Self-Calibrating Cameras Using Semidefinite Programming

Novel methods are proposed for self-calibrating a purerotating camera using semidefinite programming (SDP). Key to the approach is the use of the positive-definiteness requirement for the dual image of the absolute conic (DIAC). The problem is couched within a convex optimization framework and convergence to the global optimum is guaranteed. Experiments on various data sets indicate that the proposed algorithms more reliably deliver accurate and meaningful results. This work points the way to an alternative and more general approach to self-calibration using the advantageous properties of SDP. Algorithms are also discussed for cameras undergoing general motion

Calibration by correlation using metric embedding from non-metric similarities

This paper presents a new intrinsic calibration method that allows us to calibrate a generic single-view point camera just by waving it around. From the video sequence obtained while the camera undergoes random motion, we compute the pairwise time correlation of the luminance signal for a subset of the pixels. We show that, if the camera undergoes a random uniform motion, then the pairwise correlation of any pixels pair is a function of the distance between the pixel directions on the visual sphere. This leads to formalizing calibration as a problem of metric embedding from non-metric measurements: we want to find the disposition of pixels on the visual sphere from similarities that are an unknown function of the distances. This problem is a generalization of multidimensional scaling (MDS) that has so far resisted a comprehensive observability analysis (can we reconstruct a metrically accurate embedding?) and a solid generic solution (how to do so?). We show that the observability depends both on the local geometric properties (curvature) as well as on the global topological properties (connectedness) of the target manifold. We show that, in contrast to the Euclidean case, on the sphere we can recover the scale of the points distribution, therefore obtaining a metrically accurate solution from non-metric measurements. We describe an algorithm that is robust across manifolds and can recover a metrically accurate solution when the metric information is observable. We demonstrate the performance of the algorithm for several cameras (pin-hole, fish-eye, omnidirectional), and we obtain results comparable to calibration using classical methods. Additional synthetic benchmarks show that the algorithm performs as theoretically predicted for all corner cases of the observability analysis

Safe and Smooth: Certified Continuous-Time Range-Only Localization

A common approach to localize a mobile robot is by measuring distances to points of known positions, called anchors. Locating a device from distance measurements is typically posed as a non-convex optimization problem, stemming from the nonlinearity of the measurement model. Non-convex optimization problems may yield suboptimal solutions when local iterative solvers such as Gauss-Newton are employed. In this paper, we design an optimality certificate for continuous-time range-only localization. Our formulation allows for the integration of a motion prior, which ensures smoothness of the solution and is crucial for localizing from only a few distance measurements. The proposed certificate comes at little additional cost since it has the same complexity as the sparse local solver itself: linear in the number of positions. We show, both in simulation and on real-world datasets, that the efficient local solver often finds the globally optimal solution (confirmed by our certificate), but it may converge to local solutions with high errors, which our certificate correctly detects.Comment: 10 pages, 7 figures, accepted to IEEE Robotics and Automation Letters (this arXiv version contains supplementary appendix

Sensorimotor embedding : a developmental approach to learning geometry

textA human infant facing the blooming, buzzing confusion of the senses grows up to be an adult with common-sense knowledge of geometry; this knowledge then allows her to describe the shapes of objects, the layouts of places, and the relative locations of things naturally and effortlessly. In robotics, such knowledge is usually built in by a human designer who needs to solve complex engineering problems of sensor calibration and inference. In contrast, this dissertation presents a model for how autonomous agents can form an understanding of geometry the same way infants do: by learning from early unstructured sensorimotor experience. Through a framework called sensorimotor embedding, an agent reconstructs knowledge of its own sensor structure, the local geometry of the world, and the pose of objects within the world. The validity of this knowledge is demonstrated directly through Procrustes analysis and indirectly by using it to solve the mountain car task with different morphologies. The dissertation demonstrates how sensorimotor embedding can serve as a robust approach for acquiring geometric knowledge.Computer Science

A Full Scale Camera Calibration Technique with Automatic Model Selection – Extension and Validation

This thesis presents work on the testing and development of a complete camera calibration approach which can be applied to a wide range of cameras equipped with normal, wide-angle, fish-eye, or telephoto lenses. The full scale calibration approach estimates all of the intrinsic and extrinsic parameters. The calibration procedure is simple and does not require prior knowledge of any parameters. The method uses a simple planar calibration pattern. Closed-form estimates for the intrinsic and extrinsic parameters are computed followed by nonlinear optimization. Polynomial functions are used to describe the lens projection instead of the commonly used radial model. Statistical information criteria are used to automatically determine the complexity of the lens distortion model. In the first stage experiments were performed to verify and compare the performance of the calibration method. Experiments were performed on a wide range of lenses. Synthetic data was used to simulate real data and validate the performance. Synthetic data was also used to validate the performance of the distortion model selection which uses Information Theoretic Criterion (AIC) to automatically select the complexity of the distortion model. In the second stage work was done to develop an improved calibration procedure which addresses shortcomings of previously developed method. Experiments on the previous method revealed that the estimation of the principal point during calibration was erroneous for lenses with a large focal length. To address this issue the calibration method was modified to include additional methods to accurately estimate the principal point in the initial stages of the calibration procedure. The modified procedure can now be used to calibrate a wide spectrum of imaging systems including telephoto and verifocal lenses. Survey of current work revealed a vast amount of research concentrating on calibrating only the distortion of the camera. In these methods researchers propose methods to calibrate only the distortion parameters and suggest using other popular methods to find the remaining camera parameters. Using this proposed methodology we apply distortion calibration to our methods to separate the estimation of distortion parameters. We show and compare the results with the original method on a wide range of imaging systems