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F.S. Cohen, JinYinn Wang, "Part I: Modeling Image Curves Using Invariant 3D Object Curve Models/spl minus/a Path to 3D Recognition and Shape Estimation from Image Contours," IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 16, no. 1, pp. 112, January, 1994.  
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@article{ 10.1109/34.273721, author = {F.S. Cohen and JinYinn Wang}, title = {Part I: Modeling Image Curves Using Invariant 3D Object Curve Models/spl minus/a Path to 3D Recognition and Shape Estimation from Image Contours}, journal ={IEEE Transactions on Pattern Analysis and Machine Intelligence}, volume = {16}, number = {1}, issn = {01628828}, year = {1994}, pages = {112}, doi = {http://doi.ieeecomputersociety.org/10.1109/34.273721}, publisher = {IEEE Computer Society}, address = {Los Alamitos, CA, USA}, }  
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TY  JOUR JO  IEEE Transactions on Pattern Analysis and Machine Intelligence TI  Part I: Modeling Image Curves Using Invariant 3D Object Curve Models/spl minus/a Path to 3D Recognition and Shape Estimation from Image Contours IS  1 SN  01628828 SP1 EP12 EPD  112 A1  F.S. Cohen, A1  JinYinn Wang, PY  1994 KW  splines (mathematics); stereo image processing; Bayes methods; image recognition; image curves; invariant 3D object curve models; 3D recognition; shape estimation; image contours; affine transformation; binocular stereo imaging system; Bsplines; control points; minimum meansquare error estimation technique; Bayesian selection rule; matching algorithm; prototype curves; sample curve VL  16 JA  IEEE Transactions on Pattern Analysis and Machine Intelligence ER   
This paper and its companion are concerned with the problems of 3D object recognition and shape estimation from image curves using a 3D object curve model that is invariant to affine transformation onto the image space, and a binocular stereo imaging system. The objects of interest here are the ones that have markings (e.g., characters, letters, special drawings and symbols, etc.) on their surfaces. The 3D curves on the object are modeled as Bsplines, which are characterized by a set of parameters (the control points) from which the 3D curve can be totally generated. The Bsplines are invariant under affine transformations. That means that the affine projected object curve onto the image space is a Bspline whose control points are related to the object control points through the affine transformation. Part I deals with issues relating to the curve modeling process. In particular, the authors address the problems of estimating the control points from the data curve, and of deciding on the "best" order Bspline and the "best" number of control points to be used to model the image or object curve(s). A minimum meansquare error (mmse) estimation technique which is invariant to affine transformations is presented as a noniterative, simple, and fast approach for control point estimation. The "best" Bspline is decided upon using a Bayesian selection rule. Finally, we present a matching algorithm that allocates a sample curve to one of p prototype curves when the sample curve is an a priori unknown affine transformation of one of the prototype curves stored in the data base. The approach is tried on a variety of images of real objects.
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