Large-volume metrology instrument selection and measurability analysis

A wide range of metrology processes are involved in the manufacture of large products. In addition to the traditional tool-setting and product-verification operations, increasingly flexible metrology-enabled automation is also being used. Faced with many possible measurement problems and a very large number of metrology instruments employing diverse technologies, the selection of the appropriate instrument for a given task can be highly complex. Also, as metrology has become a key manufacturing process, it should be considered in the early stages of design, and there is currently very little research to support this. This paper provides an overview of the important selection criteria for typical measurement processes and presents some novel selection strategies. Metrics that can be used to assess measurability are also discussed. A prototype instrument selection and measurability analysis application is also presented, with discussion of how this can be used as the basis for development of a more sophisticated measurement planning tool. © 2010 Authors

Autocalibration with the Minimum Number of Cameras with Known Pixel Shape

In 3D reconstruction, the recovery of the calibration parameters of the cameras is paramount since it provides metric information about the observed scene, e.g., measures of angles and ratios of distances. Autocalibration enables the estimation of the camera parameters without using a calibration device, but by enforcing simple constraints on the camera parameters. In the absence of information about the internal camera parameters such as the focal length and the principal point, the knowledge of the camera pixel shape is usually the only available constraint. Given a projective reconstruction of a rigid scene, we address the problem of the autocalibration of a minimal set of cameras with known pixel shape and otherwise arbitrarily varying intrinsic and extrinsic parameters. We propose an algorithm that only requires 5 cameras (the theoretical minimum), thus halving the number of cameras required by previous algorithms based on the same constraint. To this purpose, we introduce as our basic geometric tool the six-line conic variety (SLCV), consisting in the set of planes intersecting six given lines of 3D space in points of a conic. We show that the set of solutions of the Euclidean upgrading problem for three cameras with known pixel shape can be parameterized in a computationally efficient way. This parameterization is then used to solve autocalibration from five or more cameras, reducing the three-dimensional search space to a two-dimensional one. We provide experiments with real images showing the good performance of the technique.Comment: 19 pages, 14 figures, 7 tables, J. Math. Imaging Vi

Evaluation of tactual displays for flight control

Manual tracking experiments were conducted to determine the suitability of tactual displays for presenting flight-control information in multitask situations. Although tracking error scores are considerably greater than scores obtained with a continuous visual display, preliminary results indicate that inter-task interference effects are substantially less with the tactual display in situations that impose high visual scanning workloads. The single-task performance degradation found with the tactual display appears to be a result of the coding scheme rather than the use of the tactual sensory mode per se. Analysis with the state-variable pilot/vehicle model shows that reliable predictions of tracking errors can be obtained for wide-band tracking systems once the pilot-related model parameters have been adjusted to reflect the pilot-display interaction

Speeding up structure from motion on large scenes using parallelizable partitions

Structure from motion based 3D reconstruction takes a lot of time for large scenes which consist of thousands of input images. We propose a method that speeds up the reconstruction of large scenes by partitioning it into smaller scenes, and then recombining those. The main benefit here is that each subscene can be optimized in parallel. We present a widely usable subdivision method, and show that the difference between the result after partitioning and recombination, and the state of the art structure from motion reconstruction on the entire scene, is negligible

Shonan Rotation Averaging: Global Optimality by Surfing SO(p)nSO(p)^n

Shonan Rotation Averaging is a fast, simple, and elegant rotation averaging algorithm that is guaranteed to recover globally optimal solutions under mild assumptions on the measurement noise. Our method employs semidefinite relaxation in order to recover provably globally optimal solutions of the rotation averaging problem. In contrast to prior work, we show how to solve large-scale instances of these relaxations using manifold minimization on (only slightly) higher-dimensional rotation manifolds, re-using existing high-performance (but local) structure-from-motion pipelines. Our method thus preserves the speed and scalability of current SFM methods, while recovering globally optimal solutions.Comment: 30 pages (paper + supplementary material). To appear at the European Conference on Computer Vision (ECCV) 202

Euclidean Structure from N>=2 Parallel Circles: Theory and Algorithms

International audienceOur problem is that of recovering, in one view, the 2D Euclidean structure, induced by the projections of N parallel circles. This structure is a prerequisite for camera calibration and pose computation. Until now, no general method has been described for N > 2. The main contribution of this work is to state the problem in terms of a system of linear equations to solve.We give a closed-form solution as well as bundle adjustment-like refinements, increasing the technical applicability and numerical stability. Our theoretical approach generalizes and extends all those described in existing works for N = 2 in several respects, as we can treat simultaneously pairs of orthogonal lines and pairs of circles within a unified framework. The proposed algorithm may be easily implemented, using well-known numerical algorithms. Its performance is illustrated by simulations and experiments with real images

Pareto optimality solution of the multi-objective photogrammetric resection-intersection problem

Reconstruction of architectural structures from photographs has recently experienced intensive efforts in computer vision research. This is achieved through the solution of nonlinear least squares (NLS) problems to obtain accurate structure and motion estimates. In Photogrammetry, NLS contribute to the determination of the 3-dimensional (3D) terrain models from the images taken from photographs. The traditional NLS approach for solving the resection-intersection problem based on implicit formulation on the one hand suffers from the lack of provision by which the involved variables can be weighted. On the other hand, incorporation of explicit formulation expresses the objectives to be minimized in different forms, thus resulting in different parametric values for the estimated parameters at non-zero residuals. Sometimes, these objectives may conflict in a Pareto sense, namely, a small change in the parameters results in the increase of one objective and a decrease of the other, as is often the case in multi-objective problems. Such is often the case with error-in-all-variable (EIV) models, e.g., in the resection-intersection problem where such change in the parameters could be caused by errors in both image and reference coordinates.This study proposes the Pareto optimal approach as a possible improvement to the solution of the resection-intersection problem, where it provides simultaneous estimation of the coordinates and orientation parameters of the cameras in a two or multistation camera system on the basis of a properly weighted multi-objective function. This objective represents the weighted sum of the square of the direct explicit differences of the measured and computed ground as well as the image coordinates. The effectiveness of the proposed method is demonstrated by two camera calibration problems, where the internal and external orientation parameters are estimated on the basis of the collinearity equations, employing the data of a Manhattan-type test field as well as the data of an outdoor, real case experiment. In addition, an architectural structural reconstruction of the Merton college court in Oxford (UK) via estimation of camera matrices is also presented. Although these two problems are different, where the first case considers the error reduction of the image and spatial coordinates, while the second case considers the precision of the space coordinates, the Pareto optimality can handle both problems in a general and flexible way