Homography Matrix Calculation Method

This article presents a custom implementation method for calculating homography matrices, following the methodology outlined in Zhang Zhengyou's influential paper. We will comprehensively examine the procedural steps and technical aspects to facilitate better understanding and practical implementation. The implementation typically involves point correspondence estimation using feature matching algorithms like SIFT or ORB, followed by solving the homogeneous linear system through Direct Linear Transform (DLT) with normalization techniques to improve numerical stability. Key functions include coordinate normalization, singular value decomposition (SVD) for matrix solving, and denormalization to obtain the final homography matrix. Additionally, we will discuss practical applications in computer vision tasks such as image stitching and perspective correction, address inherent limitations including sensitivity to outlier correspondences and planar surface assumptions, and explore future research directions in robust estimation and deep learning-based approaches. We believe this resource will be valuable for implementation purposes, and welcome any inquiries or suggestions for improvement.