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Image Segmentation Using Topological Persistence

  • Conference paper
Computer Analysis of Images and Patterns (CAIP 2007)

Part of the book series: Lecture Notes in Computer Science ((LNIP,volume 4673))

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Abstract

This paper presents a new hybrid split-and-merge image segmentation method based on computational geometry and topology using persistent homology. The algorithm uses edge-directed topology to initially split the image into a set of regions based on the Delaunay triangulations of the points in the edge map. Persistent homology is used to generate three types of regions: p-persistent regions, p-transient regions, and d-triangles. The p-persistent regions correspond to core objects in the image, while p-transient regions and d-triangles are smaller regions that may be combined in the merge phase, either with p-persistent regions to refine the core or with other p-transient and d-triangles regions to potentially form new core objects. Performing image segmentation based on topology and persistent homology guarantees several nice properties, and initial results demonstrate high quality image segmentation.

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References

  1. Canny, J.: A Computational Approach To Edge Detection. IEEE Trans. Pattern Analysis and Machine Intelligence 8, 679–714 (1986)

    Article  Google Scholar 

  2. Edelsbrunner, H.: Algorithms in Combinatorial Geometry. Springer, New York (1987)

    MATH  Google Scholar 

  3. Edelsbrunner, H.: The Union of Balls and its Dual Shape. In: Proceedings of the Ninth Annual Symposium on Computational Geometry, pp. 218–231 (1993)

    Google Scholar 

  4. Edelsbrunner, H., Letscher, D., Zomorodian, A.: Topological Persistence and Simplification. Discrete and Computational Geometry 28, 511–533 (2002)

    Article  MATH  MathSciNet  Google Scholar 

  5. Fortune, S.: A Sweepline Algorithm for Voronoi Diagrams. Algorithmica 2, 153–174 (1987)

    Article  MATH  MathSciNet  Google Scholar 

  6. Gevers, T., Smeulders, A.W.M.: Combining Region Splitting and Edge Detection through Guided Delaunay Image Subdivision. In: Proc. of the 1997 International Conference on Computer Vision and Pattern Recognition, pp. 1021–1026 (1997)

    Google Scholar 

  7. Guibas, L., Knuth, D., Sharir, M.: Randomized Incremental Construction of Delaunay and Voronoi Diagrams. Algorithmica 7, 381–413 (1992)

    Article  MATH  MathSciNet  Google Scholar 

  8. Mallat, S., Zhong, S.: Characterization of signals from Multiscale Edges. IEEE Trans. Patt. Anal. and Mach. Intell. 14, 710–732 (1992)

    Article  Google Scholar 

  9. Massey, W.: A Basic Course in Algebraic Topology. Springer, Heidelberg (1991)

    MATH  Google Scholar 

  10. Prasad, L., Skourikhine, A.N.: Vectorized Image Segmentation via Trixel Agglomeration. In: Brun, L., Vento, M. (eds.) GbRPR 2005. LNCS, vol. 3434, pp. 12–22. Springer, Heidelberg (2005)

    Google Scholar 

  11. Stelldinger, P., Ullrich, K., Meine, H.: Topologically Correct Image Segmentation Using Alpha Shapes. In: Kuba, A., Nyúl, L.G., Palágyi, K. (eds.) DGCI 2006. LNCS, vol. 4245, pp. 542–554. Springer, Heidelberg (2006)

    Chapter  Google Scholar 

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Walter G. Kropatsch Martin Kampel Allan Hanbury

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© 2007 Springer-Verlag Berlin Heidelberg

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Letscher, D., Fritts, J. (2007). Image Segmentation Using Topological Persistence. In: Kropatsch, W.G., Kampel, M., Hanbury, A. (eds) Computer Analysis of Images and Patterns. CAIP 2007. Lecture Notes in Computer Science, vol 4673. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-74272-2_73

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  • DOI: https://doi.org/10.1007/978-3-540-74272-2_73

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-74271-5

  • Online ISBN: 978-3-540-74272-2

  • eBook Packages: Computer ScienceComputer Science (R0)

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