A pp-adic RanSaC algorithm for stereo vision using Hensel lifting

A $p$-adic variation of the Ran(dom) Sa(mple) C(onsensus) method for solving the relative pose problem in stereo vision is developped. From two 2-adically encoded images a random sample of five pairs of corresponding points is taken, and the equations for the essential matrix are solved by lifting solutions modulo 2 to the 2-adic integers. A recently devised $p$-adic hierarchical classification algorithm imitating the known LBG quantisation method classifies the solutions for all the samples after having determined the number of clusters using the known intra-inter validity of clusterings. In the successful case, a cluster ranking will determine the cluster containing a 2-adic approximation to the "true" solution of the problem.Comment: 15 pages; typos removed, abstract changed, computation error remove

Trust Your IMU: Consequences of Ignoring the IMU Drift

In this paper, we argue that modern pre-integration methods for inertial measurement units (IMUs) are accurate enough to ignore the drift for short time intervals. This allows us to consider a simplified camera model, which in turn admits further intrinsic calibration. We develop the first-ever solver to jointly solve the relative pose problem with unknown and equal focal length and radial distortion profile while utilizing the IMU data. Furthermore, we show significant speed-up compared to state-of-the-art algorithms, with small or negligible loss in accuracy for partially calibrated setups. The proposed algorithms are tested on both synthetic and real data, where the latter is focused on navigation using unmanned aerial vehicles (UAVs). We evaluate the proposed solvers on different commercially available low-cost UAVs, and demonstrate that the novel assumption on IMU drift is feasible in real-life applications. The extended intrinsic auto-calibration enables us to use distorted input images, making tedious calibration processes obsolete, compared to current state-of-the-art methods

Atomic norm denoising with applications to line spectral estimation

Motivated by recent work on atomic norms in inverse problems, we propose a new approach to line spectral estimation that provides theoretical guarantees for the mean-squared-error (MSE) performance in the presence of noise and without knowledge of the model order. We propose an abstract theory of denoising with atomic norms and specialize this theory to provide a convex optimization problem for estimating the frequencies and phases of a mixture of complex exponentials. We show that the associated convex optimization problem can be solved in polynomial time via semidefinite programming (SDP). We also show that the SDP can be approximated by an l1-regularized least-squares problem that achieves nearly the same error rate as the SDP but can scale to much larger problems. We compare both SDP and l1-based approaches with classical line spectral analysis methods and demonstrate that the SDP outperforms the l1 optimization which outperforms MUSIC, Cadzow's, and Matrix Pencil approaches in terms of MSE over a wide range of signal-to-noise ratios.Comment: 27 pages, 10 figures. A preliminary version of this work appeared in the Proceedings of the 49th Annual Allerton Conference in September 2011. Numerous numerical experiments added to this version in accordance with suggestions by anonymous reviewer