Skip to main content
SpringerLink
Log in

Fast Approximation of Color Morphology

  • Conference paper
  • First Online:
Advances in Visual Computing (ISVC 2021)

Part of the book series: Lecture Notes in Computer Science ((LNIP,volume 13018))

Included in the following conference series:

Abstract

The basic filters in mathematical morphology are dilation and erosion. They are defined by a flat or non-flat structuring element that is usually shifted pixel-wise over an image and a comparison process that takes place within the corresponding mask. The algorithmic complexity of fast algorithms that realise dilation and erosion for color images usually depends on size and shape of the structuring element.

In this paper we propose and investigate an easy and fast way to make use of the fast Fourier transform for an approximate computation of dilation and erosion for color images. Similarly in construction as many other fast algorithms, the method extends a recent scheme proposed for single-channel filtering. It is by design highly flexible, as it can be used with flat and non-flat structuring elements of any size and shape. Moreover, its complexity only depends on the number of pixels in the filtered images. We analyse here some important aspects of the approximation, and we show experimentally that we obtain results of very reasonable quality while the method has very attractive computational properties.

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

Access this chapter

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 69.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 89.99
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

Institutional subscriptions

References

  1. Douglas, S.C.: Running max/min calculation using a pruned ordered list. IEEE Trans. Sig. Process. 44(11), 2872–2877 (1996)

    Article  Google Scholar 

  2. Pedrino, E.C., Saito, J.H., Senger, H., Roda, V.O.: Color mathematical morphology in a FPGA. In: Proceedings of the International Conference on Systems, Signals and Image Processing (2010)

    Google Scholar 

  3. Aptoula, E., Lefèvre, S.: On lexicographical ordering in multivariate mathematical morphology. Pattern Recogn. Lett. 29(2), 109–118 (2008)

    Article  Google Scholar 

  4. Lezoray, O., Elmoataz, A., Meurie, C.: Mathematical morphology in any color space. In: Proceedings of the International Conference of Image Analysis and Processing - Workshops, pp. 183–187 (2007)

    Google Scholar 

  5. Barnett, V.: The ordering of multivariate data. J. Roy. Stat. Soc. Ser. A (Gen.) 139(3), 318–344 (1976)

    Article  MathSciNet  Google Scholar 

  6. Sharma, G., Bala, R. (eds.): Digital Color Imaging Handbook. CRC Press (2017)

    Google Scholar 

  7. Moreland, K., Angel, E.: The FFT on a GPU. In: Proceedings of the ACM SIGGRAPH/Eurographics Conference on Graphics Hardware, pp. 112–119 (2003)

    Google Scholar 

  8. Tuzikov, A.V., Margolin, G.L., Grenov, A.I.: Convex set symmetry measurement via Minkowski addition. J. Math. Imaging Vis. 7(1), 53–68 (1997)

    Article  MathSciNet  Google Scholar 

  9. Van Droogenbroeck, M., Buckley, M.J.: Morphological erosions and openings: fast algorithms based on anchors. J. Math. Imaging Vis. 22(2), 121–142 (2005)

    Article  MathSciNet  Google Scholar 

  10. Serra, J., Soille, P. (eds.): Mathematical Morphology and its Applications to Image Processing, vol. 2. Springer, Dordrecht (2012). https://doi.org/10.1007/978-94-011-1040-2

  11. Najman, L., Talbot, H. (eds.): Mathematical Morphology: from Theory to Applications. Wiley, Hoboken (2013)

    Google Scholar 

  12. Cooley, J.W., Lewis, P.A., Welch, P.D.: Historical notes on the fast Fourier transform. Proc. IEEE 55(10), 1675–1677 (1967)

    Article  Google Scholar 

  13. Roerdink, J.B.: Mathematical morphology in computer graphics, scientific visualization and visual exploration. In: Proceedings of the 10th International Symposium on Mathematical Morphology, pp. 367–380 (2011)

    Google Scholar 

  14. Kukal, J., Majerová, D., Procházka, A.: Dilation and erosion of gray images with spherical masks. In: Proceedings of the Annual Conference of Technical Computing (2007)

    Google Scholar 

  15. Déforges, O., Normand, N., Babel, M.: Fast recursive grayscale morphology operators: from the algorithm to the pipeline architecture. J. Real-Time Image Proc. 8(2), 143–152 (2013)

    Article  Google Scholar 

  16. Moreaud, M., Itthirad, F.: Fast algorithm for dilation and erosion using arbitrary flat structuring element: improvement of Urbach and Wilkinson’s algorithm to GPU computing. In: Proceedings of the International Conference on Multimedia Computing and Systems, pp. 289–294 (2014)

    Google Scholar 

  17. Lin, X., Xu, Z.: A fast algorithm for erosion and dilation in mathematical morphology. In: Proceedings of the WRI World Congress on Software Engineering, vol. 2, pp. 185–188 (2009)

    Google Scholar 

  18. Van Herk, M.: A fast algorithm for local minimum and maximum filters on rectangular and octagonal kernels. Pattern Recogn. Lett. 13(7), 517–521 (1992)

    Article  Google Scholar 

  19. Haralick, R.M., Sternberg, S.R., Zhuang, X.: Image analysis using mathematical morphology. IEEE Trans. Pattern Anal. Mach. Intell. 9(4), 532–550 (1987)

    Article  Google Scholar 

  20. Thurley, M.J., Danell, V.: Fast morphological image processing open-source extensions for GPU processing with CUDA. IEEE J. Sel. Top. Sig. Process. 6(7), 849–855 (2012)

    Article  Google Scholar 

  21. Virtanen, P., et al.: SciPy 1.0: fundamental algorithms for scientific computing in Python. Nat. Meth. 17(3), 261–272 (2020)

    Article  Google Scholar 

  22. Van Droogenbroeck, M., Talbot, H.: Fast computation of morphological operations with arbitrary structuring elements. Pattern Recogn. Lett. 17(14), 1451–1460 (1996)

    Article  Google Scholar 

  23. Kahra, M., Sridhar, V., Breuß, M.: Fast morphological dilation and erosion for grey scale images using the Fourier transform. In: Proceedings of the 8th International Conference on Scale Space and Variational Methods, pp. 65–77 (2021)

    Google Scholar 

  24. Harris, C.R., et al.: Array programming with NumPy. Nature 585(7825), 357–362 (2020)

    Article  Google Scholar 

  25. Burgeth, B., Kleefeld, A.: An approach to color-morphology based on Einstein addition and Loewner order. Pattern Recogn. Lett. 47, 29–39 (2014)

    Article  Google Scholar 

  26. Dachsel, R., Jöster, A., Breuß, M.: Real-time retinal vessel segmentation on high-resolution Fundus images using Laplacian pyramids. In: Proceedings of the 9th Pacific Rim Symposium on Image and Video Technology, pp. 337–350 (2019)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institute for Mathematics, Brandenburg Technical University Cottbus-Senftenberg, 03046, Cottbus, Germany

    Vivek Sridhar, Michael Breuss & Marvin Kahra

Authors
  1. Vivek Sridhar
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Michael Breuss
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Marvin Kahra
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Vivek Sridhar .

Editor information

Editors and Affiliations

  1. University of Nevada, Reno, NV, USA

    George Bebis

  2. University of Texas at Arlington, Arlington, TX, USA

    Vassilis Athitsos

  3. University of South Carolina, Columbia, SC, USA

    Tong Yan

  4. City University of Hong Kong, Kowloon, Hong Kong

    Manfred Lau

  5. School of Engineering and Computing, University of Durham, Durham, Durham, UK

    Frederick Li

  6. Airbnb, New York, NY, USA

    Conglei Shi

  7. Peking University, Beijing, China

    Xiaoru Yuan

  8. Purdue University, West Lafayette, IN, USA

    Christos Mousas

  9. IST, School of Modeling, Simulation, and Training, Orlando, FL, USA

    Gerd Bruder

Rights and permissions

Reprints and permissions

Copyright information

© 2021 Springer Nature Switzerland AG

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

Sridhar, V., Breuss, M., Kahra, M. (2021). Fast Approximation of Color Morphology. In: Bebis, G., et al. Advances in Visual Computing. ISVC 2021. Lecture Notes in Computer Science(), vol 13018. Springer, Cham. https://doi.org/10.1007/978-3-030-90436-4_39

Download citation

  • DOI: https://doi.org/10.1007/978-3-030-90436-4_39

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-90435-7

  • Online ISBN: 978-3-030-90436-4

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation