基于本质矩阵变换的多角度SAR三维重建方法

Multi-view SAR 3D reconstruction method based on essential matrix transformation

摘要:

合成孔径雷达（SAR）通过多角度观测可获取目标的三维立体信息。目前,多角度SAR三维重建多针对正侧视运动轨迹开展研究,通过构建投影几何关系式,利用目标在不同SAR图之间的偏移量与投影几何的关系求解目标三维信息。此类方法缺少对投影关系的数学建模过程,并且在SAR运动轨迹包含斜视角和俯仰角的情况下,求解误差较大。基于直线SAR轨迹下的投影几何关系,建立多角度SAR投影数学模型。在该数学投影模型中,SAR成像平面像素点坐标与目标三维空间坐标的关系矩阵称为本质矩阵。多角度SAR数学模型将三维重建问题转化为矩阵逆运算问题。将本质矩阵建立的投影表达式变换为齐次线性方程组,采用奇异值分解算法求解目标三维坐标。通过星载SAR轨迹参数进行实验仿真,验证了所提投影模型与三维重建算法的有效性。

Abstract:

SAR can obtain 3D information of the target through multi-view observation. At present, multi-view SAR 3D reconstruction mainly assumes a side-looking trajectory. By constructing projective geometry equations, this type of method calculates the target offset between SAR images and derives the target height from the projective geometry. However, this type of method lacks a mathematical modeling process for the projection relationships and exhibits significant solving errors when the SAR trajectory includes squint and pitch angles. This paper analyzed the linear SAR trajectory, summarized the geometric relationship of the projection, and obtained the mathematical model of multi-view SAR projection. In the mathematical projection model, the relation matrix between pixel coordinates in the SAR imaging plane and target 3D space coordinates is called the essential matrix. The multi-view SAR mathematical model transforms the 3D reconstruction problem into a matrix inverse operation problem. The projection expression established by the essential matrix is transformed into homogeneous linear equations, and the singular value decomposition algorithm is used to solve the 3D coordinates of the target. Spaceborne SAR trajectory parameters were used for experimental simulation to verify the effectiveness of the proposed projection model and 3D reconstruction algorithm.