Euclidean Structure Recovery from Motion in Perspective Image Sequences via Hankel Rank Minimization

In this paper we consider the problem of recovering 3D Euclidean structure from multi-frame point correspondence data in image sequences under perspective projection. Existing approaches rely either only on geometrical constraints reflecting the rigid nature of the object, or exploit temporal information by recasting the problem into a nonlinear filtering form. In contrast, here we introduce a new constraint that implicitly exploits the temporal ordering of the frames, leading to a provably correct algorithm to find Euclidean structure (up to a single scaling factor) without the need to alternate between projective depth and motion estimation, estimate the Fundamental matrices or assume a camera motion model. Finally, the proposed approach does not require an accurate calibration of the camera. The accuracy of the algorithm is illustrated using several examples involving both synthetic and real data.