Image Processing Reference

In-Depth Information

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
],
MÃ¼ller
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
].

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