Toward a Model-Based Bayesian Theory for Estimating and Recognizing Parameterized 3-D Objects Using Two or More Images Taken from Different Positions.
Journal
IEEE Trans. Pattern Anal. Mach. Intell.
Journal Volume
11
Journal Issue
10
Pages
1028-1052
Date Issued
1989
Author(s)
Abstract
A new approach is introduced to estimating object surfaces in Threedimensional space from two or more images. A surface of interest here is modeled as a 3-D function known up to the values of a few parameters. Although the approach will work with any parameterization, we model objects as patches of spheres, cylinders, planes, and general quadrics-primitive objects. Primitive surface estimation is treated as the general problem of maximum likelihood parameter estimation of the a priori unknown primitive surface parameters based on two or more functionally related data sets. In our case, these data sets constitute two or more images taken by cameras at different locations and orientations. A simple geometric explanation is given for the estimation algorithm. Although various techniques can be used to implement this nonlinear estimation, we discuss the use of gradient descent. Experiments are run and discussed. Our approach includes the commonly used stereo approaches as special cases. The Cramer-Rao lower bounds are derived for the achievable error covariance matrices for estimators for the a priori unknown parameters. No surface reconstruction can be more accurate than these bounds. The dependence of the bounds on object surface pattern and on the camera and object geometry is shown explicitly. An interesting result arising in this work is that maximum-likelihood estimation of 3-D surfaces also requires maximum likelihood estimation of the pattern on the object surface. Object surface segmentation into primitive object surfaces, and primitive object-type recognition are readily implemented using the probabilistic framework developed in this paper. The attractiveness of our probabilistic formulation is that it now permits a fully Bayesian approach to 3-D surface estimation based on images taken by cameras in two or more positions. For example, recent follow-on papers include estimation of parameterized surfaces based on a large number of images taken by a moving camera [11], [27], estimation of stochastic surfaces based on images taken by cameras in two or more positions [3], and estimation of object surfaces given contour models for the patterns on the surface [28]. © 1989 IEEE
Type
journal article