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Joint IAPR International Workshops on Statistical Techniques in Pattern Recognition (SPR) and Structural and Syntactic Pattern Recognition (SSPR)

S+SSPR 2022: Structural, Syntactic, and Statistical Pattern Recognition pp 193–202Cite as

Fast Distance Transforms in Graphs and in Gmaps

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Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 13813))

Abstract

Distance Transform (DT) as a fundamental operation in pattern recognition computes how far inside a shape a point is located. In this paper, at first a novel method is proposed to compute the DT in a graph. By using the edge classification and a total order [1], the spanning forest of the foreground is created where distances are propagated through it. Second, in contrast to common linear DT methods, by exploiting the hierarchical structure of the irregular pyramid, the geodesic DT (GDT) is calculated with parallel logarithmic complexity. Third, we introduce the DT in the nD generalized map (n-Gmap) leading to a more precise and smoother DT. Forth, in the n-Gmap we define n different distances and the relation between these distances. Finally, we sketch how the newly introduced concepts can be used to simulate gas propagation in 2D sections of plant leaves.

Supported by the Vienna Science and Technology Fund (WWTF), project LS19-013, https://waters-gateway.boku.ac.at/.

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Notes

  1. 1.

    Self-inverse permutations.

  2. 2.

    red separators in Fig. 3(b).

  3. 3.

    Blue distance values belong to the 2-cell, black distances to two types of cells (Fig. 3c).

References

  1. Banaeyan, M., Batavia, D., Kropatsch, W.G.: Removing redundancies in binary images. In: International Conference on Intelligent Systems and Patterns Recognition (ISPR), Hammamet, Tunisia, 24–25 March 2022. pp. 221–233. Springer, Cham (2022). https://doi.org/10.1007/978-3-031-08277-1_19

  2. Banaeyan, M., Kropatsch, W.G.: Pyramidal connected component labeling by irregular graph pyramid. In: 2021 5th International Conference on Pattern Recognition and Image Analysis (IPRIA), pp. 1–5 (2021)

    Google Scholar 

  3. Banaeyan, M., Kropatsch, W.G.: Parallel \(\cal{O} (log(n))\) computation of the adjacency of connected components. In: International Conference on Pattern Recognition and Artificial Intelligence (ICPRAI), Paris, France, June 1–3, 2022. pp. 102–113. Springer, Cham (2022).https://doi.org/10.1007/978-3-031-09282-4_9

  4. Beamer, S., Asanovic, K., Patterson, D.: Direction-optimizing breadth-first search. In: SC ’12: Proceedings of the International Conference on High Performance Computing, Networking, Storage and Analysis. pp. 1–10 (2012). https://doi.org/10.1109/SC.2012.50

  5. Borgefors, G.: Distance transformations in arbitrary dimensions. Comput. Vis., Graphics image Process. 27(3), 321–345 (1984)

    Article  Google Scholar 

  6. Brun, L., Kropatsch, W.G.: Hierarchical graph encodings. In: Lézoray, O., Grady, L. (eds.) Image Processing and Analysis with Graphs: Theory and Practice, pp. 305–349. CRC Press (2012)

    Google Scholar 

  7. Damiand, G., Lienhardt, P.: Combinatorial Maps: Efficient Data Structures for Computer Graphics and Image Processing. CRC Press (2014)

    Google Scholar 

  8. Fabbri, R., Costa, L.D.F., Torelli, J.C., Bruno, O.M.: 2D Euclidean distance transform algorithms: a comparative survey. ACM Comput. Surv. 40(1), 1–44 (2008)

    Article  Google Scholar 

  9. Haxhimusa, Y.: The Structurally Optimal Dual Graph Pyramid and Its Application in Image Partitioning. DISKI, Berlin (2007)

    MATH  Google Scholar 

  10. Kropatsch, W.G.: Building irregular pyramids by dual graph contraction. IEE-Proc. Visi. Image Signal Process. 142(No. 6), 366–374 (1995)

    Google Scholar 

  11. Latecki, L., Eckhardt, U., Rosenfeld, A.: Well-composed sets. Comput. Image Underst. 61(1), 70–83 (1995)

    Article  Google Scholar 

  12. Lienhardt, P.: Topological models for boundary representation: a comparison with n-dimensional generalized maps. Comput. Aided Des. 23(1), 59–82 (1991)

    Article  MATH  Google Scholar 

  13. Momayyezi, M., et al.: Desiccation of the leaf mesophyll and its implications for \(\rm CO_2 \) diffusion and light processing. Plant, Cell Enviro. 45(5), 1362–1381 (2022)

    Article  Google Scholar 

  14. Pizlo, Z., Stefanov, E.: Solving large problems with a small working memory. J. Probll. Solv. 6(1), 5 (2013)

    Google Scholar 

  15. Rosenfeld, A., Pfaltz, J.L.: Sequential operations in digital picture processing. Assoc. Comput. Macch. 13(4), 471–494 (1966)

    Article  MATH  Google Scholar 

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Author information

Authors and Affiliations

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

    Majid Banaeyan, Carmine Carratù, Walter G. Kropatsch & Jiří Hladůvka

Authors
  1. Majid Banaeyan
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  2. Carmine Carratù
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  3. Walter G. Kropatsch
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  4. Jiří Hladůvka
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Corresponding author

Correspondence to Majid Banaeyan .

Editor information

Editors and Affiliations

  1. Concordia University, Montreal, QC, Canada

    Adam Krzyzak

  2. Concordia University, Montreal, QC, Canada

    Ching Y. Suen

  3. Ca Foscari University of Venice, Venezia, Italy

    Andrea Torsello

  4. Concordia University, Montreal, QC, Canada

    Nicola Nobile

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Banaeyan, M., Carratù, C., Kropatsch, W.G., Hladůvka, J. (2022). Fast Distance Transforms in Graphs and in Gmaps. In: Krzyzak, A., Suen, C.Y., Torsello, A., Nobile, N. (eds) Structural, Syntactic, and Statistical Pattern Recognition. S+SSPR 2022. Lecture Notes in Computer Science, vol 13813. Springer, Cham. https://doi.org/10.1007/978-3-031-23028-8_20

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  • DOI: https://doi.org/10.1007/978-3-031-23028-8_20

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-031-23027-1

  • Online ISBN: 978-3-031-23028-8

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