Early Approaches toNon-Rigid Reconstruction - Deformable Surface 3D Reconstruction from Monocular Images - page 13

Figure 2.2: Fitting a morphable face model to a low-resolution video sequence. © 2004 IEEE.
local surface patches Salzmann et al. [ 2008b ]. The resulting local models have the advantage over
the global ones that they can be trained from smaller training sets because local deformations are
more constrained than those of a global surface. Furthermore, surface patches can be assembled into
arbitrarily shaped global surface meshes, whose 3D deformations can then be recovered without any
additional training. This cures one weakness of global models that have to be relearned for each
individual surface, even when they all are made of a material seen previously.
While nonlinear learned models have proved effective to reconstruct complex deformations,
they can only be fitted by an iterative scheme that requires an accurate initial estimate. This is due
to the non-convexity of the objective functions they yield. As a consequence, they are best suited to
tracking application where the initial estimate is provided by the shape computed in the previous
frame.
2.3 REGULARIZATIONVIA SHAPE PARAMETERIZATION
Learned models have proved very effective for many applications. They remove the need to esti-
mate unknown and hard to measure material parameters, while yielding accurate representations of
surface deformations. However, some issues remain unsolved. First, gathering enough examples to
build a meaningful database represents a very significant amount of work, especially in the case of
highly deformable surfaces with many degrees of freedom. Second, registering the examples typically
involves a painstaking process. For example, in the case of faces Blanz and Vetter [ 1999 ], laser scans
first had to be aligned and then remeshed in order to have the same topology. This is why many other
models and parameterizations besides physics-based and statistical-learning based ones have also
been proposed. Again, several of these approaches were first introduced in the Computer Graphics
field for simulation purposes, and were later adapted to recover surface deformations from images.
Modeling a deformable surface as a triangulated mesh typically yields many degrees of free-
dom. However, as mentioned earlier, many of these degrees of freedom are coupled, which can be
enforced by using physics-based constraints or by representing the deformations as a combination of