Early Approaches toNon-Rigid Reconstruction - Deformable Surface 3D Reconstruction from Monocular Images - page 7

Graphics applications, and a precise knowledge of the physical properties of the surfaces being
modeled, which is only rarely available to Computer Vision applications. Consequently, in both
fields, a lot of effort has gone into simplifying these approaches to the point where they become
practical in their respective contexts. Below, we distinguish between the methods used in Computer
Graphics and in Computer Vision.
2.1.2 PHYSICS-BASEDMETHODS FOR COMPUTERGRAPHICS
A key driver behind the use of physics-based models in Computer Graphics has been the need to
model the deformations of clothes House and Breen [ 2000 ], preferably in real-time. In the absence
of good deformation models, artists must manually design the shape of the virtual characters' gar-
ments in each frame of a sequence. Physics-based models both constrain the feasible deformations
and make animation much easier. Several cloth models have been proposed, ranging from early
versions Ng and Grimsdale [ 1996 ], Volino et al. [ 1995 ] that only achieved visually plausible results
to much more physically-accurate and realistic ones Bridson et al. [ 2002 , 2003 ].
While physics-based approaches produce good results, they typically yield computationally
expensive solutions. Therefore, there have been many attempts at improving the speed and robust-
ness of the solvers Volino and Magnenat-Thalmann [ 2001 ]. For example, to overcome the perennial
problem that very small time steps have to be taken to avoid numerical instabilities, implicit time
integration was introduced Baraff and Witkin [ 1998 ]. Another example is the use of the Boundary
Element Method James and Pai [ 1999 ], an alternative to FEM where the original differential equa-
tions are replaced by integral equations over the boundary of the object, to speedup the simulations.
In addition to improving the resolution speed, more accurate nonlinear FEM was also studied
in Computer Graphics. This was done in particular for surgery simulation purposes Picinbono et al.
[ 2000 ], and for general deformable objects modeling Barbic and James [ 2005 ], Hirota et al. [ 2000 ],
Wu et al. [ 2001 ]. The corotational approach proved succesful in this context of large deforma-
tions Hauth and Strasser [ 2004 ], Müller et al. [ 2002 ], as well as other representations such as discrete
shells Grinspun et al. [ 2003 ], or invertible finite elements Irving et al. [ 2004 ]. Accurate nonlinear
representations being very complex, simplifications have been proposed to yield physically plausible
deformations based on elastically coupled rigid cells Botsch et al. [ 2007 ].
Finally, while advances in Mechanical Engineering have resulted in improved Com-
puter Graphics methods, the process sometimes also went the other way. Subdivision sur-
faces Catmull and Clark [ 1978 ], Doo and Sabin [ 1978 ], already well-known in the Graphics com-
munity, were introduced to the Mechanical Engineering community in the context of finite elements.
They involve representing a surface with a coarse mesh, which can then be refined following a subdi-
vision scheme Loop [ 1987 ]. This reduced the complexity of the finite element models, thus yielding
more efficient representations Cirak et al. [ 2000 ].