Homography
A 3×3 matrix representing the projective transformation between two planes, used in panorama stitching, perspective correction, and AR marker recognition to describe geometric correspondences.
A homography is a 3×3 matrix describing the projective mapping between two planes. It encodes how points on one planar surface correspond to points on another viewed from different positions, essential for panorama stitching, perspective correction, and AR marker recognition.
The matrix H has 8 degrees of freedom in homogeneous coordinates:
- Source point
(x, y, 1)multiplied by H yields(x', y', w') - Actual coordinates:
(x'/w', y'/w') - Minimum 4 point correspondences determine H uniquely
Estimation pipeline:
- Feature detection: Extract keypoints using SIFT or ORB
- Matching: Find corresponding pairs via descriptor comparison
- RANSAC: Robustly estimate H while rejecting outliers
- Refinement: Minimize reprojection error with Levenberg-Marquardt
Homography is a superset of affine transformation - it does not preserve parallelism, enabling trapezoidal and perspective distortion correction. However, a single homography assumes all points lie on one plane; scenes with varying depth require multiple homographies or alternative approaches. In OpenCV, cv2.findHomography() estimates the matrix and cv2.warpPerspective() applies it.