Pixel Approximation Errors in Common Watershed Algorithms

  • Hans Meine
  • Peer Stelldinger
  • Ullrich Köthe
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5810)


The exact, subpixel watershed algorithm delivers very accurate watershed boundaries based on a spline interpolation, but is slow and only works in 2D. On the other hand, there are very fast pixel watershed algorithms, but they produce errors not only in certain exotic cases, but also in real-world images and even in the most simple scenarios. In this work, we examine closely the source of these errors and propose a new algorithm that is fast, approximates the exact watersheds (with pixel resolution), and can be extended to 3D .


  1. 1.
    Roerdink, J.B.T.M., Meijster, A.: The watershed transform: Definitions, algorithms, and parallellization strategies. In: Goutsias, J., Heijmans, H. (eds.) Mathematical Morphology, vol. 41, pp. 187–228. IOS Press, Amsterdam (2000)Google Scholar
  2. 2.
    Meine, H., Köthe, U.: Image segmentation with the exact watershed transform. In: Villanueva, J. (ed.) Proc. Vis., Imaging, and Image Processing, pp. 400–405 (2005)Google Scholar
  3. 3.
    Meine, H.: The GeoMap Representation: On Topologically Correct Sub-pixel Image Analysis. PhD thesis, Dept. of Informatics, Univ. of Hamburg (2009)Google Scholar
  4. 4.
    Meine, H., Köthe, U., Stelldinger, P.: A topological sampling theorem for robust boundary reconstruction and image segmentation. Discrete Applied Mathematics 157, 524–541 (2008) DGCI special issueMathSciNetCrossRefzbMATHGoogle Scholar
  5. 5.
    Yao, X., Hung, Y.P.: Fast image segmentation by sliding in the derivative terrain. In: Casasent, D.P. (ed.) Intelligent Robots and Computer Vision X: Algorithms and Techniques. SPIE Conference Series, vol. 1607, pp. 369–379 (1991)Google Scholar
  6. 6.
    Vincent, L., Soille, P.: Watersheds in digital spaces: an efficient algorithm based on immersion simulations. IEEE T-PAMI 13, 583–598 (1991)CrossRefGoogle Scholar
  7. 7.
    Comaniciu, D., Meer, P.: Mean shift: A robust approach toward feature space analysis. IEEE T-PAMI 24, 603–619 (2002)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • Hans Meine
    • 1
  • Peer Stelldinger
    • 1
  • Ullrich Köthe
    • 2
  1. 1.Cognitive Systems LaboratoryUniversity of HamburgGermany
  2. 2.Heidelberg Collaboratory for Image ProcessingUniversity of HeidelbergGermany

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