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context of three-dimensional reconstruction of the human hand, an articulated model
derived from human anatomy is introduced by Lee and Kunii (
1993
), relying on pla-
nar kinematic chains consisting of rigid elements. The appearance of the hand in a
pair of stereo images is modelled and compared with the appearance in the ob-
served image. Heap and Hogg (
1996
) propose to represent the complete surface of
the hand by a deformable model. In the application scenario of three-dimensional
face reconstruction, a linear morphable model is adapted by Amberg et al. (
2007
)to
the object appearance in a stereo image pair based on silhouettes, colour variations,
and manually defined reference points.
1.5.2.5 Spacetime Stereo Vision and Scene Flow Algorithms
General Overview
An extension of the classical pairwise frame-by-frame ap-
proach to stereo vision towards a spatio-temporal analysis of a sequence of image
pairs has been introduced quite recently as spacetime stereo by several researchers
(Zhang et al.,
2003
; Davis et al.,
2005
). Both studies present a framework that aims
for a unification of stereo vision with active depth from triangulation methods such
as laser scanning and coded structured light by generalising a spatial similarity mea-
sure according to (
1.102
) to the spatio-temporal domain. Zhang et al. (
2003
) sug-
gest to utilise pixel grey values changing over time to establish disparity maps of
increased accuracy. They show that assuming a disparity value
d(u
c
,v
c
,t
c
)
which
is constant throughout a spatio-temporal image window centred at
(u
c
,v
c
,t
c
)
can
only be assumed for a surface oriented parallel to the image plane. For surfaces
of arbitrary orientation which do not move, a linear expansion for the disparity is
introduced by Zhang et al. (
2003
), corresponding to
∂d
∂u
(u
∂d
∂v
(v
d(u,v,t)
=
d(u
c
,v
c
,t
c
)
+
−
u
c
)
+
−
v
c
)
+···
.
(1.116)
For moving scenes, this representation is extended according to
∂d
∂u
(u
∂d
∂v
(v
∂d
∂t
(t
d(u,v,t)
=
d(u
c
,v
c
,t
c
)
+
−
u
c
)
+
−
v
c
)
+
−
t
c
)
+···
(1.117)
since the disparity may change over time as a result of a radial velocity of the
object. These expressions for the disparity are inserted into a similarity measure
defined by (
1.102
). Dynamic programming followed by Lucas-Kanade flow (Lu-
cas and Kanade,
1981
) is utilised to establish point correspondences and estimate
the disparities as well as their spatial and temporal first derivatives
∂d/∂u
,
∂d/∂v
,
and
∂d/∂t
. A significant improvement over classical stereo analysis is achieved
by Zhang et al. (
2003
) when a static scene is illuminated by a temporally vari-
able illumination pattern which is not necessarily strictly controlled. In these cases,
their three-dimensional reconstruction method exhibits a similar amount of detail as
three-dimensional data acquired by a laser scanner. For images displaying objects
which are illuminated in a non-controlled manner, their spacetime stereo approach
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