Homography and Image Stitching

A homography is a 3 by 3 matrix that maps points from one image plane to another in homogeneous coordinates, up to an arbitrary scale. It has eight independent degrees of freedom and can be estimated from at least four non-collinear point correspondences, usually with more points and robust outlier rejection. Its geometric scope matters: one homography relates views of a planar surface, and a rotating camera can produce a homography for a general scene when the camera center does not translate. With camera translation and objects at different depths, one global homography cannot align every point because of parallax. Panorama software uses this mapping as part of a larger pipeline. It detects and matches features in overlapping images, estimates camera relations, warps images into a common projection, adjusts exposure, chooses seams, and blends the overlap. OpenCV’s stitching module describes distinct stages such as feature finding, matching, camera estimation, warping, seam estimation, exposure compensation, and blending. Therefore, “apply a homography” is not the same as producing a polished panorama; alignment and seam decisions still affect quality. For document capture, a page is approximately planar, so four page corners can define a perspective correction that makes the page rectangular. For a wide panorama, small viewpoint shifts or nearby foreground objects can produce double edges after a single transform. Capture with overlap, rotate around the camera’s optical center when practical, and inspect moving subjects and seams. Use a more general multi-camera model or local warping when the scene violates the single-homography assumption, while checking that the correction does not bend straight structures implausibly.