Graphics Reference
In-Depth Information
(i,j)
(0,j)
(0,0)
(1,0)
(0,0)
Figure 3.9
Right: an illustration of some nodes that are allowed to go to (
i
/
n
,
j
/
n
) point on the graph.
Left: an example of a
φ
1
function restricted to a finite graph
under the elastic matching. Since we have geodesic paths denoting optimal deformations
between individual curves, we can combine these deformations to obtain full deformations
between faces.
3.5.4 Extension to Facial Surfaces Shape Analysis
Now we extend the framework from radial curves to full facial surfaces. As mentioned earlier,
we are going to represent a face surface
S
with an indexed collection of radial curves. That
is,
S
↔{
β
α
,α
∈
,α
0
]
}
[0
. Through this relation, each facial surface has been represented as
[0
,α
0
]
. The indexing provides a correspondence between curves across
faces. For example, a curve at an angle
S
an element of the set
on the probe face is matched with the curve at the
same angle on the gallery face. Figure 3.12 illustrates an example of this correspondence. With
this correspondence, we can compute pairwise geodesic paths and geodesic distances between
the matched curves across faces. This computation has several interesting properties. Firstly,
α
Figure 3.10
Examples of matching result of matching using dynamic programming
