What can be seen in three dimensions with an uncalibrated stereo rig?

What can be seen in three dimensions with an uncalibrated stereo rig?

| Olivier D. Faugeras
This paper addresses the problem of determining the kind of three-dimensional reconstructions that can be obtained from a binocular stereo rig without any three-dimensional metric calibration data. The only available information is a set of pixel correspondences between the two retinas. The paper shows that even in this case, rich non-metric reconstructions of the environment can be obtained. Specifically, it demonstrates that five arbitrary correspondences allow for a unique projective reconstruction of the environment, while four correspondences allow for an affine reconstruction. These reconstructions are defined up to certain transformations, such as projective or affine transformations. The paper argues that computer vision may have overemphasized the need for metric information, as it is often unnecessary for applications like robotics. The results show that with only five or four correspondences, it is possible to reconstruct the environment in projective or affine coordinates, respectively. The paper also discusses the implications of these findings for the development of computer vision algorithms and the use of calibration patterns. The results are supported by experimental results using a calibration pattern, demonstrating the effectiveness of the proposed methods. The paper concludes that non-metric reconstructions are sufficient for many applications and that the focus on metric information may be misplaced.This paper addresses the problem of determining the kind of three-dimensional reconstructions that can be obtained from a binocular stereo rig without any three-dimensional metric calibration data. The only available information is a set of pixel correspondences between the two retinas. The paper shows that even in this case, rich non-metric reconstructions of the environment can be obtained. Specifically, it demonstrates that five arbitrary correspondences allow for a unique projective reconstruction of the environment, while four correspondences allow for an affine reconstruction. These reconstructions are defined up to certain transformations, such as projective or affine transformations. The paper argues that computer vision may have overemphasized the need for metric information, as it is often unnecessary for applications like robotics. The results show that with only five or four correspondences, it is possible to reconstruct the environment in projective or affine coordinates, respectively. The paper also discusses the implications of these findings for the development of computer vision algorithms and the use of calibration patterns. The results are supported by experimental results using a calibration pattern, demonstrating the effectiveness of the proposed methods. The paper concludes that non-metric reconstructions are sufficient for many applications and that the focus on metric information may be misplaced.
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