Homography Matrix Calculation in Pinhole Camera Model

In our implementation, we enhance the original content by adding detailed explanations and implementation specifics while preserving the core concepts. The expanded technical description follows: In the pinhole camera model, we address the problem of homography matrix estimation between two planar surfaces. To validate our homography computation algorithm, we developed a main function with the following implementation workflow: 1. First, the program loads two input images using standard image I/O functions. These images should capture the same planar scene from different viewpoints. 2. The algorithm then reads four pairs of corresponding points from the two images. These point correspondences are crucial for calculating the homography matrix using the direct linear transformation (DLT) method. 3. We then invoke the CalcH function, which implements the homography calculation algorithm. This function takes the point correspondences as input and computes the 3×3 homography matrix H using singular value decomposition (SVD) to solve the linear system of equations derived from the point correspondences. 4. In the first image, users can interactively select a reference point using mouse input. The program captures the pixel coordinates of the selected point through callback functions. 5. Subsequently, the WarpH function is called to compute the corresponding point in the second image. This function applies the homography transformation by multiplying the selected point's homogeneous coordinates with the computed H matrix, then converting back to Cartesian coordinates. 6. Finally, the program displays the results visually, typically by showing both images side-by-side with markers indicating the original point and its computed correspondence, along with optional numerical output of the transformation results. By incorporating these detailed implementation steps and technical explanations, we successfully expand the content while maintaining the original technical foundation and enhancing the practical implementation aspects for better understanding.