共线方程线性化的矩阵模型  

Collinear Equation Linearized Matrix Model

作　　者：徐振亮[1] 李艳焕[2] 闫利[3] 晏磊[1] 

机构地区：[1]北京大学空间信息集成与3S工程应用北京市重点实验室,北京100871 [2]辽宁工程技术大学审计处,阜新123009 [3]武汉大学测绘学院,武汉430079

出　　处：《北京大学学报（自然科学版）》2016年第3期403-408,共6页Acta Scientiarum Naturalium Universitatis Pekinensis

基　　金：国家自然科学基金(11174017;41271456);北京市共建项目(SYS1000010402)资助

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。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.

关 键 词：共线方程 投影方程 投影矩阵 齐次坐标 

分 类 号：O241.6[理学—计算数学]