Abstract
A robust calibration approach for a telecentric stereo camera system for three-dimensional (3-D) surface measurements is presented, considering the effect of affine mirror ambiguity. By optimizing the parameters of a rigid body transformation between two marker planes and transforming the two-dimensional (2-D) data into one coordinate frame, a 3-D calibration object is obtained, avoiding high manufacturing costs. Based on the recent contributions in the literature, the calibration routine consists of an initial parameter estimation by affine reconstruction to provide good start values for a subsequent nonlinear stereo refinement based on a Levenberg–Marquardt optimization. To this end, the coordinates of the calibration target are reconstructed in 3-D using the Tomasi–Kanade factorization algorithm for affine cameras with Euclidean upgrade. The reconstructed result is not properly scaled and not unique due to affine ambiguity. In order to correct the erroneous scaling, the similarity transformation between one of the 2-D calibration plane points and the corresponding 3-D points is estimated. The resulting scaling factor is used to rescale the 3-D point data, which then allows in combination with the 2-D calibration plane data for a determination of the start values for the subsequent nonlinear stereo refinement. As the rigid body transformation between the 2-D calibration planes is also obtained, a possible affine mirror ambiguity in the affine reconstruction result can be robustly corrected. The calibration routine is validated by an experimental calibration and various plausibility tests. Due to the usage of a calibration object with metric information, the determined camera projection matrices allow for a triangulation of correctly scaled metric 3-D points without the need for an individual camera magnification determination.
Highlights
Fringe projection profilometry is a state-of-the-art method in order to characterize the geometry information of three-dimensional (3-D) objects, as it allows a noncontact, fast, and areal data acquisition in the micrometer range.[1,2,3] If a measurement setup with a small field-of-view (FOV) is required, telecentric lenses can be employed either in stereo vision or in single camera–projector configurations or telecentric Scheimpflug approaches.[13,14]The calibration of a telecentric structured light sensor is not as straightforward as in the entocentric case, as a telecentric camera cannot be modeled by the pinhole camera but requires the introduction of the so-called affine camera model instead
Liu et al.[12] combined the Tomasi–Kanade factorization algorithm with a 3-D calibration target in order to retrieve the parameters of a fringe projection system with telecentric camera and projector
We introduce an Aruco marker-based detection strategy as introduced by Garrido-Jurado et al.[37] in order to distinctly differentiate between the two plane marker patterns of the 3-D calibration object
Summary
Fringe projection profilometry is a state-of-the-art method in order to characterize the geometry information of three-dimensional (3-D) objects, as it allows a noncontact, fast, and areal data acquisition in the micrometer range.[1,2,3] If a measurement setup with a small field-of-view (FOV) is required, telecentric lenses can be employed either in stereo vision (with[4,5] or without additional projector6,7) or in single camera–projector configurations (with entocentric[8,9,10] or telecentric projector11,12) or telecentric Scheimpflug approaches.[13,14]The calibration of a telecentric structured light sensor is not as straightforward as in the entocentric case, as a telecentric camera cannot be modeled by the pinhole camera but requires the introduction of the so-called affine camera model instead. Fringe projection profilometry is a state-of-the-art method in order to characterize the geometry information of three-dimensional (3-D) objects, as it allows a noncontact, fast, and areal data acquisition in the micrometer range.[1,2,3] If a measurement setup with a small field-of-view (FOV) is required, telecentric lenses can be employed either in stereo vision (with[4,5] or without additional projector6,7) or in single camera–projector configurations (with entocentric[8,9,10] or telecentric projector11,12) or telecentric Scheimpflug approaches.[13,14]. As a telecentric lens ideally only maps parallel light onto the camera sensor, the projection center lies at infinity A distance change along the optical axis of the camera will not result in a dimensional change of the mapped object
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