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A Combinatorial Approach for Hyperspectral Image Segmentation

  • José Antonio Valero MedinaEmail author
  • Pablo Andrés Arbeláez Escalante
  • Iván Alberto Lizarazo Salcedo
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10116)

Abstract

A common strategy in high spatial resolution image analysis is to define coarser geometric space elements, i.e. superpixels, by grouping near pixels based on (a, b)–connected graphs as neighborhood definitions. Such an approach, however, cannot meet some topological axioms needed to ensure a correct representation of connectedness relationships. Superpixel boundaries may present ambiguities because one-dimensional contours are represented by pixels, which are two-dimensional. Additionally, the high spatial resolution available today has increased the volume of data that must be processed during image segmentation even after data reduction phases such as principal component analysis. The inherent complexity of segmentation algorithms, including texture analysis, along with the aforementioned volume of data, demands considerable computing resources. In this paper, we propose a novel way for segmenting hyperspectral imagery data by defining a computational framework based on Axiomatic Locally Finite Spaces (ALFS) provided by Cartesian complexes, which provide a geometric space that complies with the \(T_{0}\) digital topology. Our approach links also oriented matroids to geometric space representations and is implemented on a parallel computational framework. We evaluated quantitatively our approach on a subset of hyperspectral remote sensing scenes. Our results show that, by departing from the conventional pixel representation, it is possible to segment an image based on a topologically correct digital space, while simultaneously taking advantage of combinatorial features of their associated oriented matroids.

Notes

Acknowledgement

Centro de Computo de Alto Desempeño of Universidad Distrital (CECAD) provided the computing environment.

References

  1. 1.
    Grady, L.: Targeted image segmentation using graph methods (2012)Google Scholar
  2. 2.
    Lizarazo, I., Elsner, P.: Fuzzy segmentation for object-based image classification. Int. J. Remote Sens. 30, 1643–1649 (2009)CrossRefGoogle Scholar
  3. 3.
    Brun, L., Domenger, J.P., Mokhtari, M.: Incremental modifications of segmented image defined by discrete maps. J. Vis. Commun. Image Represent. 14, 251–290 (2003)CrossRefGoogle Scholar
  4. 4.
    Kovalevsky, V.A.: Geometry of locally finite spaces. Int. J. Shape Model. 14, 231–232 (2008)CrossRefGoogle Scholar
  5. 5.
    Kovalevsky, V.A.: Finite topology as applied to image analysis. Comput. Vis. Graph. Image Process. 46(2), 141–161 (1989). doi: 10.1016/0734-189X(89)90165-5 CrossRefGoogle Scholar
  6. 6.
    Kovalevsky, V.A.: Discrete topology and contour definition. Pattern Recogn. Lett. 2, 281–288 (1984)CrossRefGoogle Scholar
  7. 7.
    Kovalevsky, V.: Algorithms and data structures for computer topology. In: Bertrand, G., Imiya, A., Klette, R. (eds.) Digital and Image Geometry. LNCS, vol. 2243, pp. 38–58. Springer, Heidelberg (2001). doi: 10.1007/3-540-45576-0_3 CrossRefGoogle Scholar
  8. 8.
    Kovalevsky, V.: Algorithms in digital geometry based on cellular topology. In: Klette, R., Žunić, J. (eds.) IWCIA 2004. LNCS, vol. 3322, pp. 366–393. Springer, Heidelberg (2004). doi: 10.1007/978-3-540-30503-3_27 CrossRefGoogle Scholar
  9. 9.
    Kovalevsky, V.: Axiomatic digital topology. J. Math. Imaging Vis. 26, 41–58 (2006)MathSciNetCrossRefGoogle Scholar
  10. 10.
    Listing, J.B.: Der Census räumlicher Complexe: oder Verallgemeinerung des euler’schen Satzes von den Polyädern. Abhandlungen der Königlichen Gesellschaft der Wissenschaften in Göttingen 10, 97–182 (1862)Google Scholar
  11. 11.
    Whitney, H.: On the abstract properties of linear dependence. Am. J. Math. 57, 509–533 (1935)MathSciNetCrossRefzbMATHGoogle Scholar
  12. 12.
    Oxley, J.G.: Matroid Theory. Oxford Graduate Texts in Mathematics. Oxford University Press, Inc., New York (2006)zbMATHGoogle Scholar
  13. 13.
    Fukuda, K.: Lecture notes on oriented matroids and geometric computation. Technical report RO-2004.0621, course of Doctoral school in Discrete System Optimization, EPFL 2004 (2004)Google Scholar
  14. 14.
    De Loera, J.A., Rambau, J., Santos, F.: Triangulations: Structures for Algorithms and Applications, 1st edn. Springer, Heidelberg (2010)CrossRefzbMATHGoogle Scholar
  15. 15.
    Leung, T., Malik, J.: Detecting, localizing and grouping repeated scene elements from an image. In: Buxton, B., Cipolla, R. (eds.) ECCV 1996. LNCS, vol. 1064, pp. 546–555. Springer, Heidelberg (1996). doi: 10.1007/BFb0015565 CrossRefGoogle Scholar
  16. 16.
    Arbelaez, P., Maire, M., Fowlkes, C., Malik, J.: Contour detection and hierarchical image segmentation. IEEE Trans. Pattern Anal. Mach. Intell. 33, 898–916 (2011)CrossRefGoogle Scholar
  17. 17.
    GDAL Development Team: GDAL - Geospatial Data Abstraction Library, Version 2.1.0. Open Source Geospatial Foundation (2016)Google Scholar
  18. 18.
    Szeliski, R.: Computer Vision: Algorithms and Applications, 1st edn. Springer, New York (2010)zbMATHGoogle Scholar
  19. 19.
    Vincent, L., Soille, P.: Watersheds in digital spaces: an efficient algorithm based on immersion simulations. IEEE Trans. Pattern Anal. Mach. Intell. 13, 583–598 (1991)CrossRefGoogle Scholar
  20. 20.
    Martin, D.R., Fowlkes, C.C., Malik, J.: Learning to detect natural image boundaries using local brightness, color, and texture cues. IEEE Trans. Pattern Anal. Mach. Intell. 26, 530–549 (2004)CrossRefGoogle Scholar
  21. 21.
    Everingham, M., Van Gool, L., Williams, C.K.I., Winn, J., Zisserman, A.: The PASCAL Visual Object Classes Challenge 2008 (VOC2008) Results (2008). http://www.pascal-network.org/challenges/VOC/voc2008/workshop/index.html

Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  • José Antonio Valero Medina
    • 1
    Email author
  • Pablo Andrés Arbeláez Escalante
    • 2
  • Iván Alberto Lizarazo Salcedo
    • 3
  1. 1.Universidad DistritalBogotáColombia
  2. 2.Universidad de los AndesBogotáColombia
  3. 3.Universidad NacionalBogotáColombia

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