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 ( ˜
x 0 ) ,
S is the matrix of local modes, and
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
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