Abstract
Within image analysis the distance transform has many applications. The distance transform measures the distance of each object point from the nearest boundary. For ease of computation, a commonly used approximate algorithm is the chamfer distance transform. This paper presents an efficient linear- time algorithm for calculating the true Euclidean distance-squared of each point from the nearest boundary. It works by performing a 1D distance transform on each row of the image, and then combines the results in each column. It is shown that the Euclidean distance squared transform requires fewer computations than the commonly used 5x5 chamfer transform.
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References
Rosenfeld, A., Pfaltz, J.: Sequential Operations in Digital Picture Processing. Journal of the ACM 13(4), 471–494 (1966)
Russ, J.C.: Image Processing Handbook, 2nd edn. CRC Press, Boca Raton (1995)
Huang, C.T., Mitchell, O.R.: A Euclidean Distance Transform Using Grayscale Morphology Decomposition. IEEE Transactions on Pattern Analysis and Machine Intelligence 16(4), 443–448 (1994)
Waltz, F.M., Garnaoui, H.H.: Fast Computation of the Grassfire Transform Using SKIPSM. In: SPIE Conf. on Machine Vision Applications, Architectures and System Integration III, vol. 2347, pp. 396–407 (1994)
Creutzburg, R., Takala, J.: Optimising Euclidean Distance Transform Values by Number Theoretic Methods. In: IEEE Nordic Signal Processing Symposium, pp. 199–203 (2000)
Butt, M.A., Maragos, P.: Optimal Design of Chamfer Distance Transforms. IEEE Transactions on Image Processing 7(10), 1477–1484 (1998)
Danielsson, P.E.: Euclidean Distance Mapping. Computer Graphics and Image Processing 14, 227–248 (1980)
Rangelmam, I.: The Euclidean Distance Transformation in Arbitrary Dimensions. Pattern Recognition Letters 14, 883–888 (1993)
Shih, F.Y., Wu, Y.T.: Fast Euclidean Distance Transformation in 2 Scans Using a 3x3 Neighborhood. Computer Vision and Image Understanding 93, 109–205 (2004)
Breu, H., Gil, J., Kirkatrick, D., Werman, M.: Linear Time Euclidean Distance Transform Algorithm. IEEE Transactions on Pattern Analysis and Machine Intelligence 17(5), 529–533 (1995)
Guan, W., Ma, S.: A List-Processing Approach to Compute Voronoi Diagrams and the Euclidean Distance Transform. IEEE Transactions on Pattern Analysis and Machine Intelligence 20(7), 757–761 (1998)
Cuisenaire, O., Macq, B.: Fast Euclidean Distance Transformation by Propagation using Multiple Neighbourhoods. Computer Vision and Image Understanding 76, 163–172 (1999)
Vincent, L.: Exact Euclidean distance function by chain propagations. In: IEEE Computer Society Conference on Computer Vision and Pattern Recognition, pp. 520–525 (1991)
Eggers, H.: Two Fast Euclidean Distance Transformations in Z2 Based on Sufficient Propagation. Computer Vision and Image Understanding 69, 106–116 (1998)
Saito, T., Toriwaki, J.I.: New Algorithms for Euclidean Distance Transformations of an N-dimensional Digitised Picture with Applications. Pattern Recognition 27, 1551–1565 (1994)
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© 2004 Springer-Verlag Berlin Heidelberg
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Bailey, D.G. (2004). An Efficient Euclidean Distance Transform. In: Klette, R., Žunić, J. (eds) Combinatorial Image Analysis. IWCIA 2004. Lecture Notes in Computer Science, vol 3322. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-30503-3_28
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DOI: https://doi.org/10.1007/978-3-540-30503-3_28
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-23942-0
Online ISBN: 978-3-540-30503-3
eBook Packages: Computer ScienceComputer Science (R0)