Skip to main content
SpringerLink
Log in

From Extrema Relationships to Image Simplification Using Non-flat Structuring Functions

  • Conference paper
Mathematical Morphology and Its Applications to Signal and Image Processing (ISMM 2013)

Part of the book series: Lecture Notes in Computer Science ((LNIP,volume 7883))

Abstract

Image simplification plays a fundamental role in Image Processing to improve results in complex tasks such as segmentation. The field of Mathematical Morphology (MM) itself has established many ways to perform such improvements. In this paper, we present a new approach for image simplification which takes into account erosion and dilation from MM. The proposed method is not self-dual and only single-band signals under a discrete domain are considered. Our main focus is on the creation of concave structuring functions based on a relation between signal extrema. This relation is given by two extrema according to their degree of separation (distance) and the respective heights (contrast). From these features, a total order relation is produced, thus supplying a way to progressively simplify the signal. Some two-dimensional images are considered here to illustrate in practice this simplification behavior.

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 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
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

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Bertrand, G.: On the Dynamics. Image Vision Comput. 25(4), 447–454 (2007)

    Article  MathSciNet  Google Scholar 

  2. Beucher, S., Meyer, F.: The Morphological Approach to Segmentation: The Watershed Transformation. In: Mathematical Morphology in Image Processing. Marcel Dekker (1993)

    Google Scholar 

  3. van den Boomgaard, R., Dorst, L., Makram-Ebeid, S., Schavemaker, J.G.M.: Quadratic Structuring Functions in Mathematical Morphology. In: Mathematical Morphology and its Applications to Image and Signal Processing. Kluwer (1996)

    Google Scholar 

  4. Dorini, L.B., Leite, N.J.: Multiscale Morphological Image Simplification. In: Ruiz-Shulcloper, J., Kropatsch, W.G. (eds.) CIARP 2008. LNCS, vol. 5197, pp. 413–420. Springer, Heidelberg (2008)

    Chapter  Google Scholar 

  5. Grimaud, M.: A New Measure of Contrast: The Dynamics. In: Proc. SPIE, Image Algebra and Morphological Image Processing III, vol. 1769, pp. 292–305 (1992)

    Google Scholar 

  6. Hagyard, D., Razaz, M., Atkin, P.: Analysis of Watershed Algorithms for Greyscale Images. ICIP 3, 41–44 (1996)

    Google Scholar 

  7. Jackway, P.T., Deriche, M.: Scale-Space Properties of the Multiscale Morphological Dilation-Erosion. IEEE Trans. Pattern Anal. Mach. Intell. 18(1), 38–51 (1996)

    Article  Google Scholar 

  8. Lindeberg, T., ter Haar Romeny, B.M.: Linear Scale-Space: Basic Theory. In: Geometry-Driven Diffusion in Computer Vision. Kluwer (1994)

    Google Scholar 

  9. Meyer, F.: Levelings, Image Simplification Filter for Segmentation. J. Math. Imaging Vision, 59–72 (2004)

    Google Scholar 

  10. Meyer, F., Serra, J.: Contrasts and Activity Lattice. Signal Process 16(4), 303–317 (1989)

    Article  MathSciNet  Google Scholar 

  11. Pitas, I., Venetsanopoulos, A.N.: Order Statistics in Digital Image Processing. P. IEEE 80(12), 1893–1921 (1992)

    Article  Google Scholar 

  12. Serra, J.: Image Analysis and Mathematical Morphology, vol. 1. Academic Press (1982)

    Google Scholar 

  13. Serra, J., Salembier, P.: Connected Operators and Pyramids. In: Proc. SPIE, Image Algebra and Morphological Image Processing IV, vol. 2030, pp. 65–76 (1993)

    Google Scholar 

  14. Silva, A.G., Lotufo, R.A.: Efficient Computation of New Extinction Values from Extended Component Tree. Pattern Recogn. Lett. 32(1), 79–90 (2011)

    Article  Google Scholar 

  15. Vachier, C., Vincent, L.: Valuation of Image Extrema Using Alternating Filters by Reconstruction. In: Neural, Morphological, and Stochastic Methods in Image and Signal Processing, pp. 94–103 (1995)

    Google Scholar 

  16. Wilson, S.S.: Vector Morphology and Iconic Neural Networks. IEEE Trans. Syst. Man Cybern. 19(6), 1636–1644 (1989)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institute of Computing, University of Campinas, UNICAMP, 13083-852, Campinas, SP, Brazil

    Guilherme Polo & Neucimar J. Leite

Authors
  1. Guilherme Polo
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Neucimar J. Leite
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Centre for Image Analysis, Swedish University of Agricultural Sciences and Uppsala University, Box 337, 751 05, Uppsala, Sweden

    Cris L. Luengo Hendriks , Gunilla Borgefors  & Robin Strand ,  & 

Rights and permissions

Reprints and permissions

Copyright information

© 2013 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Polo, G., Leite, N.J. (2013). From Extrema Relationships to Image Simplification Using Non-flat Structuring Functions. In: Hendriks, C.L.L., Borgefors, G., Strand, R. (eds) Mathematical Morphology and Its Applications to Signal and Image Processing. ISMM 2013. Lecture Notes in Computer Science, vol 7883. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-38294-9_32

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-38294-9_32

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-38293-2

  • Online ISBN: 978-3-642-38294-9

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation