Multibody structure from motion (SfM) is the extension of classical SfM to dynamic scenes with multiple rigidly moving objects. Recent research has unveiled some of the mathematical foundations of the problem, but a practical algorithm which can handle realistic sequences is still missing. In this paper, we discuss the requirements for such an algorithm, highlight theoretical issues and practical problems, and describe how a static structure-from-motion framework needs to be extended to handle real dynamic scenes. Theoretical issues include different situations in which the number of independently moving scene objects changes: Moving objects can enter or leave the field of view, merge into the static background (e.g., when a car is parked), or split off from the background and start moving independently. Practical issues arise due to small freely moving foreground objects with few and short feature tracks. We argue that all of these difficulties need to be handled online as structure-from-motion estimation progresses, and present an exemplary solution using the framework of probabilistic model-scoring.

When trying to extract 3D scene information and camera motion from an image sequence alone, it is often necessary to cope with independently moving objects. Recent research has unveiled some of the mathematical foundations of the problem, but a general and practical algorithm, which can handle long, realistic sequences, is still missing. In this paper, we identify the necessary parts of such an algorithm, highlight both unexplored theoretical issues and practical challenges, and propose solutions. Theoretical issues include proper handling of different situations, in which the number of independent motions changes: objects can enter the scene, objects previously moving together can split and follow independent trajectories, or independently moving objects can merge into one common motion. We derive model scoring criteria to handle these changes in the number of segments. A further theoretical issue is the resolution of the relative scale ambiguity between such changes. Practical issues include robust 3D reconstruction of freely moving foreground objects, which often have few and short feature tracks. The proposed framework simultaneously tracks features, groups them into rigidly moving segments, and reconstructs all segments in 3D. Such an online approach, as opposed to batch processing techniques, which first track features, and then perform segmentation and reconstruction, is vital in order to handle small foreground objects.

Consider a monocular image sequence which contains independently moving objects and assume it is already segmented. In order to get a realistic 3D reconstruction of such a scene, we have to solve the relative scale ambiguity between the reconstructions of different moving objects. Recently, we demonstrated the usefulness of the so-called 'non-accidentalness and independence constraints' to disambiguate the mentioned unknown relative scale. However, this technique requires that the video segment which corresponds to the background is known beforehand. In this paper, we analyze the background detection problem in the vein of the aforementioned constraints and show that the background is not just another moving object but the one which results in the simplest overall scene interpretation.