We present a novel Structure from Motion pipeline that is capable of reconstructing accurate camera poses for panorama-style video capture without prior camera intrinsic calibration. While panorama-style capture is common and convenient, previous reconstruction methods fail to obtain accurate reconstructions due to the rotation-dominant motion and small baseline between views. Our method is built on the assumption that the camera motion approximately corresponds to motion on a sphere, and we introduce three novel relative pose methods to estimate the fundamental matrix and camera distortion for spherical motion. These solvers are efficient and robust, and provide an excellent initialization for bundle adjustment. A soft prior on the camera poses is used to discourage large deviations from the spherical motion assumption when performing bundle adjustment, which allows cameras to remain properly constrained for optimization in the absence of well-triangulated 3D points. To validate the effectiveness of the proposed method we evaluate our approach on both synthetic and real-world data, and demonstrate that camera poses are accurate enough for multiview stereo.
@cite_0: An efficient algorithmic solution to the classical five-point relative pose problem is presented. The problem is to find the possible solutions for relative camera pose between two calibrated views given five corresponding points. The algorithm consists of computing the coefficients of a tenth degree polynomial in closed form and, subsequently, finding its roots. It is the first algorithm well-suited for numerical implementation that also corresponds to the inherent complexity of the problem. We investigate the numerical precision of the algorithm. We also study its performance under noise in minimal as well as overdetermined cases. The performance is compared to that of the well-known 8 and 7-point methods and a 6-point scheme. The algorithm is used in a robust hypothesize-and-test framework to estimate structure and motion in real-time with low delay. The real-time system uses solely visual input and has been demonstrated at major conferences.
@cite_34: 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.
Constraining motion to lie on a sphere was first exploited by Ventura @cite_34 to determine the essential matrix (and thus relative pose) between two images with known camera calibration for this particular motion. The assumption of spherical motion reduces the degrees of freedom in the problem from 5 for the general case @cite_0 to 3, enabling an efficient and accurate algorithm for determining relative motion. The author demonstrates the applicability of this solver in a spherical SfM system, though he notes that the accuracy for outward-facing sequences can be poor and deviations from the spherical motion assumption cause the system to fail.