Abstract
The stochastic watershed is a segmentation algorithm that estimates the importance of each boundary by repeatedly segmenting the image using a watershed with randomly placed seeds. Recently, this algorithm was further developed in two directions: (1) The exact evaluation algorithm efficiently produces the result of the stochastic watershed with an infinite number of repetitions. This algorithm computes the probability for each boundary to be found by a watershed with random seeds, making the result deterministic and much faster. (2) The robust stochastic watershed improves the usefulness of the segmentation result by avoiding false edges in large regions of uniform intensity. This algorithm simply adds noise to the input image for each repetition of the watershed with random seeds. In this paper, we combine these two algorithms into a method that produces a segmentation result comparable to the robust stochastic watershed, with a considerably reduced computation time. We propose to run the exact evaluation algorithm three times, with uniform noise added to the input image, to produce three different estimates of probabilities for the edges. We combine these three estimates with the geometric mean. In a relatively simple segmentation problem, F-measures averaged over the results on 46 images were identical to those of the robust stochastic watershed, but the computation times were an order of magnitude shorter.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Angulo, J., Jeulin, D.: Stochastic watershed segmentation. In: 8th International Symposium on Mathematical Morphology (ISMM), pp. 265–276 (2007)
Arbelaez, P., Maire, M., Fowlkes, C., Malik, J.: Contour detection and hierarchical image segmentation. IEEE Transactions on Pattern Analysis and Machine Intelligence 33(5), 898–916 (2011)
Audigier, R., Lotufo, R.: Seed-relative segmentation robustness of watershed and fuzzy connectedness approaches. In: 20th Brazilian Symposium on Computer Graphics and Image Processing 2007, pp. 61–70 (October 2007)
Bernander, K.B., Gustavsson, K., Selig, B., Sintorn, I.M., Luengo Hendriks, C.L.: Improving the stochastic watershed. Pattern Recognition Letters 34(9), 993–1000 (2013)
Beucher, S., Lantuejoul, C.: Use of Watersheds in Contour Detection. In: International Workshop on Image Processing: Real-time Edge and Motion Detection/Estimation, Rennes, France (1979)
Coelho, L.P., Shariff, A., Murphy, R.F.: Nuclear segmentation in microscope cell images: a hand-segmented dataset and comparison of algorithms. In: IEEE International Symposium on Biomedical Imaging: From Nano to Macro, ISBI 2009, pp. 518–521. IEEE (2009)
Cousty, J., Bertrand, G., Najman, L., Couprie, M.: Watershed cuts: Minimum spanning forests and the drop of water principle. IEEE Transactions on Pattern Analysis and Machine Intelligence 31(8), 1362–1374 (2009)
Cousty, J., Bertrand, G., Najman, L., Couprie, M.: Watershed cuts: Thinnings, shortest path forests, and topological watersheds. IEEE Transactions on Pattern Analysis and Machine Intelligence 32(5), 925–939 (2010)
Malmberg, F., Luengo Hendriks, C.L.: An efficient algorithm for exact evaluation of stochastic watersheds. Pattern Recognition Letters 47, 80–84 (2014), Advances in Mathematical Morphology
Malmberg, F., Selig, B., Luengo Hendriks, C.L.: Exact evaluation of stochastic watersheds: From trees to general graphs. In: Barcucci, E., Frosini, A., Rinaldi, S. (eds.) DGCI 2014. LNCS, vol. 8668, pp. 309–319. Springer, Heidelberg (2014)
Meyer, F., Beucher, S.: Morphological segmentation. Journal of Visual Communication and Image Representation 1(1), 21–46 (1990)
Meyer, F., Stawiaski, J.: A stochastic evaluation of the contour strength. In: Goesele, M., Roth, S., Kuijper, A., Schiele, B., Schindler, K. (eds.) Pattern Recognition. LNCS, vol. 6376, pp. 513–522. Springer, Heidelberg (2010)
Salembier, P., Serra, J.: Flat zones filtering, connected operators, and filters by reconstruction. Trans. Img. Proc. 4(8), 1153–1160 (1995)
Straehle, C., Koethe, U., Knott, G., Briggman, K., Denk, W., Hamprecht, F.A.: Seeded watershed cut uncertainty estimators for guided interactive segmentation. In: 2012 IEEE Conference on Computer Vision and Pattern Recognition (CVPR), pp. 765–772. IEEE (2012)
Vincent, L., Soille, P.: Watersheds in digital spaces: an efficient algorithm based on immersion simulations. IEEE Transactions on Pattern Analysis and Machine Intelligence 13(6), 583–598 (1991)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2015 Springer International Publishing Switzerland
About this paper
Cite this paper
Selig, B., Malmberg, F., Hendriks, C.L.L. (2015). Fast Evaluation of the Robust Stochastic Watershed. In: Benediktsson, J., Chanussot, J., Najman, L., Talbot, H. (eds) Mathematical Morphology and Its Applications to Signal and Image Processing. ISMM 2015. Lecture Notes in Computer Science(), vol 9082. Springer, Cham. https://doi.org/10.1007/978-3-319-18720-4_59
Download citation
DOI: https://doi.org/10.1007/978-3-319-18720-4_59
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-18719-8
Online ISBN: 978-3-319-18720-4
eBook Packages: Computer ScienceComputer Science (R0)