar
  17. 17.
    Maurer CR, Qi R, Raghavan V (2003) A linear time algorithm for computing exact Euclidean distance transforms of binary images in arbitrary dimensions. IEEE Trans Pattern Anal Mach Intell 25(2):265–270CrossRefGoogle Scholar
  18. 18.
    Peng X, Chen W, Ma Q (2007) Feature based nonrigid image registration using a Hausdorff distance matching measure. Opt Eng 46(5):057201CrossRefGoogle Scholar
  19. 19.
    Sarve H, Lindblad J, Johansson C (2008) Registration of 2D histological images of bone implants with 3D SRµCT volumes. In: Proceedings of the 4th international symposium on visual computing, Las Vegas, NV, USA, pp 1071–1080.Google Scholar
  20. 20.
    Shonkwiler R (1991) Computing the Hausdorff set distance in linear time for any \(L_p\) point distance. Inf Process Lett 38(4):201–207CrossRefMATHMathSciNetGoogle Scholar
  21. 21.
    Tanács A, Domokos C, Sladoje N, Lindblad J, Kato Z (2009) Recovering affine deformations of fuzzy shapes. In: Proceedings of the 16th Scandinavian conference in image analysis, Oslo, Norway, pp 735–744.Google Scholar
  22. 22.
    Zhao C, Shi W, Deng Y (2005) A new Hausdorff distance for image matching. Pattern Recognit Lett 26(5):581–586CrossRefGoogle Scholar
  23. 23.
    Zwang WJ, Han QG, Wo Y (2005) Image registration based on generalized and mean Hausdorff distances. In: Proceedings of the 4th international conference on machine learning and cybernetics, Guangzhou, China, pp 5117–5121.Google Scholar

Copyright information

© Springer-Verlag London Limited 2012

Authors and Affiliations

  • Vladimir Ćurić
    • 1
  • Joakim Lindblad
    • 2
    • 3
  • Nataša Sladoje
    • 3
  • Hamid Sarve
    • 2
  • Gunilla Borgefors
    • 1
  1. 1.Centre for Image Analysis Uppsala UniversityUppsalaSweden
  2. 2.Centre for Image AnalysisSwedish University of Agricultural SciencesUppsalaSweden
  3. 3.Faculty of Technical SciencesUniversity of Novi SadNovi SadSerbia

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