Toward a Model Based-Bayesian Theory for Estimating and Recognizing Parameterized 3-D Objects Using Two or More Images Taken from Different Positions
Abstract
new approach is introduced to estimating object surfacesin three-dimensional space from two or more images. A surfaceof interest here is modeled as a 3-D function known up to the values ofa 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 estimationis treated as the general problem of maximum likelihood parameter estimationof the a priori unknown primitive surface parameters basedon two or more functionally related data sets. In our case, these datasets constitute two or more images taken by cameras at different locationsand orientations. A simple geometric explanation is given forthe estimation algorithm. Although various techniques can be used toimplement this nonlinear estimation, we discuss the use of gradientdescent. Experiments are run and discussed. Our approach includesthe commonly used stereo approaches as special cases. The Cramer-Rao lower bounds are derived for the achievable error covariance matricesfor estimators for the a priori unknown parameters. No surfacereconstruction can be more accurate than these bounds. The dependenceof the bounds on object surface pattern and on the camera andobject geometry is shown explicitly. An interesting result arising in thiswork is that maximum-likelihood estimation of 3-D surfaces also requiresmaximum likelihood estimation of the pattern on the object surface.Object surface segmentation into primitive object surfaces, andprimitive object-type recognition are readily implemented using theprobabilistic framework developed in this paper. The attractiveness ofour probabilistic formulation is that it now permits a fully Bayesianapproach to 3-D surface estimation based on images taken by camerasin two or more positions.
Document Details
- Document Type
- Technical Report
- Publication Date
- Oct 01, 1989
- Accession Number
- AD1015516
Entities
People
- Bruno Cernuschi-frias
- David B. Cooper
- Peter N. Belhumeur
- Yi-ping Hung
Organizations
- Brown University