Image Processing Reference

In-Depth Information

2.1.3 PHYSICS-BASEDMETHODS FOR COMPUTERVISION

As they became very popular in Computer Graphics for simulation and animation purposes,

physics-based models also gained acceptance in Computer Vision for non-rigid motion analy-

sis
Kambhamettu
et al.
[
1994
]. In both fields, their main purpose was to restrict the potential defor-

mations of an object to plausible ones only. However, in Computer Graphics where the simulation

results have to look realistic, physical accuracy, or at least plausibility, is more important than in Com-

puter Vision. There, the main concern is quality of fit to image data and robustness to erroneous

measurements. The role of the model is that of a regularizer that turns the model fitting process into

one that is easier to perform.

The original Snakes
Kass
et al.
[
1988
] are a good example of this. The external energy that

serves as a regularizer is written as a quadratic function that approximates the sum of the square of the

curvatures along the surface, which itself is an approximation of the true elastic deformation energy.

The fact that it is not a particularly accurate approximation of the true energy is more than made up

by the fact that it can be expressed in quadratic form, thereby allowing a very effective semi-implicit

optimization scheme. The same formulation was later extended to 2D shape recovery
Pilet
et al.

[
2008
] and 3D surface modeling from stereo
Fua and Leclerc
[
1995
] using triangulated meshes.

Many other variations of the physics-based models have been proposed since to reconstruct

surfaces from images. In the medical imaging domain,
balloon forces
Cohen and Cohen
[
1993
]

were introduced to make the surface expand from its initial state so that it could be started

from inside the object to be outlined. Deformable superquadrics
Metaxas and Terzopoulos
[
1993
],

Terzopoulos and Metaxas
[
1991
] were proposed to reconstruct more complex shapes by modeling

both global and local deformations. Finally, in
McInerney and Terzopoulos
[
1993
,
1995
], the FEM

formulation was followed more closely, and a deformable surface was modeled as a thin-plate un-

der tension. More recently, the use of the Boundary Element Method has also been advocated to

track deformable objects in 2D
Greminger and Nelson
[
2003
] and in 3D
Greminger and Nelson

[
2008
]. Comparisons of these different FEM formulations are available both specifically for medical

imaging
McInerney and Terzopoulos
[
1996
] and in a broader context
Montagnat
et al.
[
2001
].

There has been some interest in more accurate modeling of the true physics of deformable

objects via the nonlinear finite element method in Computer Vision. However, unlike in Computer

Graphics where one can tune the forces and material parameters until satisfactory deformations are

produced, recovering surface shape by fitting a model to the image data requires these parameters to

be fixed during the optimization process. Some approaches that rely on sophisticated models have

nonetheless been proposed for fitting a mesh to 3D range data
Huang
et al.
[
1995
],
Jojic and Huang

[
1997
],
Tsap
et al.
[
1998
] and for video-based shape recovery
Bhat
et al.
[
2003
],
Tsap
et al.
[
2000
].

They involve an analysis-by-synthesis approach and a more-or-less exhaustive search through the

parameter space until those that yield the best fit are found. Recently a nonlinear FEM formula-

tion
Ilic and Fua
[
2007
] has been proposed to recover the deformations of beam structures in the

image plane, where image features act as forces, as in the original Snakes
Kass
et al.
[
1988
]. To the

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