Abstract

this paper we examine methods for the detection of outliers to a least squares fit that would have been previously computationally infeasible. The fitting of linear regression models by least squares is undoubtedly the most widely used modelling procedure. A major drawback, however, is that outliers which are inevitably included in the initial fit can so distort the fitting process that the resulting fit can be arbitrary. A common practice is to search for outliers using the raw residuals. However, the use of these on their own can be misleading. Much work has been done already on detecting outliers given the case of non-orthogonal regression (reviewed in [2]), where we choose to regress against a given, dependent, variable. Unfortunately there is in this method a tacit assumption that all the error is concentrated in the dependent variable and furthermore that the dependent variable has a non-zero coefficient. In many engineering situations we cannot guarantee these conditions and we must resort to orthogonal regression, where we minimize the sum of squares of the perpendicular distances (i.e. the residuals) between each point and the fitted hyperplane. Little work has been done on outlier detection for orthogonal regression, with the exception of [15]. In this paper we outline two methodologies for outlier detection. In sections 2--5 we describe an extension of previous outlier diagnostics to the realm of orthogonal regression. The method works by assessing the amount of influence that the deletion of each point would have on the final solution. In sections 6--7 we then apply the theory we have developed to the calculation of the Fundamental matrix---a necessary first step in many structure and motion algorithms. Finally in section 8 we outline an alternative approach...

Citations