Abstract
This work reviews the watershed in the graph framework of a shortest-path forest problem using a lexicographic path cost formulation. This formulation reflects the behavior of the ordered queue-based watershed algorithm. This algorithm is compared with our proposed shortest-path forest (IFT-Image Foresting Transform), concluding that the watershed is a special case of that. Recently many different watershed approaches are being used. We point out that in some cases the watershed algorithm does not keep the optimality of the shortest-path forest solution unless the IFT algorithm is used. The main difference between the algorithms is related to permanently labeling a pixel when inserting or removing it from the queue. The watershed based on the pixel dissimilarity using IFT can segment one-pixel width regions while keeping the optimality of the shortest-path forest solution.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
S. Beucher and C. Lantuéjoul. Use of watersheds in contour detection. In International Workshop on Image Processing, Real-Time Edge and Motion Detection/Estimation, Rennes, France, 1979.
S. Beucher and F. Meyer. The morphological approach to segmentation: the watershed transformation. In E. R. Dougherty, editor, Mathematical Morphology in Image Processing, chapter 12, pages 433–481. Marcel Dekker, New York, 1993.
J. Crespo. The flat zone approach: A general low-level region merging segmentation method. Signal Processing, 62(1):37–60, 1998.
J. Crespo and R. Schafer. The flat zone approach and color images. In J. Serra and P. Soille, editors, Mathematical morphology and its applications to image processing, pages 85–92. Kluwer Academic Publishers, 1994.
R. Dial. Algorithm 360: Shortest-path forest with topological ordering. Comm. Assoc.Comput. Mach., 1969.
E. W. Dijkstra. A note on two problems in connexion with graphs. Numerische Mathematik, 1959.
A. Falcão, R. Lotufo, and G. Araujo. Image foresting transform. IEEE Trans. on Pattern Analysis and Machine Intelligence, submitted, 1999.
A. Falcão, J. Udupa, S. Samarasekera, S. Sharma, B. Hirsch, and R. Lotufo. Usersteering image segmentation paradigms: Live wire and live lane. Graphical Models and Image Processing, 60(4):233–260, 1998.
R. Lotufo, A. Falcão, and F. Zampirolli. Fast Euclidean distance transform using a graph-search algorithm. submitted, 1999.
F. Meyer. Color image segmentation. In 4th Intern. Conf. on “Image Processing and. its Applications”, page 4, Maastricht, the Netherlands, April 1992.
F. Meyer. Topographic distance and watershed lines. Signal Processing, 38: 113–125, 1994.
E. Moore. The shortest path through a maze. Proc. Internat. Symposium on the Theory of Switching, Part II, Harvard university press, Cambridge, MA, 1957.
F. Preteux. On a distance function approach for gray-level mathematical morphology. In E. R. Dougherty, editor, Mathematical Morphology in Image Processing, chapter 10, pages 323–349. Marcel Dekker, New York, 1993.
P. Salembier, P. Brigger, J. R. Casas, and M. Pardas. Morphological operators for image and video compression. IEEE Transactions on Image Processing, 5(6):881–898, 1996.
L. Vincent. Morphological algorithms. In E. R. Dougherty, editor, Mathematical Morphology in Image Processing, chapter 8, pages 255–288. Marcel Dekker, New York, 1993.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2002 Kluwer Academic/Plenum Publishers
About this chapter
Cite this chapter
Lotufo, R., Falcao, A. (2002). The Ordered Queue and the Optimality of the Watershed Approaches. In: Goutsias, J., Vincent, L., Bloomberg, D.S. (eds) Mathematical Morphology and its Applications to Image and Signal Processing. Computational Imaging and Vision, vol 18. Springer, Boston, MA. https://doi.org/10.1007/0-306-47025-X_37
Download citation
DOI: https://doi.org/10.1007/0-306-47025-X_37
Publisher Name: Springer, Boston, MA
Print ISBN: 978-0-7923-7862-4
Online ISBN: 978-0-306-47025-7
eBook Packages: Springer Book Archive