Publication 2002 Issue No. 12 - December Abstract - Three-Dimensional Topology Preserving Reduction on the 4-Subfields
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Three-Dimensional Topology Preserving Reduction on the 4-Subfields
December 2002 (vol. 24 no. 12)
pp. 1594-1605
 ASCII Text x Cherng-Min Ma, Shu-Yen Wan, Jiann-Der Lee, "Three-Dimensional Topology Preserving Reduction on the 4-Subfields," IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 24, no. 12, pp. 1594-1605, December, 2002.
 BibTex x @article{ 10.1109/TPAMI.2002.1114851,author = {Cherng-Min Ma and Shu-Yen Wan and Jiann-Der Lee},title = {Three-Dimensional Topology Preserving Reduction on the 4-Subfields},journal ={IEEE Transactions on Pattern Analysis and Machine Intelligence},volume = {24},number = {12},issn = {0162-8828},year = {2002},pages = {1594-1605},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 - JOURJO - IEEE Transactions on Pattern Analysis and Machine IntelligenceTI - Three-Dimensional Topology Preserving Reduction on the 4-SubfieldsIS - 12SN - 0162-8828SP1594EP1605EPD - 1594-1605A1 - Cherng-Min Ma, A1 - Shu-Yen Wan, A1 - Jiann-Der Lee, PY - 2002KW - Topology preservationKW - connectivity preservationKW - 3D thinning algorithmKW - thinningKW - 4-subfield thinning.VL - 24JA - IEEE Transactions on Pattern Analysis and Machine IntelligenceER -

Abstract—This paper discusses thinning on 3D binary images with the 4-subfield approach. Although a thinning algorithm concerns binary images, the algorithm itself can be represented as a set of three-color reduction templates. A thinning algorithm is topology preserving if the set of all three-color templates is topology preserving. Sufficient and necessary conditions of time complexity {\rm{O}}(n) were proposed for verifying the topological soundness of a 3D 4-subfield thinning algorithm of n three-color templates. Theories and techniques for computerizing such conditions were discussed. Two 4-subfield 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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Index Terms:
Topology preservation, connectivity preservation, 3D thinning algorithm, thinning, 4-subfield thinning.
Citation:
Cherng-Min Ma, Shu-Yen Wan, Jiann-Der Lee, "Three-Dimensional Topology Preserving Reduction on the 4-Subfields," IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 24, no. 12, pp. 1594-1605, Dec. 2002, doi:10.1109/TPAMI.2002.1114851
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