Analysis of the Watershed Algorithms Based on the Breadth-First and Depth-First Exploring Methods

In this paper, fifteen watershed algorithms are reviewed. For clarity, first we expose two graph exploring methods modified to be guidelines for understanding the approaches taken by these algorithms: the breadth-first watershed and the depth-first watershed. Both paradigms rely on the visiting order applied by the algorithms. The breadth-first is more recognizable as a seed region growing or marker expansion process, grouping both methods based on flooding and hierarchical queue. The depth-first groups the algorithms based on the drop of water simulation, forming a simple path until a regional minimum is found. We analyze and classify fifteen algorithms, and two of them were better characterized. Along with this, some useful information (i.e. use of markers and line over pixel) is organized, in order to facilitate the choice of an algorithm.

[1]  Luc Vincent,et al.  Watersheds in Digital Spaces: An Efficient Algorithm Based on Immersion Simulations , 1991, IEEE Trans. Pattern Anal. Mach. Intell..

[2]  Jing-Yu Yang,et al.  A fast watershed algorithm based on chain code and its application in image segmentation , 2005, Pattern Recognit. Lett..

[3]  Serge Beucher,et al.  Use of watersheds in contour detection , 1979 .

[4]  Michel Couprie,et al.  The tie-zone watershed: definition, algorithm and applications , 2005, IEEE International Conference on Image Processing 2005.

[5]  S. Beucher,et al.  Morphological segmentation , 1990, J. Vis. Commun. Image Represent..

[6]  Pedro Gómez Vilda,et al.  An improved watershed algorithm based on efficient computation of shortest paths , 2007, Pattern Recognit..

[7]  Gilles Bertrand,et al.  Watershed Cuts: Thinnings, Shortest Path Forests, and Topological Watersheds , 2010, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[8]  Alexandre X. Falcão,et al.  The Ordered Queue and the Optimality of the Watershed Approaches , 2000, ISMM.

[9]  Alina N. Moga,et al.  An efficient watershed algorithm based on connected components , 2000, Pattern Recognit..

[10]  Gilles Bertrand,et al.  Watershed Cuts: Minimum Spanning Forests and the Drop of Water Principle , 2009, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[11]  N. Kalouptsidis,et al.  A DISJOINT SET ALGORITHM FOR THE WATERSHED TRANSFORM , 2008 .

[12]  F. Harary,et al.  The theory of graphs and its applications , 1963 .

[13]  Edward R. Dougherty,et al.  Mathematical Morphology in Image Processing , 1992 .

[14]  Thomas H. Cormen,et al.  Introduction to algorithms [2nd ed.] , 2001 .

[15]  William A. Barrett,et al.  Toboggan-based intelligent scissors with a four-parameter edge model , 1999, Proceedings. 1999 IEEE Computer Society Conference on Computer Vision and Pattern Recognition (Cat. No PR00149).

[16]  Edsger W. Dijkstra,et al.  A note on two problems in connexion with graphs , 1959, Numerische Mathematik.

[17]  Alexandre X. Falcão,et al.  IFT-Watershed from gray-scale marker , 2002, Proceedings. XV Brazilian Symposium on Computer Graphics and Image Processing.

[18]  Yi-Ping Hung,et al.  Comparison between immersion-based and toboggan-based watershed image segmentation , 2006, IEEE Transactions on Image Processing.

[19]  Jos B. T. M. Roerdink,et al.  The Watershed Transform: Definitions, Algorithms and Parallelization Strategies , 2000, Fundam. Informaticae.

[20]  Fernand Meyer,et al.  Minimum Spanning Forests for Morphological Segmentation , 1994, ISMM.

[21]  Jorge Stolfi,et al.  The image foresting transform: theory, algorithms, and applications , 2004 .

[22]  Roberto de Alencar Lotufo,et al.  Uniquely-Determined Thinning of the Tie-Zone Watershed Based on Label Frequency , 2007, Journal of Mathematical Imaging and Vision.

[23]  Alina N. Moga,et al.  A connected component approach to the watershed segmentation , 1998 .

[24]  Roberto de Alencar Lotufo,et al.  Watershed by image foresting transform, tie-zone, and theoretical relationships with other watershed definitions , 2007, ISMM.

[25]  Hans Burkhardt,et al.  A Parallel Watershed Algorithm , 1996 .

[26]  Fernand Meyer,et al.  Topographic distance and watershed lines , 1994, Signal Process..