Fundamentals of Fundamental Matrix in Multi-View Geometry for Computer Vision

This article provides a comprehensive introduction to multi-view geometry in computer vision, with a focus on MATLAB-based rapid implementation for fundamental matrix estimation. Multi-view geometry represents a crucial domain in computer vision, addressing the reconstruction of 3D scenes from images captured from multiple viewpoints. Within this framework, the fundamental matrix serves as a key mathematical construct that characterizes the epipolar geometry between two distinct camera perspectives.

Our implementation leverages MATLAB's computational capabilities to achieve efficient fundamental matrix estimation. The solution employs two primary algorithmic approaches: Singular Value Decomposition (SVD) for robust matrix factorization and least-squares optimization for optimal parameter estimation. The SVD method ensures numerical stability during matrix decomposition, while the least-squares approach minimizes reprojection errors to enhance estimation accuracy.

Through this technical exposition, readers will gain practical experience in coding fundamental matrix solvers using MATLAB, along with deeper insights into core concepts of multi-view geometry. The implementation includes handling of point correspondences, normalization techniques for improved numerical conditioning, and validation methods for epipolar constraint satisfaction.