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<p>A parametric modeling and statistical estimation approach is proposed and simulation data are shown for estimating 3-D object surfaces from images taken by calibrated cameras in two positions. The parameter estimation suggested is gradient descent, though other search strategies are also possible. Processing image data in blocks (windows) is central to the approach. After objects are modeled as patches of spheres, cylinders, planes and general quadrics-primitive objects, the estimation proceeds by searching in parameter space to simultaneously determine and use the appropriate pair of image regions, one from each image, and to use these for estimating a 3-D surface patch. The expression for the joint likelihood of the two images is derived and it is shown that the algorithm is a maximum-likelihood parameter estimator. A concept arising in the maximum likelihood estimation of 3-D surfaces is modeled and estimated. Cramer-Rao lower bounds are derived for the covariance matrices for the errors in estimating the a priori unknown object surface shape parameters.</p>
3D object surface recognition; picturing processing; pattern recognition; Bayesian theory; parametric modeling; statistical estimation; parameter estimation; maximum likelihood estimation; Bayes methods; parameter estimation; pattern recognition; picture processing; statistical analysis
D.B. Cooper, Y.P. Hung, P.N. Belhumeur, B. Cernuschi-Frias, "Toward a Model-Based Bayesian Theory for Estimating and Recognizing Parameterized 3-D Objects Using Two or More Images Taken from Different Positions", IEEE Transactions on Pattern Analysis & Machine Intelligence, vol. 11, no. , pp. 1028-1052, October 1989, doi:10.1109/34.42835
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