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remains unchanged this approach has still problems
with appearance outliers.
Another direction of research was dedicated to re-
placing the least-squares error measure by a robust er-
ror measure in the fitting stage (Gross et al., 2006).
Later this approach was further refined by comparing
several robust error measures (Theobald et al., 2006).
The same strategy is also used in (Romdhani and Vet-
ter, 2003) and was adapted to a statistical framework
in (Yu et al., 2007). But the latter approach is lim-
ited in several ways: (a) a scale parameter is required,
which is hard to determine in general, (b) the frame-
work around the inverse compositional algorithm is
specifically tailored to tracking, and (c) the face mod-
els are built from the tracked person, which limits its
applicability for general applications.
In the context of medical image analysis a ro-
bust AAM fitting approach was presented in (Beichel
et al., 2005). In their method, which is based on the
standard AAM fitting algorithm, gross disturbances
(i.e., outliers) in the input image are avoided by ignor-
ing misleading coefficient updates in the fitting stage.
For that purpose, inlier and outlier coefficients are
identified by a Mean Shift based analysis of the resid-
ual’s modes. Then, an optimal sub-set of modes is se-
lected and only those pixels covered by the selected
mode combination are used for actual residual cal-
culation. The Robust AAM Matching (RAAM) ap-
proach shows excellent results on a number of medi-
cal data sets. However, the mode selection is compu-
tationally very complex. Thus, this method is imprac-
tical for real-time or near real-time applications.
To overcome these drawbacks we introduce a new
efficient robust AAM fitting scheme. In contrast
to existing methods the robustness (against occluded
features) is not directly included in the fitting step
but is detached. In fact, we propose to run a robust
pre-processing step first to generate undisturbed input
data and then to apply a standard AAM fitting. Since
the robust step, which is usually computationally in-
tensive, has to be performed only once (and not iter-
atively in the fitting process), the computational costs
can be reduced.
In particular, the main idea is to robustly replace
the missing feature information from a reliable model.
Thus, our work is somehow motivated by (Nguyen
et al., 2008) and (Du and Su, 2005), where beards
and eye-glasses, which are typical problems when ap-
plying an AAM approach, are removed. In (Du and
Su, 2005) a PCA model was built from facial images
that do not contain any eye-glasses. Then, in the re-
moval step the original input images are reconstructed
and the regions with the largest reconstruction errors
are identified. These pixels are iteratively replaced by
the reconstruction. But this approach can only be ap-
plied if the absolute number of missing pixels is quite
small. In contrast, in (Nguyen et al., 2008) two mod-
els are computed in parallel, one for bearded faces and
one for non-bearded faces. Then, in the removal step
for a bearded face the detected beard region is recon-
structed from the non-bearded space.
Since both methods are restricted to special types
of occlusion or limited by a pre-defined error level,
they can not be applied for general tasks. Thus, in
our approach we apply a robust PCA model (e.g.,
(Rao, 1997; Black and Jepson, 1996; Leonardis and
Bischof, 2000)) to cope with occlusions in the origi-
nal input data. For that purpose, in the learning stage
a reliable model is estimated from undisturbed data
(i.e., without any occlusions), which is then applied
to robustly reconstruct unreliable values from the dis-
turbed data. However, a drawback of these methods
is their computational complexity (i.e., iterative algo-
rithms, multiple hypothesis, etc.), which hinders prac-
tical applicability. Thus, as a second contribution, we
developed a more efficient robust PCA method that
overcomes this limitation.
Even though the proposed robust AAM fitting is
quite general, our main interest is to apply it to fa-
cial images. Thus, this application is evaluated in the
experiments in detail. However, we also note that it
is necessary that the image patch, where the robust
PCA is applied has to be roughly aligned with the
feature under consideration. In the case of our face
localization this can be ensured by using a rough face
and facial component detection algorithm inspired by
the Viola-Jones algorithm (Viola and Jones, 2004).
Moreover, the applied PCA model can handle a wide
variability in facial images.
This paper is structured as follows. In Section 2
we introduce and discuss the novel fast robust PCA
(FR-PCA) approach. In addition, we performed ex-
periments on the publicly available ALOI database,
which show that our approach outperforms existing
robust methods in terms of speed and accuracy. Next,
in Section 3, we introduce our robust AAM fitting al-
gorithm that is based on the new robust PCA scheme.
To demonstrate its benefits, we also present experi-
mental results on facial images. Finally, we discuss
our findings and conclude our work in Section 4.
2 FAST ROBUST PCA
If a PCA space U = [u
1
, . . . , u
n−1
] is estimated from n
samples, an unknown sample x = [x
1
, . . . , x
m
], m > n,
can usually be reconstructed to a sufficient degree of
accuracy by p, p < n, eigenvectors:
ACTIVE APPEARANCE MODEL FITTING UNDER OCCLUSION USING FAST-ROBUST PCA
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