Early Approaches toNon-Rigid Reconstruction - Deformable Surface 3D Reconstruction from Monocular Images - page 15

the deformations of a surface as a linear combination of modes not only bears strong connections to
statistical learning techniques, but also to physics-based models and modal analysis.
Even though using linear subspace models effectively reduces the number of degrees of free-
dom of the problem, monocular reconstruction remains ill-posed and involves many ambiguities.
Competing methods can therefore be distinguished by how they go about finding the “best” solution
in the space of all possible ones. As we will see, among other things, it can be the one that yields
the smoothest surface, that is most temporally consistent, or that best preserves geodesic distances
on the surface. Although in general not physically exact, the constraints used for reconstruction are
typically inspired by the observed physics of the object of interest.
In Chapter 4 , we will also discuss alternative parameterizations that implicitly regularize
a surface shape. Specifically, we will present a method that relies on free-form deformations to
reconstruct inextensible surfaces. Furthermore, we will discuss approaches designed to model the
deformations of developable surfaces, whose shape can be parameterized with very few degrees of
freedoms.
Finally, as mentioned in the previous sections for nonlinear FEM and learning techniques,
there often is a tradeoff between the accuracy of the model and its practicality. To overcome this
weakness, several methods among those described below have introduced regularizers that are both
realistic and easy to optimize. For instance, convex formulations were proposed for template-based
approaches, as well as closed-form solutions to non-rigid structure-from-motion. While these tech-
niques do not always give the best solutions, they yield a good initial estimate for non-convex, but
more accurate formulations of the problem.