# Efficient Motion Analysis

The Research Report of CVL

Tomas Svoboda and Tomas Pajdla.

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Abstract: Ego-motion detection and analysis provides useful tool for the navigation of autonomous vehicle. The methods estimating the motion by the analysis of epipolar geometry in image pairs often combine highly robust estimation with nonlinear optimization to beat miscorrespondences as well as Gaussian noise. However, these techniques are computationally intensive and therefore not suitable for on line ego-motion estimation on a moving vehicle. We investigate shortcuts that lead to considerable reduction of computation while attaining the robustness to miscorrespondences. The main idea of this paper is to use {\em generate and test paradigm} in treating miscorrespondences. We rank the correspondences according to their the measure of their outlierness''. The measure suppresses those correspondences which are not supported by others, hence likely wrong. The subsets of the correspondences are drawn from the correspondences with lowest outlierness. For each subset, the Essential Matrix, $E$, is computed and the best subset is chosen to maximize the quality measure of $E$ under restriction that the matrix is consistent with observed data. The quality measure, $q_E$, is given by the difference of the two largest singular values of $E$. Thanks to known calibration the difference has to be zero for each true'' Essential Matrix. In the experiments, presented in this paper, pure translations were estimated using linear methods with error generally less than \mbox{3 mm} from the scene in the distance about 1.8~m using 28 correspondences with 8 artificial miscorrespondences added i.e., with almost 28\% contamination by outliers.