Early Approaches toNon-Rigid Reconstruction - Deformable Surface 3D Reconstruction from Monocular Images - page 12

(a) (b) (c)

Figure 2.1: Morphable face models Blanz and Vetter [ 1999 ]. (a) The average face. (b) Weighted of sum
of deformation modes that depicts the face of a specific person. (c) Setting the weights to half the values
used in (b) produces an intermediate face. Courtesy of T. Vetter.

a single vector and to mix physics-based approaches with statistical learning Nastar et al. [ 1996 ].
To account for illumination variations, an Active Illumination and Appearance model was intro-
duced Kahraman et al. [ 2007 ]. In a similar spirit of being robust to illumination changes, a light-
invariant AAM was proposed Pizarro et al. [ 2008 ], which relies on a light-invariant transforma-
tion Finlayson et al. [ 2006 ]. Finally, hierarchical AAM were introduced to make image fitting more
robust and efficient Cosker et al. [ 2004 ], Peyras et al. [ 2007 ]. To this end, the fitting process is done
in a coarse-to-fine manner, starting from the whole face and refining individual parts.
The AAM were later turned into a Morphable Model Blanz and Vetter [ 1999 ],
Romdhani and Vetter [ 2003 ] designed to recover the full 3D shape of a face, which produced ex-
tremely impressive results using a single properly-lit high resolution image. It was also used to model
various expressions of a same face Blanz et al. [ 2003 ] and combined to an AAM to further account
for appearance of the face instead of shape only Xiao et al. [ 2004a ]. Fig. 2.1 depicts the model and
illustrates the fact that the space of faces modeled in this way can indeed be considered as linear
since a weighted sum of such models still looks like a face. Because the shape and texture recovery
may be perturbed by large cast shadows or specularities, it was later shown that the sensitivity to
illumination could be reduced by replacing the appearance-based component of the model by infor-
mation provided by 2D point correspondences in all pairs of consecutive images of a video sequence
in which the head moves rigidly Dimitrijevic et al. [ 2004 ], as shown in Fig. 2.2 . This is because
such correspondences tend to be affected comparatively little by illumination changes given proper
normalization.
Nonlinear methods have also proved useful for Computer Vision applications. In particular,
the GPLVM was used to learn a prior on human pose and proved able to generalize well from a
small number of training examples Urtasun et al. [ 2005 ]. Similarly, the GPDM was also applied to
constrain the 3D estimation of humans poses in video sequences Urtasun et al. [ 2006 ]. For non-rigid
surface reconstruction, a sparse GPLVM was employed to learn a prior over the deformations of