Skip to main content
SpringerLink
Log in

Edge Detection Models

  • Conference paper
Image Analysis and Recognition (ICIAR 2005)

Part of the book series: Lecture Notes in Computer Science ((LNIP,volume 3656))

Included in the following conference series:

  • 1299 Accesses

Abstract

In this paper, the Mumford-Shah (MS) model and its variations are studied for image segmentation. It is found that using the piecewise constant approximation, we cannot detect edges with low contrast. Therefore other terms, such as gradient and Laplacian, are included in the models. To simplify the problem, the gradient of the original image is used in the Rudin-Osher-Fatemi (ROF) like model. It is found that this approximation is better than the piecewise constant approximation for some images since it can detect the low contrast edges of objects. Linear approximation is also used for both MS and ROF like models. It is found that the linear approximation results are comparable with the results of the models using gradient and Laplacian terms.

This work was supported by research grants from the Natural Sciences and Engineering Research Council of Canada.

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 149.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever

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. Aubert, G., Kornprobst, P.: Mathematical Problems in Image Processing: Partial differential equations and the Calculus of Variations. Applied Mathematical Sciences, vol. 147. Springer, Heidelberg (2002)

    MATH  Google Scholar 

  2. Chan, T.F., Vese, L.A.: Active Contours without edges. IEEE transactions on Image Processing 10(2), 266–277 (2001)

    Article  MATH  Google Scholar 

  3. Charbonnier, P., Blanc-Feraud, L., Aubert, G., Barlaud, M.: Deterministic edge-preserving regularization in computer imaging. IEEE Trans. Image Process. 6, 298–311 (1997)

    Article  Google Scholar 

  4. Gao, S., Bui, T.D.: Image Segmentation and Selective Smoothing by Using Mumford-Shah Model. IEEE Transaction on Image Processing (to be published)

    Google Scholar 

  5. Gao, S.: Tien D. Bui, A new image segmentation and smoothing model. In: Proc. of IEEE int. Symposium on Biomedical Imaging: From Nano to Macro, Arlington, V.A., April 15-18, pp. 137–140 (2004)

    Google Scholar 

  6. Lee, B.R., Ben Hamza, A., Krim, H.: An active contour model for image segmentation: a variational perspective. In: Proc. IEEE international conference on acoustics speech and Signal processing, Orlando (May 2002)

    Google Scholar 

  7. Li, S.Z.: Roof-Edge Preserving Image Smoothing Based on MRFs. IEEE Transactions on Image Processing 9(6), 1134–1138 (2000)

    Article  Google Scholar 

  8. Mumford, D., Shah, J.: Optimal approximation by piecewise smooth functions and associated variational problems. Comm. Pure Appl. Math. 42, 577–685 (1989)

    Article  MATH  MathSciNet  Google Scholar 

  9. Pellegrino, F.A., Vanzella, W., Torre, V.: Edge Detection Revisited. IEEE Transactions on Systems, Man, and Cybernetics Part B: Cybernetics 34(3), 1500–1517 (2004)

    Article  Google Scholar 

  10. Sethian, J.A.: Level Set Methods and Fast Marching Methods. Cambridge University Press, Cambridge (1999)

    MATH  Google Scholar 

  11. Teboul, S., Blanc-Feraud, L., Aubert, G., Barlaud, M.: Variational Approach for Edge-Preserving Regularization Using Coupled PDEs. IEEE Transactions on Image Processing 7(3), 387–397 (1998)

    Article  Google Scholar 

  12. Tsai, A., Yezzi, A., Willsky, A.S.: Curve Evolution Implementation of the Mumford-Shah Functional for Image Segmentation, Denoising, Interpolation, and Magnification. IEEE Tran. on Image Processing 10(8), 1169–1186 (2001)

    Article  MATH  Google Scholar 

  13. Vese, L., Chan, T.F.: A Multiphase Level Set Framework for Image Segmentation Using the Mumford and Shah Model. International Journal of Computer Vision 50(3), 271–293 (2002)

    Article  MATH  Google Scholar 

  14. Vese, L.A.: Multiphase Object Detection and Image Segmentation. In: Osher, S., Paragios, N. (eds.) Geometric Level Set Methods in Imaging, Vision and Graphics, pp. 175–194. Springer, Heidelberg (2003)

    Chapter  Google Scholar 

  15. Weisenseel, R.A., Karl, W.C., Castanon, D.A.: A region-based alternative for edge-preserving smoothing. In: Proceedings of the International Conference on Image Processing, Vancouver, BC, Canada, pp. 778–781 (2000)

    Google Scholar 

  16. Blake, A., Zisserman, A.: Visual Reconstruction. The MIT Press, Cambridge (1987)

    Google Scholar 

  17. Vanzella, W., Pellegrino, F.A., Torre, V.: Self-Adaptive Regularization. IEEE Transactions on PAMI 26(6), 804–809 (2004)

    Google Scholar 

  18. Rudin, L., Osher, S., Fatemi, E.: Nonelinear Total Variation Based Noise Removal. Physica D 60, 259–268 (1992)

    Article  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Computer Science and Software Engineering, Concordia University, Montreal, QC, H3G 1M8, Canada

    Q. H. Zhang, S. Gao & Tien D. Bui

Authors
  1. Q. H. Zhang
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. S. Gao
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Tien D. Bui
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Electrical and Computer Engineering Department, University of Waterloo,  

    Mohamed Kamel

  2. FEUP - Faculdade de Engenharia, Universidade do Porto, Rua Dr. Roberto Frias, P.O. Box, 4200-465, Porto, Portugal

    Aurélio Campilho

Rights and permissions

Reprints and permissions

Copyright information

© 2005 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Zhang, Q.H., Gao, S., Bui, T.D. (2005). Edge Detection Models. In: Kamel, M., Campilho, A. (eds) Image Analysis and Recognition. ICIAR 2005. Lecture Notes in Computer Science, vol 3656. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11559573_17

Download citation

  • DOI: https://doi.org/10.1007/11559573_17

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-29069-8

  • Online ISBN: 978-3-540-31938-2

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation