Ricolfe-Viala Carlos, Sanchez-Salmeron Antonio-Jose, Martinez-Berti Enrique
Department of Systems Engineering and Automatic Control, Polytechnic University of Valencia, Camino de Vera s/n, Valencia, D.C. 46022, Spain.
Appl Opt. 2012 Jan 1;51(1):89-101. doi: 10.1364/AO.51.000089.
Camera calibration is a two-step process where first a linear algebraic approximation is followed by a nonlinear minimization. The nonlinear minimization adjusts the pin-hole and lens distortion models to the calibrating data. Since both models are coupled, nonlinear minimization can converge to a local solution easily. Moreover, nonlinear minimization is poorly conditioned since parameters with different effects in the minimization function are calculated simultaneously (some are in pixels, some in world coordinates, and some are lens distortion parameters). A local solution is adapted to parameters, which minimize the function easily, and the remaining parameters are just adapted to this solution. We propose a calibration method where traditional calibration steps are inverted. First, a nonlinear minimization is done, and after, camera parameters are computed in a linear step. Using projective geometry constraints in a nonlinear minimization process, detected point locations in the images are corrected. The pin-hole and lens distortion models are computed separately with corrected point locations. The proposed method avoids the coupling between both models. Also, the condition of nonlinear minimization increases since points coordinates are computed alone.
相机校准是一个两步过程，首先是线性代数近似，然后是非线性最小化。非线性最小化将针孔模型和镜头畸变模型调整到校准数据。由于这两个模型是耦合的，非线性最小化很容易收敛到局部解。此外，非线性最小化的条件不佳，因为在最小化函数中具有不同影响的参数是同时计算的（有些是像素单位，有些是世界坐标单位，有些是镜头畸变参数）。局部解适用于那些能轻松最小化函数的参数，而其余参数则仅适用于此解。我们提出一种校准方法，将传统校准步骤颠倒过来。首先进行非线性最小化，然后在一个线性步骤中计算相机参数。在非线性最小化过程中使用射影几何约束，对图像中检测到的点位置进行校正。利用校正后的点位置分别计算针孔模型和镜头畸变模型。所提出的方法避免了两个模型之间的耦合。而且，由于单独计算点坐标，非线性最小化的条件得到了改善。
