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X. Wang, G. Bertrand, "Some Sequential Algorithms for a Generalized Distance Transformation Based on Minkowski Operations," IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 14, no. 11, pp. 11141121, November, 1992.  
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@article{ 10.1109/34.166628, author = {X. Wang and G. Bertrand}, title = {Some Sequential Algorithms for a Generalized Distance Transformation Based on Minkowski Operations}, journal ={IEEE Transactions on Pattern Analysis and Machine Intelligence}, volume = {14}, number = {11}, issn = {01628828}, year = {1992}, pages = {11141121}, doi = {http://doi.ieeecomputersociety.org/10.1109/34.166628}, publisher = {IEEE Computer Society}, address = {Los Alamitos, CA, USA}, }  
RefWorks Procite/RefMan/Endnote  x  
TY  JOUR JO  IEEE Transactions on Pattern Analysis and Machine Intelligence TI  Some Sequential Algorithms for a Generalized Distance Transformation Based on Minkowski Operations IS  11 SN  01628828 SP1114 EP1121 EPD  11141121 A1  X. Wang, A1  G. Bertrand, PY  1992 KW  mathematical morphology; image processing; sequential algorithms; generalized distance transformation; Minkowski operations; binary images; medial axis transformation; pointtopoint distance; image processing; mathematical morphology; transforms VL  14 JA  IEEE Transactions on Pattern Analysis and Machine Intelligence ER   
A generalized distance transformation (GDT) of binary images and the related medial axis transformation (MAT) are discussed. These transformations are defined in a discrete space of arbitrary dimension and arbitrary grids. The GDT is based on successive morphological operations using alternatively N arbitrary structuring elements: N is called the period of the GDT. The GDT differs from the classical distance transformations based on a pointtopoint distance. However, the wellknown chessboard, cityblock, and hexagonal distance transformations are special cases of the oneperiod GDT, whereas the octagonal distance transformation is a special case of the twoperiod GDT. In this paper, both one and twoperiod GDTs are discussed. Different sequential algorithms are proposed for computing such GDTs. These algorithms need a maximum of two scannings of the image. The computation of the MAT is also discussed.
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