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Mathematical Morphology on Irregularly Sampled Signals

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Computer Vision – ACCV 2016 Workshops (ACCV 2016)

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Abstract

This paper introduces a new operator that can be used to approximate continuous-domain mathematical morphology on irregularly sampled surfaces. We define a new way of approximating the continuous domain dilation by duplicating and shifting samples according to a flat continuous structuring element. We show that the proposed algorithm can better approximate continuous dilation, and that dilations may be sampled irregularly to achieve a smaller sampling without greatly compromising the accuracy of the result.

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References

  1. Asplund, T., Luengo Hendriks, C.L., Thurley, M.J., Strand, R.: A new approach to mathematical morphology on one dimensional sampled signals. In: Proceedings of the 23rd ICPR 2016 (2016, to be published)

    Google Scholar 

  2. Breuß, M., Burgeth, B., Weickert, J.: Anisotropic continuous-scale morphology. In: Martí, J., Benedí, J.M., Mendonça, A.M., Serrat, J. (eds.) IbPRIA 2007. LNCS, vol. 4478, pp. 515–522. Springer, Heidelberg (2007). doi:10.1007/978-3-540-72849-8_65

    Chapter  Google Scholar 

  3. Brockett, R.W., Maragos, P.: Evolution equations for continuous-scale morphology. In: 1992 IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 1992, vol. 3, pp. 125–128. IEEE (1992)

    Google Scholar 

  4. Brockett, R.W., Maragos, P.: Evolution equations for continuous-scale morphological filtering. IEEE Trans. Signal Process. 42, 3377–3386 (1994)

    Article  Google Scholar 

  5. Gilboa, G., Osher, S.: Nonlocal operators with applications to image processing. Multiscale Model. Simul. 7, 1005–1028 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  6. Haralick, R.M., Sternberg, S.R., Zhuang, X.: Image analysis using mathematical morphology. IEEE Trans. Pattern Anal. Mach. Intell. 9, 532–550 (1987)

    Article  Google Scholar 

  7. Luengo Hendriks, C.L., van Kempen, G.M.P., van Vliet, L.J.: Improving the accuracy of isotropic granulometries. Pattern Recogn. Lett. 28, 865–872 (2007)

    Article  Google Scholar 

  8. Nanoflann: C++ header-only fork of the FLANN library for approximate nearest neighbors. https://github.com/jlblancoc/nanoflann. Accessed 21 June 2016

  9. Nyquist, H.: Certain topics in telegraph transmission theory. Trans. AIEE, 617–644 (1928). Reprinted in: Proc. IEEE 90(2), 280–305 (2002)

    Google Scholar 

  10. Onederra, I., Thurley, M., Catalan, A.: Measuring blast fragmentation at Esperanza mine using high resolution 3D laser scanning. Inst. Mater. Miner. Min. Trans. Sect. A: Mining Technol. 124, 34–46 (2015)

    Google Scholar 

  11. Sapiro, G., Kimmel, R., Shaked, D., Kimia, B.B., Bruckstein, A.M.: Implementing continuous-scale morphology via curve evolution. Pattern Recogn. 26, 1363–1372 (1993)

    Article  Google Scholar 

  12. Schöberl, M., Seller, J., Foessel, S., Kaup, A.: Increasing imaging resolution by covering your sensor. In: 2011 18th IEEE International Conference on Image Processing (ICIP), pp. 1897–1900. IEEE (2011)

    Google Scholar 

  13. Serra, J.: Image Analysis and Mathematical Morphology. Academic Press, Inc., Cambridge (1983)

    Google Scholar 

  14. Shannon, C.E.: Communication in the presence of noise. Proc. IRE 37, 10–21 (1949). Reprinted in: Proc. IEEE 86(2), 447–457 (1998)

    Google Scholar 

  15. Sutherland, I.E., Hodgman, G.W.: Reentrant polygon clipping. Commun. ACM 17, 32–42 (1974)

    Article  MATH  Google Scholar 

  16. Thurley, M.J.: Three dimensional data analysis for the separation and sizing of rock piles in mining. Ph.D. thesis, Monash University (2002)

    Google Scholar 

  17. Weickert, J.: Anisotropic Diffusion in Image Processing. Teubner, Stuttgart (1998)

    MATH  Google Scholar 

  18. Weiler, K., Atherton, P.: Hidden surface removal using polygon area sorting. In: ACM SIGGRAPH Computer Graphics, vol. 11, pp. 214–222. ACM (1977)

    Google Scholar 

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Acknowledgement

Teo Asplund was funded through grant 2014-5983 from the Swedish Research Council.

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Authors and Affiliations

  1. Centre for Image Analysis, Uppsala University, Uppsala, Sweden

    Teo Asplund & Robin Strand

  2. Flagship Biosciences Inc., Westminster, Colorado, USA

    Cris L. Luengo Hendriks

  3. Luleå University of Technology, Luleå, Sweden

    Matthew J. Thurley

Authors
  1. Teo Asplund
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  2. Cris L. Luengo Hendriks
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  3. Matthew J. Thurley
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  4. Robin Strand
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Corresponding author

Correspondence to Teo Asplund .

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Editors and Affiliations

  1. Institute of Information Science, Academia Sinica, Taipei, Taiwan

    Chu-Song Chen

  2. Tsinghua University, Beijing, China

    Jiwen Lu

  3. School of Electrical and Electronic Engineering, Nanyang Technological University, Singapore, Singapore

    Kai-Kuang Ma

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Asplund, T., Luengo Hendriks, C.L., Thurley, M.J., Strand, R. (2017). Mathematical Morphology on Irregularly Sampled Signals. In: Chen, CS., Lu, J., Ma, KK. (eds) Computer Vision – ACCV 2016 Workshops. ACCV 2016. Lecture Notes in Computer Science(), vol 10117. Springer, Cham. https://doi.org/10.1007/978-3-319-54427-4_37

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  • DOI: https://doi.org/10.1007/978-3-319-54427-4_37

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-54426-7

  • Online ISBN: 978-3-319-54427-4

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