Scalable Near-Optimal Recursive Structure from Motion

Rao-BlackWellized particle filters have achieved a breakthrough in the scalability of filters used for Structure from Motion (SFM) and Simultaneous Localization And Mapping (SLAM). The new generations of these filters employ as proposal distribution the optimal i.e, the one taking into consideration not only the previous motion of the camera, but also the most recent measurement. However the way they sample from this importance function is not optimal since the locations of 3-d features are updated using a motion predicted only from the previous state. This results in a performance lower than the Extended Kalman Filters (EKF)s. We propose in this paper an approach that bears similarity with the Random Sample Consensus (RANSAC) paradigm and that enables us to sample more efficiently from the optimal importance function. It allows us to update the depth based on a motion updated using information from the most recent image and hence the updated samples would have a higher chance to be in regions corresponding to high posterior probability. This results in a performance equal to the performance of the EKF with much higher scalability. Also, our samples being generated and updated based on random sampling of the features, this provides an improved robustness to outliers.