Abstract
We propose camera models for cameras that are equipped with lenses that can be tilted in an arbitrary direction (often called Scheimpflug optics). The proposed models are comprehensive: they can handle all tilt lens types that are in common use for machine vision and consumer cameras and correctly describe the imaging geometry of lenses for which the ray angles in object and image space differ, which is true for many lenses. Furthermore, they are versatile since they can also be used to describe the rectification geometry of a stereo image pair in which one camera is perspective and the other camera is telecentric. We also examine the degeneracies of the models and propose methods to handle the degeneracies. Furthermore, we examine the relation of the proposed camera models to different classes of projective camera matrices and show that all classes of projective cameras can be interpreted as cameras with tilt lenses in a natural manner. In addition, we propose an algorithm that can calibrate an arbitrary combination of perspective and telecentric cameras (no matter whether they are tilted or untilted). The calibration algorithm uses a planar calibration object with circular control points. It is well known that circular control points may lead to biased calibration results. We propose two efficient algorithms to remove the bias and thus obtain accurate calibration results. Finally, we perform an extensive evaluation of the proposed camera models and calibration algorithms that establishes the validity and accuracy of the proposed models.
Highlights
One problem that often occurs when working on machine vision applications that require large magnifications is that the depth of field becomes progressively smaller as the magnification increases
We have proposed models for cameras with tilt lenses that correctly model the imaging geometry of lenses for which the ray angles in object and image space differ
We have shown that the tilt can be modeled by orthographic or perspective homographies that project points from an untilted virtual image plane to the tilted image plane
Summary
One problem that often occurs when working on machine vision applications that require large magnifications is that the depth of field becomes progressively smaller as the magnification increases. We show that there are four kinds of lenses that are in common use: entocentric lenses (perspective in object and image space, with possibly differing ray angles), image-side telecentric lenses (perspective in object space, orthographic in image space), object-side telecentric (orthographic in object space, perspective in image space), and bilateral telecentric (orthographic in object and image space). Each of these kinds of lenses can be tilted, which obviously results in a different imaging geometry for each lens type. We test the proposed camera models on many real lenses (Sect. 11)
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