We study the problem of estimating the epipolar geometry
from apparent contours of smooth curved surfaces
with affine camera models. Since apparent contours are
viewpoint dependent, the only true image correspondences
are projections of the frontier points, i.e., surface points
whose tangent planes are also their epipolar planes. However,
frontier points are unknown a priori and must be estimated
simultaneously with epipolar geometry. Previous approaches
to this problem adopt local greedy search methods
which are sensitive to initialization, and may get trapped in
local minima. We propose the first algorithm that guarantees
global optimality for this problem. We first reformulate
the problem using a separable form that allows us to
search effectively in a 2D space, instead of on a 5D hypersphere
in the classical formulation. Next, in a branch-andbound
algorithm we introduce a novel lower bounding function
through interval matrix analysis. Experimental results
on both s...