d-Dimensional Reverse Euclidean Distance Transformation and Euclidean Medial Axis Extraction in Optimal Time

1. Blum, H.: A transformation for extracting descriptors of shape. In: Models for the Perception of Speech and Visual Forms, pp. 362–380. MIT Press, Cambridge (1967)

   Google Scholar 

2. Borgefors, G.: Distance transformations in digital images. Computer Vision, Graphics, and Image Processing 34(3), 344–371 (1986)

   Article  Google Scholar 

3. Borgefors, G., Nyström, I.: Efficient shape representation by minimizing the set of centers of maximal discs/spheres. Pattern Recognition Letters 18, 465–472 (1997)

   Article  Google Scholar 

4. Coeurjolly, D.: Algorithmique et géométrie discrète pour la caractérisation des courbes et des surfaces. PhD thesis, Université Lumière Lyon 2, Bron, Laboratoire ERIC (December 2002)

   Google Scholar 

5. Danielsson, P.E.: Euclidean distance mapping. CGIP 14, 227–248 (1980)

   Google Scholar 

6. Sanniti di Baja, G.: Well-shaped, stable, and reversible skeletons from the (3,4)-distance transform. J. Visual Communication and Image Representation 5, 107–115 (1994)

   Article  Google Scholar 

7. Hirata, T.: A unified linear-time algorithm for computing distance maps. Information Processing Letters 58(3), 129–133 (1996)

   Article  MATH  MathSciNet  Google Scholar 

8. Maurer Jr., C.R., Raghavan, V., Qi, R.: A linear time algorithm for computing the euclidean distance transform in arbitrary dimensions. In: Information Processing in Medical Imaging, pp. 358–364 (2001)

   Google Scholar 

9. Meijster, A., Roerdink, J.B.T.M., Hesselink, W.H.: A general algorithm for computing distance transforms in linear time. In: Mathematical Morphology and its Applications to Image and Signal Processing, pp. 331–340. Kluwer, Dordrecht (2000)

   Google Scholar 

10. Montanari, U.: Continuous skeletons from digitized images. Journal of the Association for Computing Machinery 16(4), 534–549 (1969)

    MATH  MathSciNet  Google Scholar 

11. Nilsson, F., Danielsson, P.-E.: Finding the minimal set of maximum disks for binary objects. Graphical models and image processing 59(1), 55–60 (1997)

    Article  Google Scholar 

12. Ragnemalm, I.: Contour processing distance transforms, pp. 204–211. World Scientific, Singapore (1990)

    Google Scholar 

13. Ragnemalm, I.: The Euclidean Distance Transform. PhD thesis, Linköping University, Linköping, Sweden (1993)

    Google Scholar 

14. Remy, E., Thiel, E.: Optimizing 3D chamfer masks with norm constraints. In: Int. Workshop on Combinatorial Image Analysis, pp. 39–56, Caen (July 2000)

    Google Scholar 

15. Rosenfeld, A., Pfaltz, J.L.: Sequential operations in digital picture processing. Journal of the ACM 13(4), 471–494 (1966)

    Article  MATH  Google Scholar 

16. Rosenfeld, A., Pfalz, J.L.: Distance functions on digital pictures. Pattern Recognition 1, 33–61 (1968)

    Article  MathSciNet  Google Scholar 

17. Saito, T., Toriwaki, J.I.: New algorithms for Euclidean distance transformations of an n-dimensional digitized picture with applications. Pattern Recognition 27, 1551–1565 (1994)

    Article  Google Scholar 

18. Saito, T., Toriwaki, J.-I.: Reverse distance transformation and skeletons based upon the euclidean metric for n-dimensionnal digital pictures. IECE Trans. Inf. & Syst. E77-D(9), 1005–1016 (1994)

    Google Scholar 

19. Thiel, E.: Géométrie des distances de chanfrein. Habilitation à Diriger des Recherches, Université de la Méditerranée, Aix-Marseille 2 (Décember 2001)

    Google Scholar 

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