Skip to main content
SpringerLink
Log in
Book cover

International Conference on Computer Analysis of Images and Patterns

CAIP 2019: Computer Analysis of Images and Patterns pp 363–374Cite as

Partitioning 2D Images into Prototypes of Slope Region

  • Conference paper
  • First Online:

Part of the book series: Lecture Notes in Computer Science ((LNIP,volume 11678))

Abstract

A gray scale digital image can be represented as a 2.5D surface where the height of the surface corresponds to the gray value of the respective pixel. Analysis of the gray scale image can be efficiently done by exploiting the properties of the plane graph embedded in the 2.5D surface. The vertices of the graph can be easily categorized into critical and non-critical points by use of Local Binary Patterns (LBPs). Well defined graph operations such as contraction and removal of edges are used to eliminate the non-critical points and preserve the critical points thereby reducing the size of graph. In this process, it is important to preserve the structural and topological properties of the regions of a gray scale image. After analysing the topological properties of a well composed image, we provide two prototypes of the slope region and the necessary conditions for their existence. Also we prove that every slope region conforms to either of the two prototype. Conversely the prototypes may be used to generate an image with a required topological properties.

This is a preview of subscription content, log in via an institution.

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   64.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   84.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

References

  1. Batavia, D., Kropatsch, W.G., Casablanca, R.M., Gonzalez-Diaz, R.: Congratulations! Dual graphs are now orientated!. In: Conte, D., Ramel, J.-Y., Foggia, P. (eds.) GbRPR 2019. LNCS, vol. 11510, pp. 131–140. Springer, Cham (2019). https://doi.org/10.1007/978-3-030-20081-7_13

    Chapter  Google Scholar 

  2. Batavia, D., Kropatsch, W.G., Gonzalez-Diaz, R., Casblanca, R.M.: Counting slope regions in surface graphs. In: Computer Vision Winter Workshop (2019)

    Google Scholar 

  3. Brun, L., Kropatsch, W.G.: Dual contraction of combinatorial maps. In: Kropatsch, W.G., Jolion, J.M. (eds.) 2nd IAPR-TC 2015 Workshop on Graph-based Representation, pp. 145–154. OCG-Schriftenreihe, Österreichische Computer Gesellschaft (1999). Band 126

    Google Scholar 

  4. Cayley, A.: XL. On contour and slope lines. Lond. Edinb. Dublin Philos. Mag. J. Sci. 18(120), 264–268 (1859)

    Article  Google Scholar 

  5. Cerman, M., Gonzalez-Diaz, R., Kropatsch, W.: LBP and irregular graph pyramids. In: Azzopardi, G., Petkov, N. (eds.) CAIP 2015. LNCS, vol. 9257, pp. 687–699. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-23117-4_59

    Chapter  Google Scholar 

  6. Cerman, M., Janusch, I., Gonzalez-Diaz, R., Kropatsch, W.G.: Topology-based image segmentation using LBP pyramids. Mach. Vis. Appl. 27(8), 1161–1174 (2016)

    Article  Google Scholar 

  7. Diestel, R.: Graph Theory. Graduate Texts in Mathematics (1997)

    Google Scholar 

  8. Edelsbrunner, H., Harer, J., Natarajan, V., Pascucci, V.: Morse-Smale complexes for piecewise linear 3-manifolds. In: Proceedings of the Nineteenth Annual Symposium on Computational Geometry, pp. 361–370. ACM (2003)

    Google Scholar 

  9. Haxhimusa, Y., Kropatsch, W.: Hierarchy of partitions with dual graph contraction. In: Michaelis, B., Krell, G. (eds.) DAGM 2003. LNCS, vol. 2781, pp. 338–345. Springer, Heidelberg (2003). https://doi.org/10.1007/978-3-540-45243-0_44

    Chapter  Google Scholar 

  10. Kropatsch, W.G.: Building irregular pyramids by dual graph contraction. IEE-Proc. Vis. Image Signal Process. 142(6), 366–374 (1995)

    Article  Google Scholar 

  11. Kropatsch, W.G., Casablanca, R.M., Batavia, D., Gonzalez-Diaz, R.: Computing and reducing slope complexes. In: Marfil, R., Calderón, M., Díaz del Río, F., Real, P., Bandera, A. (eds.) CTIC 2019. LNCS, vol. 11382, pp. 12–25. Springer, Cham (2019). https://doi.org/10.1007/978-3-030-10828-1_2

    Chapter  Google Scholar 

  12. Kropatsch, W.G., Casablanca, R.M., Batavia, D., Gonzalez-Diaz, R.: On the space between critical points. In: Couprie, M., Cousty, J., Kenmochi, Y., Mustafa, N. (eds.) DGCI 2019. LNCS, vol. 11414, pp. 115–126. Springer, Cham (2019). https://doi.org/10.1007/978-3-030-14085-4_10

    Chapter  Google Scholar 

  13. Lee, R.N.: Two-dimensional critical point configuration graphs. IEEE Trans. Pattern Anal. Mach. Intell. 4, 442–450 (1984)

    Article  Google Scholar 

  14. Maxwell, J.C.: L. On hills and dales: to the editors of the philosophical magazine and journal. Lond. Edinb. Dublin Philos. Mag. J. Sci. 40(269), 421–427 (1870)

    Article  Google Scholar 

  15. Wei, X., Yang, Q., Gong, Y., Ahuja, N., Yang, M.H.: Superpixel hierarchy. IEEE Trans. Image Process. 27(10), 4838–4849 (2018)

    Article  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Pattern Recognition and Image Processing Group 193/03, TU Wien, Vienna, Austria

    Darshan Batavia, Jiří Hladůvka & Walter G. Kropatsch

Authors
  1. Darshan Batavia
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Jiří Hladůvka
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Walter G. Kropatsch
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Darshan Batavia .

Editor information

Editors and Affiliations

  1. Department of Computer and Electrical Engineering and Applied Mathematics, University of Salerno, Fisciano (SA), Italy

    Mario Vento

  2. Department of Computer and Electrical Engineering and Applied Mathematics, University of Salerno, Fisciano (SA), Italy

    Gennaro Percannella

Rights and permissions

Reprints and permissions

Copyright information

© 2019 Springer Nature Switzerland AG

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

Batavia, D., Hladůvka, J., Kropatsch, W.G. (2019). Partitioning 2D Images into Prototypes of Slope Region. In: Vento, M., Percannella, G. (eds) Computer Analysis of Images and Patterns. CAIP 2019. Lecture Notes in Computer Science(), vol 11678. Springer, Cham. https://doi.org/10.1007/978-3-030-29888-3_29

Download citation

  • DOI: https://doi.org/10.1007/978-3-030-29888-3_29

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-29887-6

  • Online ISBN: 978-3-030-29888-3

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation