Digital distance transforms in 2D, 3D, and 4D

Handbook of Pattern Recognition and Computer Vision, 3rd Edition

Volumn , Issue , 2005, Pages 157-176

  Borgefors, Gunilla ^a  

^a SWEDISH UNIVERSITY OF AGRICULTURAL SCIENCES   (Sweden)

Author keywords

[No Author keywords available]

Indexed keywords

IMAGE PROCESSING; MEDICAL APPLICATIONS;

CITY BLOCK; COMPLEX ALGORITHMS; COMPUTATION ALGORITHM; DIGITISATION; DISTANCE TRANSFORMS; EUCLIDEAN DISTANCE TRANSFORMS; IMAGE PROCESSING AND ANALYSIS; WEIGHTED DISTANCE;

IMAGE ANALYSIS;

EID: 63449124191     PISSN: None     EISSN: None     Source Type: Book    
DOI: 10.1142/9789812775320_0009     Document Type: Chapter

References (29)

1. Arcelli C. and Sanniti di Baja, G. (1988). Finding Local Maxima in a Pseudo- Euclidean Distance Transform, Computer Vision, Graphics and Image Processing 43, pp. 361-367.
2. Borgefors, G. (1984). Distance Transformations in Arbitrary Dimensions, Computer Vision, Graphics and Image Processing 27, pp. 321-345.
3. Borgefors, G. (1986). Distance Transformations in Digital Images, Computer Vision, Graphics and Image Processing 34, pp. 344-371.
4. Borgefors, G. (1991). Another Comment on ‘A Note on "Distance Transformations in Digital Images’", Computer Vision, Graphics and Image Processing 54, pp. 301-306.
5. Borgefors, G. (1993). Centres of Maximal Discs in the 5-7-11 Distance Transform, In: Proc. 8th Scandinavian Conference on Image Analysis, Troms0, Norway, pp. 105-111.
6. Borgefors, G. (1996). On Digital Distance Transforms in Three Dimensions, Computer Vision and Image Understanding 64 pp. 368-376.
7. Borgefors, G. (2003). Weighted Digital Distance Transforms in Four Dimensions. Discrete Applied Mathematics 125, pp. 161-176.
8. Borgefors, G. Hartmann, T., and Tanimoto, S.L. (1990). Parallel Distance Transforms on Pyramid Machines: Theory and Implementation, Signal Processing 21, pp. 61-86.
9. Coeurjolly, D. (2003).
10. Cuisenaire O. and Macq B. (1999). Fast Euclidean Distance Transformations by Propagation Using Multiple Neighbourhoods, Computer Vision and Image Understanding 76, pp. 163-172.
11. Danielsson, P.E. (1980). Euclidean Distance Mapping, Computer Vision, Graphics and Image Processing 14, pp. 227-248.
12. Das, P.P.(1992). Best Simple Octagonal Distances in Digital Geometry, Journal of Approximation Theory 68, pp. 155-174.
13. Das, P.P. and Chatterji, B.N. (1988). Knight’s Distance in Digital Geometry, Pattern Recognition Letters 7, pp. 215-226.
14. Forchhammer, S. (1989). Euclidean Distances from Chamfer Distances for Limited Distances, In: Proc. 6th Scand. Conf. on Image Analysis, Oulu, Finland, pp. 393-400.
15. Okabe N., Toriwaki J., and Fukumura, T. (1983). Paths and Distance Functions on Three-Dimensional Digitized Pictures, Pattern Recognition Letters 1, pp. 205-212.
16. Piper, J. and Granum, E. (1987). Computing Distance Transformations in Convex and Non-Convex Domains, Pattern Recognition 20, pp. 599-615.
17. Ragnemalm, I. (1993). The Euclidean Distance Transform in Abritrary Dimensions, Pattern Recognition Letters 14, pp. 883-888.
18. Remy, E. and Thiel, E. (2003). Look-Up Tables for Medial Axis on Squared Euclidean Distance Transform, In: Discrete Geometry for Computer Imagery, Eds. Nystrom, Sanniti di Baja, and Svensson, Lecture Notes in Computer Science 2886, Springer-Verlag, pp. 224-235.
19. Rosenfeld, A. and Pfaltz, J.L. (1966). Sequential Operations in Digital Picture Processing, Journal of the ACM 13, pp. 471- 494.
20. Rosenfeld, A. and Pfaltz, J.L. (1968). Distance Functions on Digital Pictures, Pattern Recognition 1, pp. 33-61.
21. Rosin, P.R. and West, G.A.W. (1995). Salience Distance Transforms, Graphical Models and Image Processing 57, pp. 483-521.
22. Sethian, J.A. (1999). Level Set Methods and Fast Marching Methods, Cambridge University Press, Cambridge, U.K.
23. Sintorn, I.M. and Borgefors, G. (2001). Weighted Distance Transforms in Rectangular Grids, In: Proc. 11th International Conference on Image Analysis and Processing, Palermo, Italy, Eds. Ardizzone and Di Gesu, pp. 322-326.
24. Sintorn, I.M. and Borgefors, G. (2004). Weighted Distance Transforms for Volume Images Digitized in Elongated Voxel Grids, Pattern Recognition Letters 25, pp. 571-580.
25. Svensson, S. and Borgefors, G. (2002). Digital Distance Transforms in 3D Images Using Information From Neighbourhoods up to 5 x 5 x 5, Computer Vision and Image Understanding 88 pp. 24-53.
26. Toivanen, P. (1996). New Geodesic Distance Transforms for Grey-Scale Images, Pattern Recognition Lettersl7, pp. 437-450.
27. Vossepoel, A.M. (1988). A Note on: ‘Distance Transformations in Digital Images’, Computer Vision, Graphics and Image Processing 43, pp. 88-97.
28. Yamashita, M. and Ibaraki, T. (1986). Distance Denned by Neighborhood Sequences, Pattern Recognition 19, pp. 237-246.
29. Ye, Q.Z. (1988). The Signed Euclidean Distance Transform and Its Applications, In: Proc. 9th International Conference on Pattern Recognition, Rome, Italy, pp. 495-499.