Two view constraints on the epipoles from few correspondences
This work addresses a specific bottleneck in computer vision for applications like 3D reconstruction, though it appears incremental as it builds on known constraints rather than introducing a new paradigm.
The paper tackles the problem of reducing the number of point correspondences needed to compute the fundamental matrix in two-view geometry by leveraging cross ratio invariance from epipolar line homography, resulting in a method that requires fewer than the typical 7 points when prior information about the epipoles is available, as demonstrated in a buddy search application.
In general it requires at least 7 point correspondences to compute the fundamental matrix between views. We use the cross ratio invariance between corresponding epipolar lines, stemming from epipolar line homography, to derive a simple formulation for the relationship between epipoles and corresponding points. We show how it can be used to reduce the number of required points for the epipolar geometry when some information about the epipoles is available and demonstrate this with a buddy search app.