The collinear equation serves as the cornerstone for establishing geometric relationships in photogrammetry, Nerf, and 3DGS theory. Its nonlinear optimization across diverse spatial domains profoundly influences the calculation accuracy of camera distortion, interior and exterior orientation parameters, and modeling quality of the ultimate reconstruction of real-world 3D scenes. At its core, the collinear equation hinges on three fundamental elements: image points, three-dimensional spatial features, and the parameterization of three-dimensional rotations. The research progress is delineated for parameterization methods of the collinear equation, focusing on these pivotal components. Additionally, it outlines potential avenues for future research, aiming to pave the way for advancements in this field. By transcending the confines of Euclidean space, novel perspectives are proposed on the collinear equation, envisioning the application in angular domain space. This fresh approach promises to provide valuable insights for improving the accuracy of camera state estimation and the overall modeling quality of real-world 3D scenes, stemming from a deep understanding of theoretical principles.

作为摄影测量、Nerf和3DGS理论建立几何关系的基础, 共线方程在不同空间域的参数化方法对相机畸变参数和内外方位参数的计算精度以及实景三维的建模质量有源头级的重要影响。围绕共线方程参数化的3个核心要素(二维图像点、空间三维点和三维旋转), 总结共线方程参数化方法的研究进展, 分析未来有潜力的研究方向。同时, 还对全角域空间变换的方法进行展望, 为共线方程跳出欧式空间提供新思路, 为从理论源头提升相机状态的估计精度和实景三维的建模质量提供新见解。