Browsing by Author "Ezebili, Ifeanyi Francis"

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    A model for accurate error propagation in a convergent stereovision system.
    (Stellenbosch : Stellenbosch University, 2024-02) Ezebili, Ifeanyi Francis; Schreve, K.; Stellenbosch University. Faculty of Engineering. Dept. of Mechanical and Mechatronic Engineering.
    ENGLISH ABSTRACT: Stereovision is a camera-based imaging technique that facilitates the reconstruction of the 3-space coordinates and depth of a scene point using the images acquired from two cameras. Generally, stereovision finds application in autonomous vehicle navigation, mobile robots, parts inspection for quality assurance, and tracking and identification of objects. Like the output of a typical metrological system, the 3D coordinates measured with a stereovision system have associated measurement uncertainties. Such uncertainties practically emerge from the errors which are concomitant with each of the steps involved in stereo camera measurement. In this dissertation an analytic epipole-featured model is developed and proposed for structure computation and 3-space depth measurement in convergent stereo camera imaging. The proposed reconstruction model is predicated on the image sensor parameters of both cameras, left and right, together with two extrinsic parameters, namely the baseline distance and the stereo projection angle of the scene point. The intrinsic parameters are normalized with respect to the focal lengths of the cameras. The proposed model is characterized by less computational complexity and short execution time and can be employed in active vision-based metrology in which the imaging stereo cameras are rotated about their vertical axes relative to each other. The terms virtual depth and depth factor or depth coefficient are subsequently introduced and described. Both quantities together define the depth of a world point relative to the coordinate frame of the reference camera. From the developed reconstruction model, an equivalence relation between coplanar parallel and convergent stereo camera imaging systems is established. The relation states that for double-view geometry in computer vision, disparity in a row-aligned, coplanar-parallel stereo camera configuration is equivalent to the baseline-to-depth-factor ratio in a convergent stereo camera configuration. This baseline-to-depth-factor ratio in convergent stereo camera imaging is termed convergent stereo disparity and can be identified and equated with the image rectification process in a practical conventional coplanar-parallel stereo camera setup. Incorporating the epipoles in the developed reconstruction model facilitates the establishment of the stereo equivalence relation and the definition of convergent stereo disparity in stereovision. Furthermore, generalized mathematical analyses are done to model and study the variation of depth sensitivity and relative depth uncertainty with respect to convergent stereovision system parameters for 3-space points using the developed reconstruction model. It is observed that different values of left and right focal lengths are required to achieve high sensitivity coefficient, a condition that is not conformable with the conventional practice of having the same left and right focal lengths in stereo camera imaging. Regarding the variation of the stereo projection and stereo convergence angles, there are trade-offs between depth sensitivity coefficient and relative depth uncertainty. It is found that a stereo convergence angle of 90° yields the best relative depth uncertainty value at which the focal length-normalized epipole-to-principal point distances on both image planes are reciprocals. The analytic derivations and graphical characteristics of the depth sensitivity coefficient would give a stereovision system designer some information regarding the margin by which the estimated depth of a scene point changes for a drift in the value of any stereo camera parameter, and also some idea in respect of the potential trade-offs involved in the choice of certain parameters. The performance of the developed reconstruction model is studied, and its accuracy tested by comparing the 3-space coordinates it predicts to those obtained by Gold Standard triangulation algorithm and to the ground truth results. In terms of execution speed the proposed reconstruction model exhibited a computation time of 0.6 ms compared to 6.2 ms and 9.9 ms recorded for the Direct Linear Transformation (DLT) and Gold Standard triangulation algorithms respectively. The measurement errors determined by theoretical methods based on the law of error propagation incorporating the analytic reconstruction model (with and without full input covariance matrices) are compared with those obtained by the experimental approach. Strong correlations are found to exist between the two sets of values obtained, indicating the validity of the error model. The study of measurement error using the reconstruction model shows that accounting for the covariances of all the stereo camera parameters in vision-based metrology predicts smaller errors compared to when the covariances of the parameters are ignored. It is also found that it makes no significant difference if full or diagonal input covariance matrices are used in the theoretical computation of error compared to the experimental approach to determining the error. The error model derived in this work and predicated on the developed epipole-dependent reconstruction model would be useful in the design of high-precision stereovision systems.