Abstract
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 .
Download to read the full chapter text
Chapter PDF
Similar content being viewed by others
References
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)
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)
Meine, H.: The GeoMap Representation: On Topologically Correct Sub-pixel Image Analysis. PhD thesis, Dept. of Informatics, Univ. of Hamburg (2009)
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 issue
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)
Vincent, L., Soille, P.: Watersheds in digital spaces: an efficient algorithm based on immersion simulations. IEEE T-PAMI 13, 583–598 (1991)
Comaniciu, D., Meer, P.: Mean shift: A robust approach toward feature space analysis. IEEE T-PAMI 24, 603–619 (2002)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2009 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Meine, H., Stelldinger, P., Köthe, U. (2009). Pixel Approximation Errors in Common Watershed Algorithms. In: Brlek, S., Reutenauer, C., Provençal, X. (eds) Discrete Geometry for Computer Imagery. DGCI 2009. Lecture Notes in Computer Science, vol 5810. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-04397-0_17
Download citation
DOI: https://doi.org/10.1007/978-3-642-04397-0_17
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-04396-3
Online ISBN: 978-3-642-04397-0
eBook Packages: Computer ScienceComputer Science (R0)