  Depth position highly affects lens distortion, especially in close-range
photography, which limits the measurement accuracy of existing stereo vision
systems. Moreover, traditional depth-dependent distortion models and their
calibration methods have remained complicated. In this work, we propose a
minimal set of parameters based depth-dependent distortion model (MDM), which
considers the radial and decentering distortions of the lens to improve the
accuracy of stereo vision systems and simplify their calibration process. In
addition, we present an easy and flexible calibration method for the MDM of
stereo vision systems with a commonly used planar pattern, which requires
cameras to observe the planar pattern in different orientations. The proposed
technique is easy to use and flexible compared with classical calibration
techniques for depth-dependent distortion models in which the lens must be
perpendicular to the planar pattern. The experimental validation of the MDM and
its calibration method showed that the MDM improved the calibration accuracy by
56.55% and 74.15% compared with the Li's distortion model and traditional
Brown's distortion model. Besides, an iteration-based reconstruction method is
proposed to iteratively estimate the depth information in the MDM during
three-dimensional reconstruction. The results showed that the accuracy of the
iteration-based reconstruction method was improved by 9.08% compared with that
of the non-iteration reconstruction method.
