Finding the Minimum-Cost Path Without Cutting Corners

  • R. Joop van Heekeren
  • Frank G. A. Faas
  • Lucas J. van Vliet
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4522)


Applying a minimum-cost path algorithm to find the path through the bottom of a curvilinear valley yields a biased path through the inside of a corner. DNA molecules, blood vessels, and neurite tracks are examples of string-like (network) structures, whose minimum-cost path is cutting through corners and is less flexible than the underlying centerline. Hence, the path is too short and its shape too stiff, which hampers quantitative analysis. We developed a method which solves this problem and results in a path whose distance to the true centerline is more than an order of magnitude smaller in areas of high curvature. We first compute an initial path. The principle behind our iterative algorithm is to deform the image space, using the current path in such a way that curved string-like objects are straightened before calculating a new path. A damping term in the deformation is needed to guarantee convergence of the method.


Persistence Length Eikonal Equation High Contrast Image Pattern Recognition Letter Fast March 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


  1. 1.
    Adalsteinsson, D., Sethian, J.A.: A fast level set method for propagating interfaces. Journal of Computational Physics 118(2), 269–277 (1995)zbMATHCrossRefMathSciNetGoogle Scholar
  2. 2.
    Born, M., Wolf, E.: Principles of Optics, 6th edn. Pergamon Press, Oxford (1980)Google Scholar
  3. 3.
    Danielsson, P.-E., Lin, Q.: A modified fast marching method. In: Bigun, J., Gustavsson, T. (eds.) SCIA 2003. LNCS, vol. 2749, pp. 1154–1161. Springer, Heidelberg (2003)CrossRefGoogle Scholar
  4. 4.
    Fouard, C., Gedda, M.: An Objective Comparison Between Gray Weighted Distance Transforms and Weighted Distance Transforms on Curved Spaces. In: Kuba, A., Nyúl, L.G., Palágyi, K. (eds.) DGCI 2006. LNCS, vol. 4245, pp. 259–270. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  5. 5.
    Meijering, E., Jacob, M., Sarria, J.-C.F., Steiner, P., Hirling, H., Unser, M.: Design and validation of a tool for neurite tracing and analysis in fluorescence microscopy images. Cytometry 58A(2), 167–176 (2004)CrossRefGoogle Scholar
  6. 6.
    Saha, P.K., Wehrli, F.W., Gomberg, B.R.: Fuzzy distance transform: Theory, algorithms, and applications. Computer Vision and Image Understanding 86(3), 171–190 (2002)zbMATHCrossRefGoogle Scholar
  7. 7.
    Toivanen, P.J.: New geodesic distance transforms for gray-scale images. Pattern Recognition Letters 17(5), 437–450 (1996)CrossRefGoogle Scholar
  8. 8.
    Tsitsiklis, J.N.: Efficient algorithms for globally optimal trajectories. IEEE Transactions on Automatic Control 40(9), 1528–1538 (1995)zbMATHCrossRefMathSciNetGoogle Scholar
  9. 9.
    Verbeek, P.W., Verwer, B.J.H.: Shading from shape, the eikonal equation solved by grey-weighted distance transform. Pattern Recognition Letters 11, 681–690 (1990)zbMATHCrossRefGoogle Scholar

Copyright information

© Springer Berlin Heidelberg 2007

Authors and Affiliations

  • R. Joop van Heekeren
    • 1
  • Frank G. A. Faas
    • 1
  • Lucas J. van Vliet
    • 1
  1. 1.Quantitative Imaging Group, Delft University of TechnologyThe Netherlands

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