Structure from Motion on a Sphere
We describe a special case of structure from motion where the camera rotates on a sphere. The camera’s optical axis lies perpendicular to the sphere’s surface. In this case, the camera’s pose is minimally represented by three rotation parameters. From ana
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Abstract. We describe a special case of structure from motion where the camera rotates on a sphere. The camera’s optical axis lies perpendicular to the sphere’s surface. In this case, the camera’s pose is minimally represented by three rotation parameters. From analysis of the epipolar geometry we derive a novel and efficient solution for the essential matrix relating two images, requiring only three point correspondences in the minimal case. We apply this solver in a structure-from-motion pipeline that aggregates pairwise relations by rotation averaging followed by bundle adjustment with an inverse depth parameterization. Our methods enable scene modeling with an outward-facing camera and object scanning with an inward-facing camera.
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Introduction
Accurate visual 3D reconstruction is highly dependent on establishing sufficient baseline between images so that the translation between them can be reliably estimated and 3D points can be accurately triangulated. However, we have found that, in practice, it is difficult for an untrained user to capture image sequences with sufficient baseline; typically, the natural inclination is to rotate the camera instead of translating it, which causes the structure-from-motion system to fail. In this work, we instead specifically target camera rotation as the basis for structure from motion. The critical assumption here is that the camera rotates at some fixed distance from the origin, with its optical axis aligned with the ray between the origin and the camera center. We call this “spherical motion.” The camera could be pointing inward or outward. An example of an inwardfacing camera would be object scanning setups such as a turntable or spherical gantry. An example of an outward-facing camera would be a typical user capturing a panorama – the user holds the camera away from their body at a fixed distance while rotating. In either case, the global scale of the 3d reconstruction is unknown, as is always the case in pure monocular structure-from-motion. The global scale is determined by the radius of the sphere, which we arbitrarily set to unit length. However, what is interesting about this particular case of camera motion is that the relative scale between camera pairs is known, because the radius of the sphere is fixed. This is a distinct advantage over general monocular camera motion estimation, where the relative scale of the translation between camera c Springer International Publishing AG 2016 B. Leibe et al. (Eds.): ECCV 2016, Part III, LNCS 9907, pp. 53–68, 2016. DOI: 10.1007/978-3-319-46487-9 4
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J. Ventura
pairs must be determined by point triangulation and scale propagation, which is highly susceptible to scale drift. With spherical camera motion, we can directly compose relative pose estimates to determine the complete camera trajectory without needing to propagate scale. A second advantage is that the relative pose between cameras is fully determined by three rotational degrees of freedom and so can be estimated from three point correspondences as opposed to the five co
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