Robust facial features tracking using geometric constraints and relaxation

Abstract

This work presents a robust technique for tracking a set of detected points on a human face. Facial features can be manually selected or automatically detected. We present a simple and efficient method for detecting facial features such as eyes and nose in a color face image. We then introduce a tracking method which, by employing geometric constraints based on knowledge about the configuration of facial features, avoid the loss of points caused by error accumulation and tracking drift. Experiments with different sequences and comparison with other tracking algorithms, show that the proposed method gives better results with a comparable processing time.

Full text

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Robust Facial Features Tracking Using Geometric
Constraints and Relaxation
D´ esir´ e Sidib´ e#1, Philippe Montesinos∗2, Alain Tr´ emeau#3
#Universit´ e Jean Monnet, Laboratoire Hubert Curien - UMR CNRS 5516
18 rue du Professeur B. Lauras, 42000 Saint-Etienne, France
1dro.desire.sidibe@univ-st-etienne.fr
3alain.tremeau@univ-st-etienne.fr
∗LGI2P, Ecole des Mines Ales
Parc Scientifique Georges Besse, 30035 Nimes cedex 1, France
2philippe.montesinos@ema.fr
Abstract—This work presents a robust technique for tracking
a set of detected points on a human face. Facial features can be
manually selected or automatically detected. We present a simple
and efficient method for detecting facial features such as eyes and
nose in a color face image. We then introduce a tracking method
which, by employing geometric constraints based on knowledge
about the configuration of facial features, avoid the loss of points
caused by error accumulation and tracking drift. Experiments
with different sequences and comparison with other tracking
algorithms, show that the proposed method gives better results
with a comparable processing time.
I. INTRODUCTION
Automatic human face analysis and recognition has re-
ceived significant attention during the past decades, due to
the emergence of many potential applications such as person
identification, video surveillance, teleconferencing and human
computer interaction. An automatic face recognition usually
begins with the detection of face pattern, and then proceeds to
normalize the face images using information about the location
and appearance of facial features such as eyes and mouth.
Therefore, detecting faces and facial features is a crucial step.
Many methods for solving the face detection problem have
been proposed in the literature [1] and most of them can be
put into a two-stage framework. The first stage focuses on face
candidates, i.e. regions that may contain a face are marked.
In the second stage, the face candidates are sent to a “face
verifier”, which will decide whether the candidates are real
faces or not. Different methods put emphasis on one or the
other of these stages [2].
In this work, we are interested in the detection and tracking
of facial features in a human computer interaction application.
Among all facial features, eyes can be considered the most
salient and stable [3], [4]. We present a simple and efficient
eye detection method based on both skin color modeling
and geometric characteristics of human eyes. Based on the
positions of eyes, other facial features such as nose and mouth
are detected. The method is simple since it needs no training
examples of eyes and is robust to face rotation in the image
978-1-4244-4652-0/09/$25.00 c ?2009IEEE
plane. Once facial features are detected in a frame, they are
tracked in the video sequence. We present a robust technique
for tracking these facial features using geometric constraints
about their configuration. Exploiting the knowledge that the
features being tracked belong to a face, no points are lost
during tracking. This knowlegde is used through a relaxation
scheme.
The remainder of the paper is organized as follows. In
Section 2 we review some existing work about facial features
detection and tracking. The proposed facial features detection
method is described in Section 3. Then, the robust tracking
algorithm is addressed in Section 4. Some experimental results
showing the validity of the method, are given in Section 5.
Finally, concluding remarks are given in Section 6.
II. RELATED WORK
Automatic detection of facial features in video sequences is
generally performed after a face is detected in a frame. Many
approaches have been proposed to detect faces [1]. Recently,
methods based on machine learning techniques have proven to
be very effective for face detection and the detector proposed
by Viola and Jones is now one of the most popular [5].
Eyes can be considered the most salient and stable features
in a human face in comparison with other facial features.
Therefore, extraction of eyes is often a crucial step in many
face detection algorithms [3], [4]. Many image-based eye
detection techniques have been proposed recently and a review
on eye detection techniques can be found in [6]. Han et al.
[3] use morphological operations and a labeling process to
search for potential face regions. Then, they use a trained
backpropagation neural network to identify faces and their
locations. Similar ideas are used by Wu and Zhou [2]. They
employ size and intensity information to find eye-analogue
segments from gray scale image, and exploit geometrical
relationships to filter out the possible eye-analogue pairs.
Huang and Wechsler [7] use genetic algorithms to evolve some
finite state automata to discover the most likely eye locations.
Then, optimal features are selected and a decision tree is built
to classify whether the most salient locations identified earlier
are eyes. Kawaguchi and Rizon [8] use intensity and edge
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Author manuscript, published in "IEEE MMSP 09, 11th IEEE International Workshop on MultiMedia Signal Processing, Rio de Janeiro
: Brazil (2009)"
DOI : 10.1109/MMSP.2009.5293329

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information to locate the iris. The main techniques they use
are template matching, separability filter and Hough transform.
Song et al. [6] use similar ideas to detect eyes based on multi-
resolution wavelet transform.
The main objective of tracking is to roughly predict and
estimate the location of a target object in each frame of the
image sequence. In the context of face tracking, proposed
methods can be classified into two categories. On the one
hand, if the target being tracked is the entire face region, then
kernel-based methods such as Mean Shift [9] or CamShift
(Continuously Adaptive Mean Shift) [10] are used and give
good results. On the other hand, if individual features are
tracked, then a point tracker is used. Several point trackers
have been proposed. Among them, it is worth mentioning the
Kanade-Lucas-Tomasi, KLT for short, tracker [11] [12]. KLT
tracker is used to track facial features by Bourel et al. [13]
and by Colmenarez et al. [14]. It is based on minimizing a
measure of dissimilarity between the appearance of a feature
in the current and the last frames. In general, for reliable
and fast processing, the maximum interframe displacement is
limited. Spors and Rabenstein [15] use a luminance-adapted
block matching technique to track eyes in a video sequence.
Block matching is performed using a reference eye pattern and
the extracted eye region from the previous frame. To cope with
temporal changes in brightness, after the matching process,
each reference pattern is adapted by the difference between
the detected eye region in the current frame and the reference
pattern.
The main problem with these tracking methods is the loss
of points during tracking. A point may be lost because of
illumination variation, head motion, temporary occlusion, or
gradual error accumulation. Moreover, if there is a large in-
terframe displacement, error in features localization increases
and may cause a drift away from the correct positions. To deal
with these problems, Bourel et al. [13] propose a method to
recover the lost points using their known positions in previous
frames. In this work, facial features are recovered based on
some empirical knowledge about the type of feature, i.e. lip
corners, nose, etc.
The relaxation labeling technique, which was first intro-
duced by Rosenfeld et al. [16], has been widely used in
the computer vision community. The principal idea of a
relaxation scheme is to use the information provided by the
neighbourhood of each feature in order to improve consitency
and reduce ambiguity. One main limitation of this technique
is its high complexity when using a large number of features.
However, it has been shown that this complexity can be signif-
icantly reduced employing a sparse matrix representation [17].
Moreover, in the context of facial features tracking, the number
of features is generally very small.
III. FACIAL FEATURES DETECTION
Our facial features detection method is based on skin color
information. A first step of skin detection is used to reduce the
search region for facial features. Human skin color is widely
used as an important cue for face detection. Many different
color spaces have been employed and Terrillon et al. [18]
have shown that the tint-saturation-luma (TSL) space and
the normalized RGB space provide best results for Gaussian
models.
A. Skin color modeling and detection
Skin color distribution can be modeled by an elliptical
Gaussian probability density function (pdf), defined as:
1
2π|Σs|1/2e−1
where c is a color vector and (µs,Σs) are the distribution
parameters. These parameters are estimated from a training
sample. We used a set of 1,158,620 skin pixels, manually
selected from different images. The images are chosen in order
to represent people belonging to several ethnic groups, and a
wide range of illumination conditions.
A more sophisticated model, a mixture model, is often
used in the literature. It is a generalization of the single
Gaussian model. The pdf in that case is the sum of several
single Gaussians. However, Caetano et al. [19] have shown
that both models give comparable results, except when a high
true positive rate is needed (more than 80%). In that case,
the performance of mixture models exceeds single model’s
performance. Since we use skin detection as an initial step to
reduce the search region for facial features, a single Gaussian
model is adopted.
Once the skin color distribution’s parameters are obtained
from the training sample, the Mahalanobis distance from a
color vector c to mean vector µs, given the covariance matrix
Σs, is used to measure how ”skin like” the color c is:
f(c|skin) =
2(c−µs)TΣ−1
s(c−µs),
(1)
λs(c) = (c − µs)TΣ−1
s(c − µs).
(2)
Given an input image, for each pixel x, x = (r,g) in the
normalized RGB color space, x is considered a skin pixel if
the distance λs(x) is less than a predifined threshold [18].
B. Eye detection
The eye detection method starts by considering as potential
eye regions, the non-skin regions within a detected face region.
Obviously, eyes should be within a face region and eyes should
not be detected as skin by the skin detector. The use of skin
color information makes a clear difference with the work of
Wu and Zhou [2] and Han et al. [3] where eyes are detected
based on the assumption that they are darker than other parts of
the face. In these methods, eye-analogue segments are found
in the entire image resulting in a high number of possible pairs
to check. On the contrary, we have to find eye-analogue pairs
among a reduced number of potential eye regions.
An ellipse is fitted to each potential eye region using
connected component analysis. Let Rk be a potential eye
region and (xk,yk) its centroid. Then Rk, reduced to an
ellipse, defines ak, bk and θk which are, respectively, the
length of the major axis, the length of the minor axis and
the orientation of the major axis of the ellipse. Finally, a pair
of potential eye regions is considered as eyes if it satisfies
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(a)(b)(c)
Fig. 1.
detected. c) Eye detection result (eyes centers are depicted by white crosses).
Skin and eye detection example. a) Original image. b) Skin region
some constraints based on anthropological characteristics of
human eyes. Let Ri and Rj be two potential eye regions.
Then (Ri,Rj) corresponds to a pair of eyes if the following
equations are satisfied:
?
•
1 <ai
1 <
bi< 3
aj
bj< 3
(3)
•
|θi− θj| < 20o
(4)
•
ai+ aj
2
< dij< 3ai+ aj
2
(5)
The parameters in (3) and (5) are chosen according to
the fact that for human eyes, if we denote by we and he
respectively the width and the height of an eye, the average
value for we/heis 2 and, averagely, the distance between two
eyes is dij= 2we[2]. Equation (4) is based on the fact that
the two major axis should have the same orientation. A final
constraint is the alignment of the two major axis, i.e. for two
eye regions they belong to the same line.
Using these rules, the algorithm sometimes detects not only
eyes, but also eyebrows. To discard regions corresponding to
eyebrows, we use the fact that the center part of an eye region
is darker than other parts. Then a simple histogram analysis
of the region is done for selecting eye regions, since, an eye
region should exhibit two peaks while an eyebrow region
shows only one. An example of eye detection result is shown
in Fig. 1. Once eyes are detected, the position of the nose is
obtained based on the symmetry of facial features.
IV. ROBUST TRACKING ALGORITHM
As mention before, the main problem with points tracking
methods such as KLT or block matching, is the loss of points
during tracking. A point may be lost because of different
reasons. In the context of facial features tracking, the main
causes include illumination variation, head motion, temporary
occlusion, or gradual error accumulation. Moreover, in case
of fast head motion, there is a large interframe displacement
and the correct positions of facial features are lost rapidily.
Nevertheless, lost points can be detected and their correct
positions can be recovered. This strategy has been adopted
by Bourel et al. [13] who propose a method to recover lost
points using their known positions in previous frames and
some knowledge about the type of each individual feature.
Instead of recovering lost points, our goal is to design a robust
tracking method which avoid imprecisions in facial features
localization.
A. Using geometric constraints through a relaxation scheme
Imprecisions of tracking algorithms are due to the fact that
the features are tracked individually. Thus, a facial feature’s
position is estimated from frame to frame independently from
the positions of other features. However, one knows that the
positions of facial features are not independent and are related
by some geometric constraints. These constraints are imposed
by the configuration of human faces and can be employed in
the tracking algorithm through a relaxation scheme.
Let us consider two sets of features u = {u1,...,un} and
v = {v1,...,vm}, from two different images It and It+1.
If we define for each feature ui a set of initial probabilities
p0
associated with vk, then, a relaxation process is designed
to update the probabilities until a consistent distribution is
reached [16]. One standard updating rule is:
i(k),k = 1,...,m; p0
i(k) being the probability that ui is
pt+1
i
(k) =
pt
kpt
i(k)qt
i(k)qt
i(k)
i(k),
?
??
(6)
where
qt
i(k) =
?
j
wij
l
pij(k,l)pt
j(l)
?
,
(7)
and pij(k,l) is the probability that feature uican be associated
with feature vkunder the condition that feature ujis associated
with vl. The scalars wijare weights that indicate the relative
influence of neighbourhing features on each other.
The conditional probabilities, pij(k,l), represent the contex-
tual information that helps improving consistency and, thus,
insure that correct features are associated. In our application of
facial features tracking, we can use the constraints imposed by
the configuration of human faces to compute these conditional
probabilities. For example, if we are tracking the two eyes
and the nose, then the triangle formed by these three features
must be preserved from frame to frame. In other words,
the displacement of all three features are interrelated. The
geometric constraints can be expressed, in terms of conditional
probabilities, as follows:
pij(k,l) =
?
j??=i; j??=j
l??=k; l??=l
f(|(
?
− − − →
uj?ui,− − − →
uj?uj)−(
?
− − →
vl?vk,− − →
vl?vl)|) e
−(|
dkl?
dij?−
dll?
djj?|)
(8)
where the function f is defined by:
f(x) =
?
1−x
η
0
if x < η
otherwise
The different terms in (8) have following meanings:
• pij(k,l) is the probability that feature uican be associ-
ated with feature vkunder the condition that its neighbour
ujis associated with vl.
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• dij is the Euclidean distance between feature ui and
feature uj.
• (
− − − →
uj?uj.
Therefore, for any feature uiand for each of its neighbour
uj, the triangles formed by ui, ujand any other feature u?
preserved in the image sequence. Note that since the number
of features being tracked is generally small, all features are
considered to be neighbours with one another.
?
− − − →
uj?uiand− − − →
uj?ui,− − − →
uj?uj) is the angle formed by the two vectors
j, are
B. Self-reinitialization
In the proposed tracking method, as well as in the KLT or
block matching methods, one has to specify a search window
size. In order to make this parameter independent from the
considered sequence, we set the search window size to be
equal to the distance between the two eyes. This has the
effect of automatically scaling the window for every sequence.
However, a problem arises if the person moves towards or
away from the camera. In that case, the window size is not
adapted since the distance between eyes in the current frame
is different from the distance computed in the first frame.
To overcome this issue, we introduce a reinitialization of
the tracking procedure using the eye detector described in
Section III-B. For each frame It, we define a measure Qt
of the precision of the tracking method by:
Qt= min{sc(ut
i,vt−1
i
) is the correlation coefficient between a
window centered at feature uiin Itand a window centered at
its corresponding position viin frame It−1. If Qtexceeds a
defined threshold, then the tracking procedure is reinitialized
using the eye detector to get the new positions and search
window size.
i,vt−1
i
), i = 2,...,n},
(9)
where sc(ut
V. EXPERIMENTAL RESULTS
In this section, we show experimental results obtained by the
proposed detection and tracking methods. For facial features
detection, we use the AR face database [20] in order to
compare our results with those described by Song et al. [6] and
Kawaguchi and Rizon [8], who used the same database. For
tracking, we used a set of 5 image sequences showing small,
medium and large interframe displacement. The sequences are
in MPEG1 format, 320x240 color pixels and at 25 frames per
second.
A. Facial features detection
The AR face database contains color images of frontal view
faces with different facial expressions, illumination condition
and occlusions. For a direct comparison, we used the same
subset of the database employed in [6] and [8], which contains
63 images.
A commonly used criterion for the performance evaluation
of an eye detection method is the relative error defined
by [21]:
err =max(dl,dr)
dlr
,
(10)
where dlis the left eye disparity, i.e. the distance between the
manually detected eye position and the automatically detected
position, dris the right eye disparity, and dlris the Euclidean
distance between the manually detected left and right eye
positions. In [6], the detection is considered to be correct if
err < 0.25.
Using this criterion, the proposed detection method achieves
a performance of 100% correct detection. An example of
detection result is shown in Fig. 1c.
For comparison, Kawaguchi and Rizon [8] reported a cor-
rect detection rate of 96.8%, and Song et al. [6] a correct
detection rate of 98.4%. The methods in [8] and [6] can deal
with gray scale images but they need the detection of the
reflected light dots as a cue for eye localization, which is not
needed by our approach.
B. Facial features tracking
Given a sequence, we use the detection method described
in Section III-B to detect eyes in the first frame. Then, three
facial features, the two eyes and the nose, are tracked using
the tracking method described in Section IV. We used five
sequences whose length varies between 60 and 600 frames.
The first three sequences show small interframe displacement,
while the two last sequences contain fast head motion and,
therefore, large interframe displacement.
For all of the 5 sequences used in our experiments, facial
features have been correctly tracked with no loss despite large
head motion in some of the sequences. Figure 2 shows an
example of tracking results obtained by three methods, i.e.
the KLT tracker, the block matching method and our relaxation
based tracking, using Sequence #3. As it can be seen, the KLT
tracker gives good results for the first frames of the sequence,
but due to error accumulation, the features gradually drift
from their correct positions and are totally lost at frame 130.
The block matching method gives very poor results because
it is based on correlation only. On the contrary, considering
geometric constraints through the tracking procedure, our
method can correctly tracks all feature in the entire sequence.
For a quantitative evaluation, lets define a tracking error for
each facial feature in a sequence as follows:
? =
1
N
N
?
i=1
dispi,
(11)
where N is the lenght of the sequence, and dispi is the
Euclidean distance between the manually detected position of
the feature and its tracked position in frame i of the sequence.
For each sequence, we consider the mean value of the errors
for all facial features as the tracking error. Table I shows
tracking errors obtained by the three methods. As it can be
seen, our relaxation-based tracker gives the best results. In
particular, when the interframe displacement, i.e. the distance
between the position of the features in two succesive frames,
is large, both the KLT tracker and the block matching method
lead to important localization errors (Sequences #4 and #5).
In contrast, our approach gives very good results in such cases
as shown by an example in Fig 3.
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TABLE II
AVERAGE PROCESSING TIME WITH A 1.7 GHZ CPU
Block-Matching
44
23
KLT tracker
66
15
Our tracker
46
22
time per frame (ms)
# frames per second
Another important issue appears when one or both eyes are
closed. In that situation, the correlation based block matching
method and the KLT traker fail because patterns in consecutive
frames do not correspond. Considering the geometric rela-
tionship between features, makes our method robust to such
intensity variation. Thus, closed eyes are correctly tracked.
The results shown in Table II summarize the average
processing time needed for each of the three tracking method
on a 1.7 Ghz CPU personal computer. As it can be seen, one
important aspect of our method is that considering geometric
constraints through a relaxation scheme does not increase
the processing time per frame. This is because the number
of tracked features is very small. So our method provides
better results with a comparable processing time. Note that
the processing time for the KLT tracker in Table II includes
time needed to compute image derivatives.
VI. CONCLUSION
In this paper an efficient and robust facial features tracking
method is proposed. It is based on, first, detecting facial
features using a robust skin region detector which provides
face candidates. Then using some simple rules derived from
anthropological characteristics, eyes are selected within face
regions. Once facial features are detected, they are tracked
in the video sequence. We have shown how considering
geometric constraints between facial features can make the
tracking algorithm more robust and, thus, avoid the loss of
points and tracking drift.
Experiments with different sequences show that our tracking
method performs better than the well known KLT tracker with
comparable execution time, in particular when the interframe
displacement is large. It is also worth to mention that the
proposed tracking algorithm is not limited to facial features
tracking. It can be useful for general point tracking application.
However, both the detection and tracking algorithms
searches for facial features in frontal views. So, the method
do not apply for out of plane rotation. Trying to solve this
overcome could be an interesting future research direction.
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TABLE I
COMPARISON OF TRACKING ERRORS FOR FIVE SEQUENCES
Sequence #1
2.42
1.24
0.13
Sequence #2
8.05
5.81
0.89
Sequence #3
21.14
8.52
1.37
Sequence #4
33.77
14.27
2.16
Sequence #5
39.86
23.19
2.84
Block-Matching
KLT tracker
Our tracker
Fig. 2. Facial features tracking results. Each row shows the frames 1, 30, 80 and 130 of the sequence #3. First row: KLT tracker; Middle row: block matching
method; Last row: our tracking method.
Fig. 3.
shown.
A example of tracking result with our approach in the presence of large interframe displacement. Frames 1, 40, 60 and 110 of the sequence #5 are
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