Graphics Reference
In-Depth Information
Nose tip
Upper lip
Lower lip
(a) Face with open
mouth
(c) Face with closed
mouth
(b) Radial curves matching
(d) Geodesic between curves
Figure 3.11
Examples of shape matching and geodesic deforming radial curves extracted from two
faces: (a) a curve on an open mouth, (b) a result of matching using dynamic programming, (c) a curve
on closed mouth, and (d) a geodesic path between curves (a) and (c)
it provides a Riemannian distance between shapes of facial surfaces by combining distances
between the corresponding radial curves. The distance between two facial surfaces is given by
α
0
d
s
q
1
,
q
2
α
.
1
α
0
[0
,α
0
]
[0
,α
0
]
d(
S
1
S
2
)
d:
S
×
S
→ R
≥
0
,
,
=
α
α
=
1
Here,
q
i
α
i
α
denotes the SRVF of the radial curve
β
on the
i
th,
i
=
1
,
2 facial surface, and
d
s
is the geodesic distance between the curves represented by
q
i
α
.
Reference radial curves
2
S
=
∪
c
1
S
=
∪
c
2
α
1
α
α
α
Figure 3.12
Faces comparison by pairwise curves comparisons
