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Improved Euclidean transform method using Voronoi diagram  

Jang Seok Hwan (한양대학교 전자전기컴퓨터 공학부 영상공학 연구실)
Park Yong Sup (씨멘스 메디칼 초음파 연구소)
Kim Whoi Yul (한양대학교 전자전기컴퓨터 공학부)
Publication Information
The Journal of Korean Institute of Communications and Information Sciences / v.29, no.12C, 2004 , pp. 1686-1691 More about this Journal
Abstract
In this paper, we present an improved method to calculate Euclidean distance transform based on Guan's method. Compared to the conventional method, Euclidean distance can be computed faster using Guan's method when the number of feature pixels is small; however, overall computational cost increases proportional to the number of feature pixels in an image. To overcome this problem, we divide feature pixels into two groups: boundary feature pixels (BFPs) and non-boundary feature pixels (NFPs). Here BFPs are defined as those in the 4-neighborhood of foreground pixels. Then, only BFPs are used to calculate the Voronoi diagram resulting in a Euclidean distance map. Experimental results indicate that the proposed method takes 40 Percent less computing time on average than Guan's method. To prove the performance of the proposed method, the computing time of Euclidean distance map by proposed method is compared with the computing time of Guan's method in 16 images that are binary and the size of 512${\times}$512.
Keywords
distance transform; Euclidean distance; Voronoi transform; Voronoi diagram; image processing;
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1 L. Ji and J. Piper, 'Fast Homotopy-Preserving Skeletons Using Mathematical Morphology,' IEEE Transactions on Pattern Analysis and Machine Intelligence, vol.14, no.6, pp.653-664, 1992   DOI   ScienceOn
2 김덕욱, 김덕수, 조동수, Kokichi Sugihara, '점집합의 보로노이 다이어그램을 이용한 원 집합이 보로노이 다이어그램의 계산. I. 위상학적측면', 한국 CAD/CAM 학회 논문집, 제 6권 제 1호, pp.24-30, 2001
3 W. Guan, and S. Ma, 'A list-processing approach to compute Voronoi diagrams and the Euclidean distance transform,' IEEE Transactions on Pattern Analysis and Machine Intelligence, vol.20, no.7, pp.757-761, 1998   DOI   ScienceOn
4 D. W. Paglieroni, 'Distance Transforms,' Computer Vision, Graphics, and Image Processing: Graphical Models and Image Processing, vol. 54, pp. 56-74, 1992
5 Y. Ge, C. R. Maurer, Jr., and J. M. Fitzpatrick, 'Surface-Based 3-D Image Registration Using the Iterative Closest Point Algorithm with a Closest Point Transform,' Medical Imaging: Image Processing, vol2710, pp.358-367, 1996
6 U. Montanari, 'A Method for Obtaining Skeletons Using A Quasi-Euclidean Distance,' Journal of ACM, vol.15, no.4, pp.600-624, 1968   DOI
7 F. Aurenhammer, 'Voronoi Diagrams - A Survey of a Fundamental Geometric Data Structure,' ACM Computing Surves, vol.23, no.3, pp.345-405, 1991   DOI
8 P. P. Das and P. P Chakrabarti, 'Distance functionsin digital geometry,' Information Sciences, vol. 42, pp. 113-136, 1987   DOI   ScienceOn
9 M. Yamashita and T. Ibaraki, 'Distances defined by neighborhood sequences,' Pattern Recognition, vol. 19, pp. 237-246, 1986   DOI   ScienceOn
10 G. Borgefors, 'Distance Transformations in Digital Images,' Computer Graphics and Image Processing, vol. 34, pp. 344-371, 1986   DOI   ScienceOn
11 C. L. Orbert, Algorithms in 2D for Detection of Object Orientation Using Distance Transformations, Ph.D. Thesis, Uppsala University, 1993
12 I. Ragnemalm, The Euclidean Distance Transform, Ph.D. Thesis, Linkoping University, Linkoping, Sweden, 1993
13 J. M. Fitzpatrick, D. L. G. Hill, and C. R. Maurer, Jr., 'Image Registration', Handbook of Medical Imaging, vol. 2, pp. 447-513, SPIP Press, 2000