A Robust Nonparametric Estimation Framework for Implicit Image Models

Robust model fitting is important for computer vision tasks due to the occurrence of multiple model instances, and, unknown nature of noise. The linear errors-in-variables (EIV) model is frequently used in computer vision for model fitting tasks. This paper presents a novel formalism to solve the problem of robust model fitting using the linear EIV framework. We use Parzen windows to estimate the noise density and use a maximum likelihood approach for robust estimation of model parameters. Robustness of the algorithm results from the fact that density estimation helps us admit an a priori unknown multimodal density function and parameter estimation reduces to estimation of the density modes. We also propose a provably convergent iterative algorithm for this task. The algorithm increases the likelihood function at each iteration by solving a generalized eigenproblem. The performance of the proposed algorithm is empirically compared with Least Trimmed Squares(LTS) — a state-of-the-art robust estimation technique, and Total Least Squares(TLS) — the optimal estimator for additive white Gaussian noise. Results for model fitting on real range data are also provided.