Nothing Special   »   [go: up one dir, main page]

skip to main content
article

The Watershed Transform: Definitions, Algorithms and Parallelization Strategies

Published: 01 April 2000 Publication History

Abstract

The watershed transform is the method of choice for image segmentation in the field of mathematical morphology. We present a critical review of several definitions of the watershed transform and the associated sequential algorithms, and discuss various issues which often cause confusion in the literature. The need to distinguish between definition, algorithm specification and algorithm implementation is pointed out. Various examples are given which illustrate differences between watershed transforms based on different definitions and/or implementations. The second part of the paper surveys approaches for parallel implementation of sequential watershed algorithms.

References

[1]
Alnuweiri, H. M., and Prasanna, V. K. Parallel architectures and algorithms for image component labeling. IEEE Trans. Patt. Anal. Mach. Intell. 14, 10 (1992), 1014-1034.
[2]
Berge, C. Théorie des Graphes et ses Applications. Dunod, Paris, 1958.
[3]
Beucher, S. Watershed, hierarchical segmentation and waterfall algorithm. In Mathematical Morphology and its Applications to Image Processing, J. Serra and P. Soille, Eds. Kluwer Acad. Publ., Dordrecht, 1994, pp. 69-76.
[4]
Beucher, S., and Lantuéjoul, C. Use of watersheds in contour detection. In Proc. International Workshop on Image Processing, Real-Time Edge and Motion Detection/Estimation, Rennes, september (1979).
[5]
Beucher, S., and Meyer, F. The morphological approach to segmentation: the watershed transformation. In Mathematical Morphology in Image Processing, E. R. Dougherty, Ed. Marcel Dekker, New York, 1993, ch. 12, pp. 433-481.
[6]
Bieniek, A., Burkhardt, H., Marschner, H., Nölle, M., and Schreiber, G. A parallel watershed algorithm. In Proc. 10th Scandinavian Conference on Image Analysis (SCIA'97), Lappeenranta, Finland (1997), pp. 237-244.
[7]
Bieniek, A., and Moga, A. A connected component approach to the watershed segmentation. In Mathematical Morphology and its Applications to Image and Signal Processing, H. J. A. M. Heijmans and J. B. T. M. Roerdink, Eds. Kluwer Acad. Publ., Dordrecht, 1998, pp. 215-222.
[8]
Cormen, T. H., Leiserson, C. E., and Rivest, R. L. Introduction to Algorithms. MIT Press, 1990.
[9]
Digabel, H., and Lantuéjoul, C. Iterative algorithms. In Actes du Second Symposium Européen d'Analyse Quantitative des Microstructures en Sciences des Matériaux, Biologie et Médecine, Caen, 4-7 October 1977 (1978), J.-L. Chermant, Ed., Riederer Verlag, Stuttgart, pp. 85-99.
[10]
Dijkstra, E. W. A note on two problems in connexion with graphs. Numerische Mathematik 1 (1959), 269-271.
[11]
Dijkstra, E. W. Co-operating sequential processes. In Programming Languages, F. Genuys, Ed. Academic Press, New York, 1968, pp. 43-112.
[12]
Dobrin, B. P., Viero, T., and Gabbouj, M. Fast watershed algorithms: analysis and extensions. In SPIE 1994; Vol. 2180. Proc. IS&T/SPIE Symposium on Electronic Imaging Science & Technology, Nonlinear Image Processing V, February 6-10, 1994, San Jose Convention Center, CA. (1994), pp. 209-220.
[13]
Embrechts, H., Roose, D., and Wambacq, P. Component labelling on a mimd multiprocessor. Comp. Vis. Graph. Im. Proc. 75, 2 (1993), 155-165.
[14]
Fiorio, C., and Gustedt, J. Two linear time union-find strategies for image processing. Theoretical Computer Science A 154, 2 (Feb. 1996), 165-181.
[15]
Foster, I. Designing and Building Parallel Programs. Addison Wesley, Reading, MA, 1994.
[16]
Gropp, W., Lusk, E., and Skjellum, A. Using MPI: Portable Parallel Programming with the Message Passing Interface. MIT Press, Cambridge, MA, 1995.
[17]
Guillemin, V., and Pollack, A. Differential Topology. Prentice-Hall, Englewood Cliffs, NJ, 1974.
[18]
Haralick, R. M., and Shapiro, L. G. Survey: image segmentation techniques. Comp. Vis. Graph. Im. Proc. 29 (1985), 100-132.
[19]
Klein, J. C., Lemonnier, F., Gauthier, M., and Peyrard, R. Hardware implementation of the watershed zone algorithm based on a hierarchical queue structure. In Proc. IEEE Workshop on Nonlinear Signal and Image processing, June 20-22, Neos Marmaras, Halkidiki, Greece (1995), I. Pitas, Ed., pp. 859-862.
[20]
Lantuéjoul, C. La squelettisation et son application aux mesures topologiques des mosaïques poly-cristallines . PhD thesis, Ecole des Mines, Paris, 1978.
[21]
Meijster, A., and Roerdink, J. B. T. M. A proposal for the implementation of a parallel watershed algorithm. In Computer Analysis of Images and Patterns, V. Hlavá¿ and R. ¿ára, Eds., vol. 970 of Lecture Notes in Computer Science. Springer-Verlag, New York-Heidelberg-Berlin, 1995, pp. 790-795.
[22]
Meijster, A., and Roerdink, J. B. T. M. Computation of watersheds based on parallel graph algorithms. In Mathematical Morphology and its Applications to Image and Signal Processing, P. Maragos, R. W. Shafer, and M. A. Butt, Eds. Kluwer Acad. Publ., Dordrecht, 1996, pp. 305-312.
[23]
Meijster, A., and Roerdink, J. B. T. M. A disjoint set algorithm for the watershed transform. In Proc. IX European Signal Processing Conference (EUSIPCO'98), September 8 - 11, 1998, Rhodes, Greece (1998), S. Theodoridis, I. Pitas, A. Stouraitis, and N. Kalouptsidis, Eds., pp. 1665-1668.
[24]
Meyer, F. Un algorithme optimal de ligne de partage des eaux. In Proceedings 8th Congress AFCET, Lyon-Villeurbane, France (1992), vol. 2, pp. 847-859.
[25]
Meyer, F. Topographic distance and watershed lines. Signal Processing 38 (1994), 113-125.
[26]
Meyer, F., and Beucher, S. Morphological segmentation. J. Visual Commun. and Image Repres. 1, 1 (1990), 21-45.
[27]
Moga, A. Parallel watershed algorithms for image segmentation. PhD thesis, Tampere University of Technology, Tampere, Finland, Feb. 1997.
[28]
Moga, A. N., Cramariuc, B., and Gabbouj, M. Parallel watershed transformation algorithms for image segmentation. Parallel Computing 24 (1998), 1981-2001.
[29]
Moga, A. N., and Gabbouj, M. A parallel watershed algorithm based on the shortest path computation. In Parallel Programming and Applications, P. Fritzson and L. Finmo, Eds. IOS Press, 1995.
[30]
Moga, A. N., and Gabbouj, M. Parallel image component labeling with watershed transformation. IEEE Trans. Patt. Anal. Mach. Intell. 19, 5 (May 1997), 441-450.
[31]
Moga, A. N., and Gabbouj, M. Parallel marker-based image segmentation with watershed transformation. Journal of Parallel and Distributed Computing 51, 1 (1998), 27-45.
[32]
Moga, A. N., Viero, T., Dobrin, B. P., and Gabbouj, M. Implementation of a distributed watershed algorithm. In Mathematical Morphology and its Applications to Image Processing, J. Serra and P. Soille, Eds. Kluwer Acad. Publ., Dordrecht, 1994, pp. 281-288.
[33]
Moga, A. N., Viero, T., Gabbouj, M., Nölle, M., Schreiber, G., and Burkhardt, H. Parallel watershed algorithm based on sequential scanning. In Proc. IEEE Workshop on Nonlinear Signal and Image processing, June 20-22, Neos Marmaras, Halkidiki, Greece (1995), I. Pitas, Ed., pp. 991-994.
[34]
Moore, E. F. The shortest path through a maze. In Proc. Intern. Symp. on Theory of Switching, 1957 (1959), vol. 30 of Annals of the computation laboratory of Harvard University, pp. 285-292.
[35]
Nackman, L. R. Two-dimensional critical point con_guration graphs. IEEE Trans. Patt. Anal. Mach. Intell. 6, 4 (1984), 442-450.
[36]
Najman, L., and Schmitt, M. Watershed of a continuous function. Signal Processing 38 (1994), 99-112.
[37]
Noguet, D., Merle, A., and Lattard, D. A data dependent architecture based on seeded region growing strategy for advanced morphological operators. In Mathematical Morphology and its Applications to Image and Signal Processing, P. Maragos, R. W. Shafer, and M. A. Butt, Eds. Kluwer Acad. Publ., Dordrecht, 1996, pp. 235-243.
[38]
Nölle, M., Schreiber, G., and Schulz-Mirbach, H. PIPS-a general purpose parallel image processing system. In Proceedings 16th DAGM-Symposium Mustererkennung, Vienna (Sept. 1994), G. Kropatsch, Ed., Reihe Informatik XPress, Springer-Verlag, New York-Heidelberg-Berlin, pp. 271-309.
[39]
Preteux, F. On a distance function approach for gray-level mathematical morphology. In Mathematical Morphology in Image Processing, E. R. Dougherty, Ed. Marcel Dekker, New York, 1993, ch. 10, pp. 323-349.
[40]
PVM: Parallel Virtual Machine, a user's guide and tutorial for networked parallel computing, 1994.
[41]
Quinn, M. Parallel Computing. Theory and Practice. McGraw-Hill, New York, NY, 1994.
[42]
Roerdink, J. B. T. M., and Meijster, A. Segmentation by watersheds: definition and parallel implementation. In Advances in Computer Vision, F. Solina, W. G. Kropatsch, R. Klette, and R. Bajcsy, Eds. Springer, Wien, New York, 1997, pp. 21-30.
[43]
Rosenfeld, A., and Pfaltz, J. Distance functions on digital pictures. Pattern Recognition 1 (1968), 33-61.
[44]
Rosenfeld, A., and Pfaltz, J. L. Sequential operations in digital picture processing. J. Ass. Comp. Mach. 13 (1966), 471-494.
[45]
Samet, H. Connected component labeling using quadtrees. J. Ass. Comp. Mach. 28, 3 (1981), 487-501.
[46]
Serra, J. Image Analysis and Mathematical Morphology. Academic Press, New York, 1982.
[47]
Tarjan, R. E. Data Structures and Network Algorithms. SIAM, 1983.
[48]
Tarjan, R. E., and van Leeuwen, J. Worst-case analysis of set union algorithms. J. Ass. Comp. Mach. 31, 2 (1984), 245-281.
[49]
Verbeek, P. W., and Verwer, B. J. H. Shading from shape, the eikonal equation solved by gray-weighted distance transform. Pattern Recognition Letters 11 (1990), 681-690.
[50]
Viero, T. Algorithms for image sequence filtering, coding and image segmentation. PhD thesis, Tampere University of Technology, Tampere, Finland, Jan. 1996.
[51]
Vincent, L. Algorithmes Morphologiques a Base de Files d'Attente et de Lacets. Extension aux Graphes. PhD thesis, Ecole Nationale Supérieure des Mines de Paris, Fontainebleau, 1990.
[52]
Vincent, L., and Soille, P. Watersheds in digital spaces: an efficient algorithm based on immersion simulations. IEEE Trans. Patt. Anal. Mach. Intell. 13, 6 (1991), 583-598.

Cited By

View all
  • (2023)Detecting Anomalous Solder Joints in Multi-sliced PCB X-ray Images: A Deep Learning Based ApproachSN Computer Science10.1007/s42979-023-01765-64:3Online publication date: 6-Apr-2023
  • (2022)An AI-Based Decision Support System for Quality Control Applied to the Use Case Donor CorneaArtificial Intelligence in HCI10.1007/978-3-031-05643-7_17(257-274)Online publication date: 26-Jun-2022
  • (2021)Adaptive tuning of SLIC parameter KMultimedia Tools and Applications10.1007/s11042-021-10900-580:17(25649-25672)Online publication date: 1-Jul-2021
  • Show More Cited By

Recommendations

Comments

Please enable JavaScript to view thecomments powered by Disqus.

Information & Contributors

Information

Published In

cover image Fundamenta Informaticae
Fundamenta Informaticae  Volume 41, Issue 1,2
April 2000
258 pages

Publisher

IOS Press

Netherlands

Publication History

Published: 01 April 2000

Author Tags

  1. mathematical morphology
  2. parallel implementation
  3. sequential algorithms
  4. watershed definition
  5. watershed transform

Qualifiers

  • Article

Contributors

Other Metrics

Bibliometrics & Citations

Bibliometrics

Article Metrics

  • Downloads (Last 12 months)0
  • Downloads (Last 6 weeks)0
Reflects downloads up to 02 Oct 2024

Other Metrics

Citations

Cited By

View all
  • (2023)Detecting Anomalous Solder Joints in Multi-sliced PCB X-ray Images: A Deep Learning Based ApproachSN Computer Science10.1007/s42979-023-01765-64:3Online publication date: 6-Apr-2023
  • (2022)An AI-Based Decision Support System for Quality Control Applied to the Use Case Donor CorneaArtificial Intelligence in HCI10.1007/978-3-031-05643-7_17(257-274)Online publication date: 26-Jun-2022
  • (2021)Adaptive tuning of SLIC parameter KMultimedia Tools and Applications10.1007/s11042-021-10900-580:17(25649-25672)Online publication date: 1-Jul-2021
  • (2021)A brain tumor detection system using gradient based watershed marked active contours and curvelet transformTransactions on Emerging Telecommunications Technologies10.1002/ett.417032:9Online publication date: 8-Sep-2021
  • (2020)Uncovering the topology of time-varying fMRI data using cubical persistenceProceedings of the 34th International Conference on Neural Information Processing Systems10.5555/3495724.3496303(6900-6912)Online publication date: 6-Dec-2020
  • (2020)Automatically Finding the Number of Clusters for Large Datasets based on CoresetsProceedings of the 2020 4th International Conference on Big Data and Internet of Things10.1145/3421537.3421538(1-6)Online publication date: 22-Aug-2020
  • (2020)Temporal Action Detection with Structured Segment NetworksInternational Journal of Computer Vision10.1007/s11263-019-01211-2128:1(74-95)Online publication date: 1-Jan-2020
  • (2020)Techniques and applications for soccer video analysis: A surveyMultimedia Tools and Applications10.1007/s11042-020-09409-079:39-40(29685-29721)Online publication date: 1-Oct-2020
  • (2020)Detection and segmentation of iron ore green pellets in images using lightweight U-net deep learning networkNeural Computing and Applications10.1007/s00521-019-04045-832:10(5775-5790)Online publication date: 1-May-2020
  • (2019)HEHLKAPPEProceedings of the 14th International Conference on Availability, Reliability and Security10.1145/3339252.3340102(1-8)Online publication date: 26-Aug-2019
  • Show More Cited By

View Options

View options

Get Access

Login options

Media

Figures

Other

Tables

Share

Share

Share this Publication link

Share on social media