Distance Between Vector-Valued Representations of Objects in Images with Application in Object Detection and Classification

Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10256)

Abstract

We present a novel approach to measuring distances between objects in images, suitable for information-rich object representations which simultaneously capture several properties in each image pixel. Multiple spatial fuzzy sets on the image domain, unified in a vector-valued fuzzy set, are used to model such representations. Distance between such sets is based on a novel point-to-set distance suitable for vector-valued fuzzy representations. The proposed set distance may be applied in, e.g., template matching and object classification, with an advantage that a number of object features are simultaneously considered. The distance measure is of linear time complexity w.r.t. the number of pixels in the image. We evaluate the performance of the proposed measure in template matching in presence of noise, as well as in object detection and classification in low resolution Transmission Electron Microscopy images.

References

  1. 1.
    Bloch, I.: On fuzzy distances and their use in image processing under imprecision. Pattern Recogn. 32, 1873–1895 (1999)CrossRefGoogle Scholar
  2. 2.
    Bloch, I., Maître, H.: Fuzzy mathematical morphologies: a comparative study. Pattern Recogn. 28(9), 1341–1387 (1995)MathSciNetCrossRefGoogle Scholar
  3. 3.
    Borgefors, G.: Distance transformations in digital images. Comput. Vis. Graph. Image Process. 34, 344–371 (1986)CrossRefGoogle Scholar
  4. 4.
    Dražić, S., Sladoje, N., Lindblad, J.: Accurate estimation of feret’s diameter of a shape from pixel coverage digitization. Pattern Recogn. Lett. 80, 37–45 (2016)CrossRefGoogle Scholar
  5. 5.
    Eiter, T., Mannila, H.: Distance measures for point sets and their computation. Acta Informatica 34(2), 103–133 (1997)MathSciNetCrossRefMATHGoogle Scholar
  6. 6.
    Lindblad, J., Ćurić, V., Sladoje, N.: On set distances and their application to image registration. In: Proceedings of the IEEE International Symposium Image Signal Processing and Analysis (ISPA), pp. 449–454 (2009)Google Scholar
  7. 7.
    Lindblad, J., Sladoje, N.: Linear time distances between fuzzy sets with applications to pattern matching and classification. IEEE Trans. Image Process. 23(1), 126–136 (2014)MathSciNetCrossRefGoogle Scholar
  8. 8.
    Rosenfeld, A.: Fuzzy digital topology. Inf. Control 40, 76–87 (1979)MathSciNetCrossRefMATHGoogle Scholar
  9. 9.
    Rosenfeld, A.: The fuzzy geometry of image subsets. Pattern Recogn. Lett. 2, 311–317 (1984)CrossRefGoogle Scholar
  10. 10.
    Saha, P.K., Udupa, J.K.: Relative fuzzy connectedness among multiple objects: theory, algorithms, and applications in image segmentation. Comput. Vis. Image Underst. 82(1), 42–56 (2001)CrossRefMATHGoogle Scholar
  11. 11.
    Saha, P.K., Wehrli, F.W., Gomberg, B.R.: Fuzzy distance transform: theory, algorithms, and applications. Comput. Vis. Image Underst. 86, 171–190 (2002)CrossRefMATHGoogle Scholar
  12. 12.
    Sladoje, N., Lindblad, J.: Estimation of moments of digitized objects with fuzzy borders. In: Roli, F., Vitulano, S. (eds.) ICIAP 2005. LNCS, vol. 3617, pp. 188–195. Springer, Heidelberg (2005). doi:10.1007/11553595_23 CrossRefGoogle Scholar
  13. 13.
    Sladoje, N., Lindblad, J.: High precision boundary length estimation by utilizing gray-level information. IEEE Trans. Pattern Anal. Mach. Intell. 31(2), 357–363 (2009)Google Scholar
  14. 14.
    Sladoje, N., Nyström, I., Saha, P.K.: Measurements of digitized objects with fuzzy borders in 2D and 3D. Image Vis. Comput. 23, 123–132 (2005)CrossRefGoogle Scholar
  15. 15.
    Suveer, A., Sladoje, N., Lindblad, J., Dragomir, A., Sintorn, I.-M.: Automated detection of cilia in low magnification transmission electron microscopy images using template matching. In: Proceedings of IEEE International Symposium on Biomedical Imaging (ISBI), pp. 386–390 (2016)Google Scholar
  16. 16.
    Zadeh, L.: Fuzzy sets. Inf. Control 8, 338–353 (1965)CrossRefMATHGoogle Scholar
  17. 17.
    Öfverstedt, J., Sladoje, N., Lindblad, J.: Distance between vector-valued fuzzy sets based on intersection decomposition with applications in object detection. In: Angulo, J., et al. (eds.) ISMM 2017. LNCS, vol. 10225, pp. 395–407. Springer, Cham (2017). doi:10.1007/978-3-319-57240-6_32 Google Scholar

Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  1. 1.Centre for Image Analysis, Department of ITUppsala UniversityUppsalaSweden
  2. 2.Mathematical Institute of Serbian Academy of Sciences and ArtsBelgradeSerbia

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