Advertisement

Shortest Route on Height Map Using Gray-Level Distance Transforms

  • Leena Ikonen
  • Pekka Toivanen
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2886)

Abstract

This article presents an algorithm for finding and visualizing the shortest route between two points on a gray-level height map. The route is computed using gray-level distance transforms, which are variations of the Distance Transform on Curved Space (DTOCS). The basic Route DTOCS uses the chessboard kernel for calculating the distances between neighboring pixels, but variations, which take into account the larger distance between diagonal pixels, produce more accurate results, particularly for smooth and simple image surfaces. The route opimization algorithm is implemented using the Weighted Distance Transform on Curved Space (WDTOCS), which computes the piecewise Euclidean distance along the image surface, and the results are compared to the original Route DTOCS. The implementation of the algorithm is very simple, regardless of which distance definition is used.

References

  1. 1.
    Borgefors, G.: Distance Transformations in Digital Images. Computer vision, Graphics, and Image Processing 34, 344–371 (1986)CrossRefGoogle Scholar
  2. 2.
    Ikonen, L., Toivanen, P., Tuominen, J.: Shortest Route on Gray-Level Map using Distance Transform on Curved Space. In: Proc. of Scandinavian Conference on Image Analysis, pp. 305–310 (2003)Google Scholar
  3. 3.
    Kimmel, R., Amir, A., Bruckstein, A.: Finding Shortest Paths on Surfaces Using Level Sets Propagation. IEEE Transactions on Pattern Analysis and Machine Intelligence 17(6), 635–640 (1995)CrossRefGoogle Scholar
  4. 4.
    Kimmel, R., Kiryati, N.: Finding Shortest Paths on Surfaces by Fast Global Approximation and Precise Local Refinement. International Journal of Pattern Recognition and Artificial Intelligence 10, 643–656 (1996)CrossRefGoogle Scholar
  5. 5.
    Lin, P., Chang, S.: A Shortest Path Algorithm for a Nonrotating Object Among Obstacles of Arbitrary Shapes. IEEE Transactions on Systems, Man, and Cybernetics 23(3), 825–833 (1993)CrossRefMathSciNetGoogle Scholar
  6. 6.
    Piper, J., Granum, E.: Computing Distance Transformations in Convex and Non-Convex Domains. Pattern Recognition 20(6), 599–615 (1987)CrossRefGoogle Scholar
  7. 7.
    Rosenfeld, A., Pfaltz, J.L.: Sequential Operations in Digital Picture Processing. Journal of the Association for Computing Machinery 13(4), 471–494 (1966)zbMATHGoogle Scholar
  8. 8.
    Rosin, P., West, G.: Salience Distance Transforms. Graphical Models and Image Processing 56(6), 483–521 (1995)CrossRefGoogle Scholar
  9. 9.
    Saha, P.K., Wehrli, F.W., Gomberg, B.R.: Fuzzy Distance Transform: Theory, Algorithms and Applications. Computer Vision and Image Understanding 86, 171–190 (2002)zbMATHCrossRefGoogle Scholar
  10. 10.
    Saab, Y., VanPutte, M.: Shortest Path Planning on Topographical Maps. IEEE Transactions on Systems, Man, and Cybernetics–Part A: Systems and Humans 29(1), 139–150 (1999)CrossRefGoogle Scholar
  11. 11.
    Toivanen, P.J.: Convergence properties of the Distance Transform on Curved Space (DTOCS). In: Proc. of Finnish Signal Processing Symposium, pp. 75–79 (1995)Google Scholar
  12. 12.
    Toivanen, P.J.: Image Compression by Selecting Control Points Using Distance Function on Curved Space. Pattern Recognition Letters 14, 475–482 (1993)zbMATHCrossRefGoogle Scholar
  13. 13.
    Toivanen, P.: New geodesic distance transforms for gray-scale images. Pattern Recognition Letters 17, 437–450 (1996)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2003

Authors and Affiliations

  • Leena Ikonen
    • 1
  • Pekka Toivanen
    • 1
  1. 1.Lappeenranta University of TechnologyLappeenrantaFinland

Personalised recommendations