Computation of Fundamental Matrix for 3D Reconstruction

To implement fundamental matrix computations required for 3D reconstruction in computer vision using MATLAB, the following steps are necessary: First, camera intrinsic and extrinsic parameters must be determined through calibration. Second, the fundamental matrix is calculated based on camera motion trajectories using point correspondences between image pairs. Third, Singular Value Decomposition (SVD) is applied to decompose the fundamental matrix into the essential matrix. Finally, 3D reconstruction can be performed using the essential matrix to recover camera poses and 3D point locations through triangulation. Prior to computation, image preprocessing steps such as distortion correction using camera calibration parameters and keypoint extraction using detectors like SIFT or SURF are required. Additionally, optimization methods like RANSAC (Random Sample Consensus) algorithm can be incorporated to improve calculation accuracy and robustness by eliminating outlier correspondences. Key MATLAB functions involved include: cameraCalibrator for parameter estimation, estimateFundamentalMatrix for fundamental matrix computation, svd() for matrix decomposition, and triangulate for 3D point recovery. The implementation typically involves managing point correspondences, handling matrix rank constraints, and applying proper normalization techniques for numerical stability.