Homography-Based PnP Solution to Reject Outliers

Abstract

In this article, a homography-based perspective- <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${n}$ </tex-math></inline-formula> -point ( <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\text{P}{n}\text{P}$ </tex-math></inline-formula> ) solution is proposed to reject the outliers and estimate the relative pose. The point correspondences for the 3-D point coordinates and the 2-D image projections are first obtained by the image processing, and the homography is applied to derive the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\text{P}{n}\text{P}$ </tex-math></inline-formula> solution into a linear system. Then, considering the outlier correspondences, a determinant error function with an adjugate matrix is proposed to predict the image projections. These image projection predictions are compared with the measurement projections to obtain the error distributions, which are analyzed to decrease the percentage of outliers. Given the decreased percentage of outliers, an iterative null space reweighting method is applied by a homography matrix to reject all the remaining outliers. Finally, the plane norm direction constraint is coupled with the direct linear transformation (DLT) method to refine the final pose. Numerical simulations are conducted to evaluate the performance of the proposed method.