TY - JOUR

T1 - Toward a statistically optimal method for estimating geometric relations from noisy data

T2 - 2003 IEEE Computer Society Conference on Computer Vision and Pattern Recognition

AU - Okatani, Takayuki

AU - Deguchi, Koichiro

PY - 2003

Y1 - 2003

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=0043016327&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0043016327&partnerID=8YFLogxK

M3 - Conference article

AN - SCOPUS:0043016327

SN - 1063-6919

VL - 1

SP - I/432-I/439

JO - Proceedings of the IEEE Computer Society Conference on Computer Vision and Pattern Recognition

JF - Proceedings of the IEEE Computer Society Conference on Computer Vision and Pattern Recognition

Y2 - 18 June 2003 through 20 June 2003

ER -