Inverse Depth to Depth Conversion for Monocular SLAM

Recently it has been shown that an inverse depth parametrization can improve the performance of real-time monocular EKF SLAM, permitting undelayed initialization of features at all depths. However, the inverse depth parametrization requires the storage of 6 parameters in the state vector for each map point. This implies a noticeable computing overhead when compared with the standard 3 parameter XYZ Euclidean encoding of a 3D point, since the computational complexity of the EKF scales poorly with state vector size. In this work we propose to restrict the inverse depth parametrization only to cases where the standard Euclidean encoding implies a departure from linearity in the measurement equations. Every new map feature is still initialized using the 6 parameter inverse depth method. However, as the estimation evolves, if according to a linearity index the alternative XYZ coding can be considered linear, we show that feature parametrization can be transformed from inverse depth to XYZ for increased computational efficiency with little reduction in accuracy. We present a theoretical development of the necessary linearity indices, along with simulations to analyze the influence of the conversion threshold. Experiments performed with with a 30 frames per second real-time system are reported. An analysis of the increase in the map size that can be successfully managed is included.