Error analysis of camera parameter estimation based on collinear features

Feature points for camera parameter estimation are detected in noisy images. Therefore, the feature points and also the camera parameters can only be estimated with limited accuracy. In case of collinear feature points, it is possible to benefit from this geometrical regularity which results in an increased accuracy of the camera parameters. In this paper, a complete theoretical covariance propagation starting from the error of the feature points up to the error of the estimated camera parameters is performed. Additionally, by determining the Fisher information matrix the Cramer-Rao bounds for the covariance of the corrected feature point positions are determined. To demonstrate the impact of collinearity on the accuracy of the camera parameters, a covariance propagation is performed with varying feature point error covariances.Onay Urfalioglu, Thorsten Thormahlen, Hellward Broszio, Patrick Mikulasti

Extrinisic Calibration of a Camera-Arm System Through Rotation Identification

Determining extrinsic calibration parameters is a necessity in any robotic system composed of actuators and cameras. Once a system is outside the lab environment, parameters must be determined without relying on outside artifacts such as calibration targets. We propose a method that relies on structured motion of an observed arm to recover extrinsic calibration parameters. Our method combines known arm kinematics with observations of conics in the image plane to calculate maximum-likelihood estimates for calibration extrinsics. This method is validated in simulation and tested against a real-world model, yielding results consistent with ruler-based estimates. Our method shows promise for estimating the pose of a camera relative to an articulated arm's end effector without requiring tedious measurements or external artifacts. Index Terms: robotics, hand-eye problem, self-calibration, structure from motio

View Registration Using Interesting Segments of Planar Trajectories

We introduce a method for recovering the spatial and temporal alignment between two or more views of objects moving over a ground plane. Existing approaches either assume that the streams are globally synchronized, so that only solving the spatial alignment is needed, or that the temporal misalignment is small enough so that exhaustive search can be performed. In contrast, our approach can recover both the spatial and temporal alignment. We compute for each trajectory a number of interesting segments, and we use their description to form putative matches between trajectories. Each pair of corresponding interesting segments induces a temporal alignment, and defines an interval of common support across two views of an object that is used to recover the spatial alignment. Interesting segments and their descriptors are defined using algebraic projective invariants measured along the trajectories. Similarity between interesting segments is computed taking into account the statistics of such invariants. Candidate alignment parameters are verified checking the consistency, in terms of the symmetric transfer error, of all the putative pairs of corresponding interesting segments. Experiments are conducted with two different sets of data, one with two views of an outdoor scene featuring moving people and cars, and one with four views of a laboratory sequence featuring moving radio-controlled cars

Algebraic error analysis of collinear feature points for camera parameter estimation

Cataloged from PDF version of article.In general, feature points and camera parameters can only be estimated with limited accuracy due to noisy images. In case of collinear feature points, it is possible to benefit from this geometrical regularity by correcting the feature points to lie on the supporting estimated straight line, yielding increased accuracy of the estimated camera parameters. However, regarding Maximum-Likelihood (ML) estimation, this procedure is incomplete and suboptimal. An optimal solution must also determine the error covariance of corrected features. In this paper, a complete theoretical covariance propagation analysis starting from the error of the feature points up to the error of the estimated camera parameters is performed. Additionally, corresponding Fisher Information Matrices are determined and fundamental relationships between the number and distance of collinear points and corresponding error variances are revealed algebraically. To demonstrate the impact of collinearity, experiments are conducted with covariance propagation analyses, showing significant reduction of the error variances of the estimated parameters. (C) 2010 Elsevier Inc. All rights reserved

Reliability in Constrained Gauss-Markov Models: An Analytical and Differential Approach with Applications in Photogrammetry

This report was prepared by Jackson Cothren, a graduate research associate in the Department of Civil and Environmental Engineering and Geodetic Science at the Ohio State University, under the supervision of Professor Burkhard Schaffrin.This report was also submitted to the Graduate School of the Ohio State University as a dissertation in partial fulfillment of the requirements for the Ph.D. degree.Reliability analysis explains the contribution of each observation in an estimation model to the overall redundancy of the model, taking into account the geometry of the network as well as the precision of the observations themselves. It is principally used to design networks resistant to outliers in the observations by making the outliers more detectible using standard statistical tests.It has been studied extensively, and principally, in Gauss- Markov models. We show how the same analysis may be extended to various constrained Gauss-Markov models and present preliminary work for its use in unconstrained Gauss-Helmert models. In particular, we analyze the prominent reliability matrix of the constrained model to separate the contribution of the constraints to the redundancy of the observations from the observations themselves. In addition, we make extensive use of matrix differential calculus to find the Jacobian of the reliability matrix with respect to the parameters that define the network through both the original design and constraint matrices. The resulting Jacobian matrix reveals the sensitivity of reliability matrix elements highlighting weak areas in the network where changes in observations may result in unreliable observations. We apply the analytical framework to photogrammetric networks in which exterior orientation parameters are directly observed by GPS/INS systems. Tie-point observations provide some redundancy and even a few collinear tie-point and tie-point distance constraints improve the reliability of these direct observations by as much as 33%. Using the same theory we compare networks in which tie-points are observed on multiple images (n-fold points) and tie-points are observed in photo pairs only (two-fold points). Apparently, the use of two-fold tiepoints does not significantly degrade the reliability of the direct exterior observation observations. Coplanarity constraints added to the common two-fold points do not add significantly to the reliability of the direct exterior orientation observations. The differential calculus results may also be used to provide a new measure of redundancy number stability in networks. We show that a typical photogrammetric network with n-fold tie-points was less stable with respect to at least some tie-point movement than an equivalent network with n-fold tie-points decomposed into many two-fold tie-points