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Fast Statistically Geometric Reasoning About Uncertain Line Segments in 2D- and 3D-Space

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Pattern Recognition (DAGM 2004)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 3175))

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Abstract

This work addresses the two major drawbacks of current statistical uncertain geometric reasoning approaches. In the first part a framework is presented, that allows to represent uncertain line segments in 2D- and 3D-space and perform statistical test with these practically very important types of entities. The second part addresses the issue of performance of geometric reasoning. A data structure is introduced, that allows the efficient processing of large amounts of statistical tests involving geometric entities. The running times of this approach are finally evaluated experimentally.

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References

  1. Bayer, R., McCreight, E.: Organization and maintenance of large ordered indexes. Acta Informatica 1, 173–189 (1972)

    Article  Google Scholar 

  2. Beder, C.: Joinalgorithmus für Mengen unsicherer geometrischer Elemente. Technical report, Institut für Photogrammetrie (2003)

    Google Scholar 

  3. Beder, C.: A unified framework for the automatic matching of points and lines in multiple oriented images. In: Proc. 20th ISPRS Congress, Istanbul, Turkey (2004)

    Google Scholar 

  4. Finkel, R., Bentley, J.: Quad trees: A data structure for retrieval on composite keys. Acta Informatica 4, 1–9 (1974)

    Article  MATH  Google Scholar 

  5. Brunn, A., Förstner, W.: S. Heuel. Statistically testing uncertain geometric relations. In: Proc. DAGM 2000, Kiel, Germany, pp. 17–26 (2000)

    Google Scholar 

  6. Guttman, A.: R-trees: A dynamic index structure for spatial searching. In: Proc. ACM SIGMOD Int. Conf. on Management of Data, pp. 47–57 (1984)

    Google Scholar 

  7. Heuel, S.: Points, lines and planes and their optimal estimation. In: Radig, B., Florczyk, S. (eds.) DAGM 2001. LNCS, vol. 2191, pp. 92–99. Springer, Heidelberg (2001)

    Chapter  Google Scholar 

  8. Heuel, S., Förstner, W.: Matching, reconstructing and grouping 3d lines from multiple views using uncertain projective geometry. In: CVPR 2001, IEEE, Los Alamitos (2001)

    Google Scholar 

  9. Jung, F., Paparoditis, N.: Extracting 3d free-form surface boundaries of manmade objects from multiple calibrated images: A robust, accurate and high resolving power edgel matching and chaining approach. In: Proc. of the ISPRS Conf. Photogrammetric Image Analysis, pp. 39–44 (2003)

    Google Scholar 

  10. Knuth, D.E.: Sorting and Searching. The Art of Computer Programming, vol. 3. Addison-Wesley, Reading (1998)

    Google Scholar 

  11. Lowe, D.G.: Perceptual Organization and Visual Recognition. Kluwer Academic Publishers, Dordrecht (1985)

    Google Scholar 

  12. Schneider, R., Seeger, R., Beckmann, N., Kriegel, H.: The R*-tree: An efficient and robust access method for points and rectangles. In: Proc. ACM SIGMOD Symposium on Principles of Database Systems, pp. 322–331 (1990)

    Google Scholar 

  13. Stolfi, J.: Oriented Projective Geometry. Academic Press, London (1991)

    MATH  Google Scholar 

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Beder, C. (2004). Fast Statistically Geometric Reasoning About Uncertain Line Segments in 2D- and 3D-Space. In: Rasmussen, C.E., Bülthoff, H.H., Schölkopf, B., Giese, M.A. (eds) Pattern Recognition. DAGM 2004. Lecture Notes in Computer Science, vol 3175. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-28649-3_46

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  • DOI: https://doi.org/10.1007/978-3-540-28649-3_46

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-22945-2

  • Online ISBN: 978-3-540-28649-3

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