A Minimal Set of Parameters Based Depth-Dependent Distortion Model and Its Calibration Method for Stereo Vision Systems

TL;DR

Depth position strongly influences lens distortion in close-range stereo, limiting measurement accuracy for traditional distortion models. The authors introduce a minimal eight-parameter depth-dependent distortion (MDM) that unifies depth-dependent radial and decentering distortions, together with a flexible planar-pattern calibration method that relaxes perpendicularity constraints. A three-step calibration approach (Zhang initialization, linear MDM estimation, and joint Levenberg–Marquardt optimization) plus an iteration-based 3D reconstruction method addresses depth-information coupling and yields substantial accuracy gains. Experimental results demonstrate up to approximate 78% calibration-error reduction compared with Brown’s model, and a ~9% improvement in 3D reconstruction accuracy when using the iterative approach, highlighting practical impact for precise stereo measurement in close-range settings.

Abstract

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.

Figures (8)

• Figure 1: Stereo vision system and transformations of different frames. ${O_W}$ is the origin of the world coordinate system, ${O_C^L}$ is the origin of the left camera coordinate system, ${O_C^R}$ is the origin of the right camera coordinate system, ${K_L}$ and ${K_R}$ are the intrinsic parameters of the left and right cameras, respectively. [$R_L^W$,$T_L^W$] and [$R_R^W$,$T_R^W$] are the transformation matrices between the world coordinate system and the left and right camera coordinate systems.
• Figure 2: Linear constraints on the left and right images
• Figure 3: Experimental setup
• Figure 4: Schematic diagram of the checkerboard layout
• Figure 5: Relationship between the calibration accuracy and the number of calibration image pairs. (a) Relationship between the number of calibration images and $E_1^{i, j}$ of the MDM-R. (b) Relationship between the number of calibration images and $E_1^{i, j}$ of the MDM.