When a homography is a valid model

WHAT THIS TESTS The question probes understanding of multi-view geometry, specifically the assumptions baked into using a single homography and what breaks them.

A GOOD ANSWER COVERS Validity conditions: a homography, a 3x3 projective transform between image planes, correctly maps all correspondences in exactly two cases. First, pure rotation: the camera rotates about its optical center with zero translation, so depth cancels and any scene works. Second, planar scene: all observed points lie on a single plane, so even with camera translation the points map by one homography. Failure: when the camera translates and the scene has 3D depth, near and far points shift differently, producing parallax that no single homography can capture, causing ghosting in stitching. General model: in that case the two views are related by epipolar geometry, encoded by the fundamental matrix for uncalibrated cameras or the essential matrix for calibrated ones, which constrains corresponding points to epipolar lines rather than a one-to-one mapping.

COMMON WRONG ANSWERS Claiming a homography aligns any two photos, ignoring parallax. Or saying it only needs the same camera, missing the rotation-or-plane condition. Or confusing the fundamental matrix with a homography.

LIKELY FOLLOW-UPS Why does panorama capture instruct you to rotate, not walk. What artifacts does parallax create in stitching. What does the fundamental matrix encode. How would you detect that a homography model is inadequate.

ONE CONCRETE EXAMPLE Standing still and panning a phone to shoot a panorama satisfies the pure-rotation condition, so consecutive frames align with homographies cleanly and the seams blend without artifacts. This is exactly why panorama apps instruct you to pivot in place rather than walk. If you instead walk sideways while shooting a room with both foreground and background objects, the near and far objects shift by different amounts, so a single homography cannot align both and the stitch shows ghosting. To handle that translating case you would estimate the fundamental or essential matrix and reconstruct depth, since the relationship is now full epipolar geometry rather than a planar mapping.