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This paper addresses the problem of simultaneous estimation of a vehicle's ego motion and motions of multiple moving objects in the scene–called eoru motions –through a monocular vehicle-mounted camera. Localization of multiple moving objects and estimation of their motions is crucial for autonomous vehicles. Conventional localization and mapping techniques (e.g., visual odometry and simultaneous localization and mapping) can only estimate the ego motion of the vehicle. The capability of a robot localization pipeline to deal with multiple motions has not been widely investigated in the literature. We present a theoretical framework for robust estimation of multiple relative motions in addition to the camera ego motion. First, the framework for general unconstrained motion is introduced and then it is adapted to exploit the vehicle kinematic constraints to increase efficiency. The method is based on projective factorization of the multiple-trajectory matrix . First, the ego motion is segmented and then several hypotheses are generated for the eoru motions . All the hypotheses are evaluated and the one with the smallest reprojection error is selected. The proposed framework does not need any a priori knowledge of the number of motions and is robust to noisy image measurements. The method with a constrained motion model is evaluated on a popular street-level image dataset collected in urban environments (the KITTI dataset), including several relative ego-motion and eoru-motion scenarios. A benchmark dataset ( Hopkins 155 ) is used to evaluate this method with a general motion model. The results are compared with those of the state-of-the-art methods considering a similar problem, referred to as multibody structure from motion in the computer vision community.

In this paper, we analyze and extend the recently proposed closed-form online pose-chain simultaneous localization and mapping (SLAM) algorithm. Pose-chains are a specific type of extremely sparse pose-graphs and a product of contemporary SLAM front-ends, which perform accurate visual odometry and reliable appearance-based loop detection. They are relevant for challenging robotic applications in large-scale 3-D environments for which frequent loop detection is not desired or not possible. Closed-form online pose-chain SLAM efficiently and accurately optimizes pose-chains by exploiting their Lie group structure. The convergence and optimality properties of this solution are discussed in detail and are compared against state-of-the-art iterative methods. We also provide a novel solution space, that of similarity transforms, which has not been considered earlier for the proposed algorithm. This allows for closed-form optimization of pose-chains that exhibit scale drift, which is important to monocular SLAM systems. On the basis of extensive experiments, specifically targeting 3-D pose-chains and using a total of 60 km of challenging binocular and monocular data, it is shown that the accuracy obtained by closed-form online pose-chain SLAM is comparable with that of state-of-the-art iterative methods, while the time it needs to compute its solution is orders of magnitudes lower. This novel SLAM technique thereby is relevant to a broad range of robotic applications and computational platforms.