Geometric Interpretations of Compatibility for Fundamental Matrices
arxiv(2024)
摘要
In recent work, algebraic computational software was used to provide the
exact algebraic conditions under which a sixtuple {F^ij} of fundamental
matrices, corresponding to 4 images, will be compatible, i.e. there will
exist cameras {P_i}_i=1^4 such that each pair P_i,P_j has fundamental
matrix F^ij; it has been further demonstrated that quadruplewise
compatibility is sufficient for the problem of n>4 images. We expand on these
prior results by proving equivalent geometric conditions for compatibility. We
find that when the camera centers are in general position, compatibility can be
characterized via the intersections of epipolar lines in each image. When the
camera centers are coplanar, compatibility occurs when the prior condition
holds and additionally any one camera center can be reconstructed via the other
three.
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