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(a)
(b)
(c)
(d)
(e)
Figure 4.3 Multiple components (a) may intersect (b1), move apart (b2), or move across (b3).
(c) Simulating a cylindrical scan and (d) smoothing the new border vertices (e) solves these problems
Component blending. A drawback of fitting each component separately is that inconsisten-
cies may appear at the borders of the components. During the fine fitting, the border triangles of
two components may start to intersect, move apart, or move across (Fig. 4.3). The connectivity
of the complete mesh remains the same, so two components moving apart remain connected
with elongated triangles at their borders. We solve these inconsistencies by means of a post
processing step, as described in more detail below.
Knowing that the morphable face model is created from cylindrical range scans and that the
position of the face instance does not change, it is easy to synthetically rescan the generated
face instance. Each triangle of the generated face instance S fine is assigned to a component
(Fig. 4.3 a ). A cylindrical scanner is simulated, obtaining a cylindrical depth image d (
θ,
y )
θ
with a surface sample for angle
, height y with radius distance d from the y-axis through the
center of mass of S (Fig. 4.3 c ). Basically, each sample is the intersection point of a horizontal
ray with its closest triangle, so we still know to which component it belongs. The cylindrical
depth image is converted to a 3D triangle mesh by connecting the adjacent samples and
projecting the cylindrical coordinates to 3D. This new mesh S fine has a guaranteed resolution
depending on the step sizes of
and y , and the sampling solves the problem of intersecting
and stretching triangles. However, ridges may still appear at borders where components moved
across. Therefore, Laplacian smoothing is applied to the border vertices and their neighbors
(Fig. 4.3 d ). Laplacian smoothing moves each vertex toward the center of mass of its connected
vertices. Finally, data further then 110 mm from the tip of the nose is removed to have the final
model S final (Fig. 4.3 e ) correspond to the segmented face. In Section 4.3.6, we evaluate both
the single and multiple component fits.
θ
4.3.6 Results
In this section, we evaluate our fitting results for the UND, GAVAB, and BU-3DFE data sets.
We perform a qualitative and quantitative evaluation of the acquired model fits and compare
the results with other model-fitting methods. To prove that the use of multiple components
improves the fitting accuracy over a single component, we compare the quantitative mea-
sures and relate the fitting accuracy to face recognition by applying different face-matching
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