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time, the size of V t is a parameter, that is, the accuracy/noisy reconstruction depends on
larger/smaller of the used window. It should be also adapted to deforming objects speed.
Spacetime stereo matching. This stereo-matching schema combines both spatial matching
and temporal one to limit the matching ambiguities. The function F ( x r ) is analogous to
Equations 1.35 and 1.36 and is given by
t 0 ))) 2
F ( x r )
=
( I l ( V st ( x l ,
t 0 ))
I r ( V st ( x r ,
,
(1.37)
V st
Here V st represents a spatiotemporal volume instead of a window in a spatial-based matching
or a vector in a temporal-based matching. Figure 1.14 illustrates the spatial and the spacetime
stereo matchings to establish correspondences between the pixels in I l and those in I r .
The images are already rectified. Figure 1.15 e shows the reconstruction result operated by
spatio-temporal stereo matching using a volume of size (9
5). This time, the spacetime
approach cover more shape details than in Fig. 1.15 d , however, it also yields artifacts due
to the over-parametrization of the depth map. An improvement of this reconstruction using
a global spacetime stereo matching with the same volume size is given in Fig. 1.15 f . (See 2
for video illustrations of these reconstructions).
×
5
×
1.4.5 Template-based Post-processing
Recently, template-based approaches emerge due to its simplicity and robustness to noisy range
data. Outputs of shape recovery techniques present often imperfections like spikes, holes dues
to self-occlusions or the absorption of projected lights by dark regions of the face. The template
generic model provides a strong geometric prior and thus leads to high quality reconstructions
with automated hole-filling and noise removal. Correspondence estimation is often facilitated
by the use of tracked marker points or hand-selected landmarks correspondences. The template-
based literature consist on template-to-data registration then fitting and could allowing 3D
face tracking and expressions cloning. These stages are described in detail in the following
paragraphs. For the rest of this section, let
M
P
denotes the template model and
denotes the
target data.
Landmarks Detection
This step consists on manually or automatically facial keypoints detection (eyebrows, eyes,
nose, mouth contours, etc.). These facial keypoints are important in the following stages. In
particular, they could be used in coarse rigid registration to prepare the fine one, and they are
often used as control points in the warping/fitting procedure. Automatic 3D face landmarking
is one active research topic studied within the 3D face recognition and expression recognition
applications. Many approaches are designed and try to face the pose variation and external
occlusion problems (Segundo et al., 2010; Mehryar et al., 2010; Zhao et al., 2011).
2 http://grail.cs.washington.edu/projects/stfaces/
 
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