Heteroscedastic Regression in Computer Vision: Problems with Bilinear Constraint
International Journal of Computer Vision - Special issue on a special section on visual surveillance
A Bayesian Method for Fitting Parametric and Nonparametric Models to Noisy Data
IEEE Transactions on Pattern Analysis and Machine Intelligence
Statistical Optimization for Geometric Computation: Theory and Practice
Statistical Optimization for Geometric Computation: Theory and Practice
Bayesian Model Estimation and Selection for Epipolar Geometry and Generic Manifold Fitting
International Journal of Computer Vision
Statistical Bias of Conic Fitting and Renormalization
IEEE Transactions on Pattern Analysis and Machine Intelligence
International Journal of Computer Vision
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In many problems of computer vision we have to estimate parameters in the presence of nuisance parameters increasing with the amount of data. It is known that unlike in the cases without nuisance parameters, maximum likelihood estimation (MLE) is not optimal in the presence of nuisance parameters. By optimal we mean that the resulting estimate is unbiased and its variance attains the theoretical lower bound in an asymptotic sense. Thus, naive application of MLE to computer vision have a potential problem. This applies to a wide range of problems from conic fitting to bundle adjustment. For this nuisance parameter problem, studies have been conducted in statistics for a long time, whereas they have been little known in computer vision community. We cast light to the methods developed in statistics for obtaining optimal estimates and explores the possibility of applying them to computer vision problems. In this paper we focus on the cases where data and nuisance parameters are linearly connected. As examples, optical flow estimation and affine structure and motion problems are considered. Through experiments, we show that the estimation accuracy is improved in several cases.