Abstract:

Using the matrix expression form of computer vision projection equation, the collinear equation is constructed into matrix equation. With the projection matrix element as a composite function, this paper realizes the unification derivation of each variable of the collinear equation based on the matrix analysis method. Compared with the traditional analytical method of linearization, the form of matrix analysis process is quite succinct and easy to understand, which can be used to the numerical solution of linear library application. For the various construction form of the rotation matrix, this method has better adaptability. The constructed matrix of collinear equation has important enlightenment significance for using computer vision method.

Key words: collinear equation, projection equation, projection matrix, homogeneous coordinates

摘要：

借鉴计算机视觉投影方程的矩阵表达形式, 将解析形式下的共线方程构造为矩阵方程表达, 再以投影矩阵元素作为复合函数并基于矩阵分析方法, 实现共线方程对各变量的统一求导。首先, 与传统解析法线性化相比, 矩阵分析过程工整, 形式简洁, 易于理解, 便于应用线性库进行数值解算; 其次, 对于不同构造形式下的旋转矩阵, 该方法都具有较好的适应性; 最后, 构建的共线方程的矩阵形式对于摄影测量借鉴计算机视觉方法也有重要启示意义。

关键词: 共线方程, 投影方程, 投影矩阵, 齐次坐标