  A recent trend in Non-Rigid Structure-from-Motion (NRSfM) is to express
local, differential constraints between pairs of images, from which the surface
normal at any point can be obtained by solving a system of polynomial
equations. The systems of equations derived in previous work, however, are of
high degree, having up to five real solutions, thus requiring a computationally
expensive strategy to select a unique solution. Furthermore, they suffer from
degeneracies that make the resulting estimates unreliable, without any
mechanism to identify this situation.
  In this paper, we show that, under widely applicable assumptions, we can
derive a new system of equation in terms of the surface normals whose two
solutions can be obtained in closed-form and can easily be disambiguated
locally. Our formalism further allows us to assess how reliable the estimated
local normals are and, hence, to discard them if they are not. Our experiments
show that our reconstructions, obtained from two or more views, are
significantly more accurate than those of state-of-the-art methods, while also
being faster.
