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CherngMin Ma, ShuYen Wan, JiannDer Lee, "ThreeDimensional Topology Preserving Reduction on the 4Subfields," IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 24, no. 12, pp. 15941605, December, 2002.  
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@article{ 10.1109/TPAMI.2002.1114851, author = {CherngMin Ma and ShuYen Wan and JiannDer Lee}, title = {ThreeDimensional Topology Preserving Reduction on the 4Subfields}, journal ={IEEE Transactions on Pattern Analysis and Machine Intelligence}, volume = {24}, number = {12}, issn = {01628828}, year = {2002}, pages = {15941605}, doi = {http://doi.ieeecomputersociety.org/10.1109/TPAMI.2002.1114851}, 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  ThreeDimensional Topology Preserving Reduction on the 4Subfields IS  12 SN  01628828 SP1594 EP1605 EPD  15941605 A1  CherngMin Ma, A1  ShuYen Wan, A1  JiannDer Lee, PY  2002 KW  Topology preservation KW  connectivity preservation KW  3D thinning algorithm KW  thinning KW  4subfield thinning. VL  24 JA  IEEE Transactions on Pattern Analysis and Machine Intelligence ER   
Abstract—This paper discusses thinning on 3D binary images with the 4subfield approach. Although a thinning algorithm concerns binary images, the algorithm itself can be represented as a set of threecolor reduction templates. A thinning algorithm is topology preserving if the set of all threecolor templates is topology preserving. Sufficient and necessary conditions of time complexity {\rm{O}}(n) were proposed for verifying the topological soundness of a 3D 4subfield thinning algorithm of n threecolor templates. Theories and techniques for computerizing such conditions were discussed. Two 4subfield thinning algorithms on 3D images, one for generating medial curves, and the other one for generating medial surfaces, are proposed and proved to preserve topology by our sufficient and necessary conditions.
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