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Figure 5.11 (a) 3D annotated facial shape model (70 landmarks); (b) 3D closed curves extracted around
the landmarks; (c) 3D curve-based patches composed of 20 level curves with a size fixed by a radius
λ 0 = 20 mm; (d) extracted patches on the face
border. Contrary to the MPEG-4 feature points specification that annotates the cheeks center
and bone, in BU-3DFE there were no landmarks associated with the cheek regions. Thus, two
extra landmarks at both cheeks, obtained by extracting the middle point along the geodesic
path between the mouth corner and the outside eye corner was added.
We propose to represent each facial scan by a set of patches around the landmarks. Let r l
be the reference point and P l a given patch centered on this point and localized on the facial
surface denoted by S . Each patch will be represented by an indexed collection of level curves.
To extract these curves, we use the Euclidean distance function
to characterize the
length between r l and any point p on S . Indeed, unlike the geodesic distance, the Euclidean
distance is sensitive to deformations. Besides it enables deriving curve extraction in a fast and
simple way. Using this function, the curves as level sets is defined as the following:
r l
p
: c l
r l .
λ ={
p
S
|
r l
p
= λ }⊂
S
[0
0 ]
.
(5.5)
Each c l
λ
is a closed curve, consisting of a collection of points situated at an equal distance
λ
from r l . Figure 5.11 summarizes the scheme of patches extraction.
Framework for 3D Shape Analysis
Once the patches are extracted, we aim to study their shape and design and a similarity measure
between corresponding ones on different scans under different expressions. This is motivated
by the common belief that people smile, or convey any other expression, the same way, or more
appropriately certain regions taking part in a specific expression undergo practically the same
dynamical deformation process. We expect that certain corresponding patches associated with
the same given expression will be deformed in a similar way, whereas those associated with
two different expressions will deform differently. The following sections describe the shape
analysis of closed curves in
3 , initially introduced by Joshi et al. (2007), and its extension to
analyze shape of local patches on facial surfaces.
R
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