Extending Filter-based Structure from Motion to Large Baselines

Filter-based Structure from Motion (SfM) approaches work usually in two steps: prediction and update. Prediction is the process of determining a prior distribution of the state vector at time t+1 from the previous distribution at time t. Update is the process of adjusting the predicted distribution so it complies with the new received measurements at time t+1. A key issue in those two steps is that the prediction and update should use statistically independent data and hence the same data can not be used in both of them. In Bayesian SfM filters that maintain a state vector composed of a set of 3D features and of the camera motion, and that use the projections of the 3D features in the images as measurements for the filter, this two step process faces a serious problem in the case where the baseline between successive frames (i.e. the displacement between the camera centers) is wide. This is because the previous estimate of the state vector at time t does not allow to solely determine an estimate of the motion at t+1 accurate enough for the filtering as there would be a significant change of motion between t and t+1. In this paper, we provide a probabilistic solution to this problem by using features that are matched in the last three frames only. We show that this solution provides reliable prediction of the motion across large baselines.