A consistency result for the normalized eight-point algorithm

Abstract

A recently proposed argument to explain the improved performance of the eight-point algorithm that results from using normalized data [IEEE Trans. Pattern Anal. Mach. Intell., 25(9):1172-1177, 2003] relies upon adoption of a certain model for statistical data distribution. Under this model, the cost function that underlies the algorithm operating on the normalized data is statistically more advantageous than the cost function that underpins the algorithm using unnormalized data. Here we extend this explanation by introducing a more refined, structured model for data distribution. Under the extended model, the normalized eight-point algorithm turns out to be approximately consistent in a statistical sense. The proposed extension provides a link between the existing statistical rationalization of the normalized eight-point algorithm and the approach of M¨uhlich and Mester for enhancing total least squares estimation methods via equilibration. Our contribution forms part of a wider effort to rationalize and interrelate foundational methods in vision parameter estimation.