This Article 
 Bibliographic References 
 Add to: 
Watersheds in Digital Spaces: An Efficient Algorithm Based on Immersion Simulations
June 1991 (vol. 13 no. 6)
pp. 583-598

A fast and flexible algorithm for computing watersheds in digital gray-scale images is introduced. A review of watersheds and related motion is first presented, and the major methods to determine watersheds are discussed. The algorithm is based on an immersion process analogy, in which the flooding of the water in the picture is efficiently simulated using of queue of pixel. It is described in detail provided in a pseudo C language. The accuracy of this algorithm is proven to be superior to that of the existing implementations, and it is shown that its adaptation to any kind of digital grid and its generalization to n-dimensional images (and even to graphs) are straightforward. The algorithm is reported to be faster than any other watershed algorithm. Applications of this algorithm with regard to picture segmentation are presented for magnetic resonance (MR) imagery and for digital elevation models. An example of 3-D watershed is also provided.

[1] L.E. Band, "Topographic partition of watersheds with digital elevation models,"Water Resources Res., vol. 22, no. 1, pp. 15-24, 1986.
[2] M. Benali, "Du choix des mesures dans les procédures de reconnaissances des formes et d'analyse de texture," Ph.D. dissertation, School of Mines, Paris, 1986.
[3] S. Beucher and C. Lantuéjoul, "Use of watersheds in contour detection," inProc. Int. Workshop Image Processing, Real-Time Edge and Motion Detection/Estimation, Rennes, France, Sept. 17-21, 1979.
[4] S. Beucher, "Watersheds of functions and picture segmentation," inProc. IEEE Int. Conf. Acoustics, Speech, and Signal Processing, Paris, France, May 1982, pp. 1928-1931.
[5] S. Beucher, "Obstacle detection and vehicle trajectories,"Prometheus Image Processing Meeting, Paris, France, May 18, 1989.
[6] S. Beucher, "Segmentation d'images et morphologie mathématique," Ph.D. dissertation, School of Mines, Paris, France, June 1990.
[7] G. Borgefors, "Distance transformations in digital images,"Comput. Vision, Graphics, Image Processing, vol. 34, pp. 334-371, 1986.
[8] J. F. Canny, "A computational approach to edge detection,"IEEE Trans. Pattern Anal. Machine Intell., vol. PAMI-8, pp. 679-697, 1986.
[9] S.H. Collins, "Terrain parameters directly from a digital terrain model,"Canadian Surveyor, vol. 29, no. 5, pp. 507-518, 1975.
[10] P.E. Danielsson, "Euclidean distance mapping,"Comput. Graphics Image Processing, vol. 14, pp. 227-248, 1980.
[11] H. Digabel and C. Lantuéjoul, "Iterative algorithms," inProc. 2nd European Symp. Quantitative Analysis of Microstructures in Material Science, Biology and Medicine, Caen, France, Oct. 1977, J. L. Chermant, Ed. Stuttgart, West Germany: Riederer Verlag, 1978, pp. 85-99.
[12] D. Douglas, "Experiments to locate ridges and channels to create a new type of digital elevation model,"Cartographica, vol. 23, no. 4, pp. 29-61, 1986.
[13] F. Doyle, "Digital terrain models: An overview,"Photogram. Eng. Remote Sensing, vol. 44, no. 12, pp. 1481-1485, Dec. 1978.
[14] F. Friedlander, "A sequential algorithm for detecting watersheds on a gray level image,"Acta Stereologica, vol. 6/III (Proc 7th Int. Cong. For Stereology), Caen, France, pp. 663-668, Sept. 1987.
[15] A. Gagalowicz, "A new approach for image segmentation," inProc. 8th Int. Conf. Pattern Recognition, Paris, France, Oct. 1986.
[16] M. Golay, "Hexagonal pattern transforms," inProc. IEEE Trans. Comput., vol. C-18, no. 8, Aug. 1969.
[17] M. Grimaud, "Intervertebral disk segmentation," School of Mines, Paris, France. Internal Rep. CMM, Jan. 1990.
[18] R. Haralick and L. Shapiro, "Survey: Image segmentation techniques,"Comput. Vision, Graphics, Image Processing, vol. 29, pp. 100-132, 1985.
[19] F. Harary,Graph Theory. Reading, MA: Addision-Wesley, 1969.
[20] H.J.A.M. Heijmans and A. Toet,Morphological Sampling, Center Math. Comput. Sci., Amsterdam, The Netherlands, Internal Rep. AM- R8913, Aug. 1989.
[21] J.L. Horowitz and T. Pavlidis, "Picture segmentation by a directed split and merge procedure," inProc 2nd Int. Conf. Pattern Recognition, 1974, nn 424-433.
[22] E.J. Isaac and R. C. Singleton, "Sorting by address calculation,"J. ACM, vol. 3, pp. 169-174, 1956.
[23] C. Lantuéjoul, "Skeletonization in quantitative metallography," inIssues of Digital Image Processing, R.M. Haralick and J.C. Simon, Eds. Groningen, The Netherlands: Sijthoff and Noordhoff, 1980.
[24] C. Lantuéjoul and F. Maisonneuve, "Geodesic methods in quantitative image analysis,"Pattern Recognition, vol. 17, pp. 177-187, 1984.
[25] B. Lay, "Recursive algorithms in mathematical morphology,"Acta Stereologica, vol. 6/III (Proc. 7th Int. Cong. for Stereology), Caen, France, pp. 691-696, Sept. 1987.
[26] H. Lorin,Sorting and Sort Systems(The System Programming Series). Reading, MA: Addison-Wesley, 1975.
[27] F. Maisonneuve, "Sur le partage des eaux," School of Mines, Paris, France, Internal Rep. CMM, 1982.
[28] D. Marks, J. Dozier, and J. Frew, "Automated basin delineation from digital elevation data,"Geoprocessing, vol. 2, pp. 299-311, 1984.
[29] D. Marr,Vision. New York: Freeman, 1982.
[30] M. Matheron,Random Sets and Integral Geometry. New York: Wiley, 1975.
[31] F. Meyer, "Cytologic quantitative et morphologie mathématique," Ph.D. dissertation, School of Mines, Paris, France, 1979.
[32] F. Meyer, "Skeletons and perceptual graphs,"Signal Processing, vol. 16, no. 4, pp. 335-363, Apr. 1989.
[33] H. Minkowski, "Allgemein lehrsätzeüber konvexe polyeder,"Nach. Ges. Wiss. Göttingen, pp. 198-219, 1897.
[34] O. Monga, "An optimal region growing algorithm for image segmentation,"Int. J. Pattern Recog. Artificial Intell., vol. 3, no. 4, Dec. 1987.
[35] J. Piper and E. Granum, "Computing distance transformations in convex and non convex domains,"Pattern Recog., vol. 20, pp. 599-615, 1987.
[36] T.K. Puecker and D.H. Douglas, "Detection of surface-specific points by local parallel processing of discrete terrain elevation data,"Comput. Vision, Graphics, Image Processing, vol. 4, pp. 375-387, 1975.
[37] I. Ragnemalm, "Contour processing distance transforms," inProgress in Image Analysis and Processing, Cantoniet al., Eds. Cleveland, OH: World Scientific, 1990, pp. 204-212.
[38] A. Rosenfeld and J. Pfaltz, "Sequential operations in digital picture processing,"J. ACM, vol. 4, 1966.
[39] M. Schmitt, "Des algorithmes morphologiquesàl'intelligence artificielle," Ph.D. dissertation, School of Mines, Paris, France, Feb. 1989.
[40] J. Serra,Image Analysis and Mathematical Morphology. London: Academic, 1982.
[41] J. Serra, Ed.,Image Analysis and Mathematical Morphology, Part II: Theoretical Advances. London: Academic, 1988.
[42] J. Serra and L. Vincent,Lecture Notes on Morphological Filtering, School of Mines, Cahiers du Centre de Morphologie Mathématique, Paris, France, vol. 8, 98 pp., 1989.
[43] P. Soille and M. Ansoult, "Automated basin delineation from DEMs using mathematical morphology,"Signal Processing, vol. 20, pp. 171-182, 1990.
[44] P. Soille, "Inversion d'images multispectrales par la morphologie mathématique," School of Mines, Paris, France, Internal Rep. CMM, Jan. 1990.
[45] S. R. Sternberg, "Grayscale morphology,"Comput. Vision, Graphics, Image Processing, vol. 35, pp. 333-355, 1986.
[46] B. J. H. Verwer, P.W. Verbeek and S.T. Dekker, "An efficient uniform cost algorithm applied to distance transforms,"IEEE Trans. Pattern Anal. Machine Intell., vol. 11, pp. 425-429, 1989.
[47] L. Vincent, "Graphs and mathematical morphology,"Signal Processing, vol. 16, no. 4, pp. 365-388, Apr. 1989.
[48] L. Vincent, "Mathematical morphology for graphs applied to image description and segmentation," inProc. Electronic Imaging West, Pasedena, CA, Apr. 1989, pp. 313-318.
[49] L. Vincent and S. Beucher, "The morphological approach to Segmentation: An introduction," School of Mines, Paris, France, Internal Rep. CMM, July 1989.
[50] L. Vincent, "Algorithmes morphologiquesàbase de files d'attente et de lacets. Extension aux graphes," Ph.D. dissertation, School of Mines, Paris, France, May 1990.
[51] L. Vincent, "Morphological transformations of binary images with arbitrary structuring elements,"Signal Processing, vol. 22, no. 1, Jan. 1991.
[52] L. J. Van Vilet and B.J.H. Verwer, "A contour processing method for fast binary neighborhood operations,"Pattern Recog. Lett., vol. 7, pp. 27-36, Jan. 1988.

Index Terms:
magnetic resonance imagery; computerised picture processing; watersheds; digital gray-scale images; pseudo C language; picture segmentation; digital elevation models; computerised picture processing
L. Vincent, P. Soille, "Watersheds in Digital Spaces: An Efficient Algorithm Based on Immersion Simulations," IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 13, no. 6, pp. 583-598, June 1991, doi:10.1109/34.87344
Usage of this product signifies your acceptance of the Terms of Use.