Image Processing Reference

In-Depth Information

Figure 4.11:
Reconstruction of deformable surfaces made of different materials undergoing complex

deformations. In all four cases, we show the reconstructed 3D mesh overlaid on the input image and

below a side view of the same mesh. © 2011 IEEE.

assigned a penalty proportional to its Mahalanobis distance to the mean shape. To avoid optimizing

the individual patches independently, and therefore having to enforce consistency
a posteriori
, the

technique exploits the fact that the local mode weights

˜

c
can be directly obtained from the vertex

coordinates as

=
S
T
(
˜

˜

c

x

−˜

x
0
) ,

(4.13)

S
is the matrix of local modes, and

where

x
is the vector containing the mesh vertices associated

to a single patch. Note that this amounts to marginalizing out the mode weights, as is done in

probabilistic PCA
Tipping and Bishop
[
1999
]. The resulting regularization term for a single patch

can then be expressed as

˜

L
1
/
2

c
=

L
1
/
2
S
T
(

x
0
)
2

˜

x

˜

−˜

,

(4.14)

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