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G. Taubin, "Estimation of Planar Curves, Surfaces, and Nonplanar Space Curves Defined by Implicit Equations with Applications to Edge and Range Image Segmentation," IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 13, no. 11, pp. 11151138, November, 1991.  
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@article{ 10.1109/34.103273, author = {G. Taubin}, title = {Estimation of Planar Curves, Surfaces, and Nonplanar Space Curves Defined by Implicit Equations with Applications to Edge and Range Image Segmentation}, journal ={IEEE Transactions on Pattern Analysis and Machine Intelligence}, volume = {13}, number = {11}, issn = {01628828}, year = {1991}, pages = {11151138}, doi = {http://doi.ieeecomputersociety.org/10.1109/34.103273}, 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  Estimation of Planar Curves, Surfaces, and Nonplanar Space Curves Defined by Implicit Equations with Applications to Edge and Range Image Segmentation IS  11 SN  01628828 SP1115 EP1138 EPD  11151138 A1  G. Taubin, PY  1991 KW  pattern recognition; algebra; optimisation; edge segmentation; planar curves; surfaces; nonplanar space curves; implicit equations; range image segmentation; parametric representation; 2D; 3D; zeros; object recognition; object position estimation; algebra; curve fitting; optimisation; pattern recognition VL  13 JA  IEEE Transactions on Pattern Analysis and Machine Intelligence ER   
The author addresses the problem of parametric representation and estimation of complex planar curves in 2D surfaces in 3D, and nonplanar space curves in 3D. Curves and surfaces can be defined either parametrically or implicitly, with the latter representation used here. A planar curve is the set of zeros of a smooth function of two variables xy, a surface is the set of zeros of a smooth function of three variables xyz, and a space curve is the intersection of two surfaces, which are the set of zeros of two linearly independent smooth functions of three variables xyz For example, the surface of a complex object in 3D can be represented as a subset of a single implicit surface, with similar results for planar and space curves. It is shown how this unified representation can be used for object recognition, object position estimation, and segmentation of objects into meaningful subobjects, that is, the detection of 'interest regions' that are more complex than high curvature regions and, hence, more useful as features for object recognition.
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