article · 1996

Modeling and performance characterization of parameter estimation using perspective geometry

Xufei Liu

Cited by 2Abstract and details only

Abstract

3D parameter estimation is the key part to many computer vision tasks. This dissertation presents a general framework for deriving the optimal solution of the 3D parameters, which includes mathematical modeling, numerical optimization and covariance propagation. The mathematical modeling is based on the partial object models, the projection model and the perturbation model. A partial model of a 3D object consists of the geometric relations between the 3D features of the object. These features are projected onto 2D images. Due to the existence of noise, the observed image features are perturbed. To derive the 3D object parameters from the observations poses an optimal estimation problem, which can be transformed into a constrained optimization problem. The constraint equations represent the geometric relations in the partial model. Numerical optimization techniques can be applied to derive the optimal solution. A good initial approximation is often required for ensuring the convergence. Because observations are perturbed by noise, the derived optimal solution deviates from the true parameter values. To determine the uncertainty we can propagate the covariance matrix of the observation errors through the error propagation model, which is a locally linearized model at the optimal point. The computation of the error propagation model for optimization problem is discussed. The optimisation approach is applied to the building model estimation problem in RADIUS project, in which the 3D parameters of the buildings need to be determined from multiple aerial images. A partial model database of the buildings is constructed for modeling. The estimation is performed in two steps. At first the 3D corner points in the buildings are computed from the detected image points through multi-image triangulation. A closed form formula for the error propagation model in the triangulation is derived, through which the covariance matrices of the 3D points can be estimated. Then a constrained optimization problem is formulated by incorporating the point information and the partial models. To provide an initial solution to the numerical methods, the maximum likelihood estimators for the parameters of the planes and the lines are derived. The approximate solution is iteratively updated by using the derivatives of the objective function and the constraints. Once an optimal solution is found, we can perform error propagation to determine the covariances of the estimated parameters. To verify the optimisation framework and the algorithms, an experimental protocol based on statistical test is designed. The experiment includes data and model generation, error propagation, and hypothesis test. The experimental results validated the optimization algorithm, the error propagation model and their implementation.

Cite this paper

APA 7

Liu, X. (1996). Modeling and performance characterization of parameter estimation using perspective geometry.

MLA 9

Liu, Xufei. “Modeling and performance characterization of parameter estimation using perspective geometry.” 1996.

Chicago

Liu, Xufei. 1996. “Modeling and performance characterization of parameter estimation using perspective geometry.”

Harvard

Liu, X. (1996) ‘Modeling and performance characterization of parameter estimation using perspective geometry’.

BibTeX

@article{liu1996modeling,
  title = {{Modeling and performance characterization of parameter estimation using perspective geometry}},
  author = {Liu, Xufei},
  year = {1996}
}

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