Robust estimation of rigid-body 3-D motion parameters based on point correspondences

The estimation of rigid-body 3-D motion parameters using point correspondences from a pair of images under perspective projection is, typically, very sensitive to noise. We present a novel robust method combining two approaches: (1) the SVD analysis of a linear operator resulting from the feature points and the displacement vectors and (2) a modified version of the well-known weighted least-squares method proposed by Huber in the context of robust statistics. We give a detailed rank analysis of the involved linear operator and study the effects of noise. We also propose a robust method guided by the structure of this operator, using weighted least squares and data partitioning. The method has been tested on artificial data and on real image sequences showing a remarkable robustness, even in the presence of up to 50% outliers in the data set.