computervision project

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CVPR 2016 Submission #LL. CONFIDENTIAL REVIEW COPY. DO NOT DISTRIBUTE.
A Study on Face Alignment Algorithms
Anonymous CVPR submission
Paper ID LL
Abstract
This paper studies recent development in face align-
ment. We summarize and critique three regression based
face alignment algorithms. We also implement the super-
vised descent method. Our implementation gives reason-
able results compared to the one reported by the author.
1. Introduction
Face alignment, also known as facial feature detection,
refers to locating p facial landmarks x ∈ Rp
(such as eye
brows and corners of mouth) in a face image I ∈ Rm
of m pixels. Recently, regression based face alignment is
showing promising results. Basically, those methods try to
find a series of regression matrix Rk
, k = 1, 2, · · · that
maps the image data to the movement of landmarks ∆xk
such the initial landmarks x0
are refined progressively by
xk
= xk−1
+ ∆xk
to find the optimal landmarks loca-
tions x∗
. In this paper, we review three regression based
methods[14][10][13] and implement one of them[14].
2. Summarize and Critique
2.1. SDM:Supervised descent method
2.1.1 Problem formulation and algorithm
Supervised descent method[14] formulates the face align-
ment problem as a minimization problem
∆x∗
= argmin
∆x
f(∆x) = argmin
∆x
h(I(x0 + ∆x)) − φ∗
2
2
(1)
where h(I(x)) is the SIFT[9] feature extraction function
that calculates feature values of image I at landmarks x and
φ∗ = h(I(x∗
)) denotes the SIFT values at the ground truth
landmarks x∗
.
One classic method to solve minimization problems is
the Newton’s method [3]. Yet Newton’s method requires to
compute the inverse of the Hessian of the function, which
is not only computational expensive for large data size but
also infeasible for non-differentiable functions, such as the
SIFT operator here.
To overcome the limitation of Newton’s method, in-
stead of calculating the descent direction using the Hessian,
supervised descent method learns such descent directions
from training data. More specifically, the algorithm learns
a sequence of mapping matrix Rk that maps the local fea-
tures φ at landmark x to the motion of landmarks ∆x from
training dataset {Ii} with known landmarks {x∗
i }
argmin
Rk,bk
Ii xi
k
∆xki
∗ − Rk
φk
i − bk 2
(2)
and updates the location of landmarks by
xk
= xk−1
+ Rk−1
φk−1
+ bk−1
(3)
where ∆xki
∗ = x∗
i − xki
is the displacement between the
ground truth landmarks and the estimated landmarks at the
kth
stage for image i.
2.1.2 Evaluation and results
The algorithm is first validated on simple analytic functions
and compared to Newtons method. Then the algorithm was
tested on the LFPW datasets[2][12] and evaluated by the
distance between the landmarks found by the algorithm and
the ground truth landmarks provided. Finally the algorithm
was tested for facial feature tracking on video dataset[1][7]
where the algorithm tries to detect facial landmarks in each
frame.
Validation on analytic function shows the algorithm con-
verges faster than Newton’s method experimentally. Re-
sults on the LFPW dataset show the supervised descent
method outperforms two other recently proposed meth-
ods and the algorithm is also reported to work well on
video data (though no quantitative results are provided).
The method can handle images with illumination and pose
changes pretty well. Yet for face images with extreme posi-
tion change (such as a side face) and sever occlusion, the al-
gorithm shows large error as compared to the ground truth.
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2.2. LBF:Local binary features regression
2.2.1 Problem formulation and algorithm
SDM uses the classic SIFT method for feature extraction.
LBF[10] proposes to improve the accuracy of face align-
ment by learning local features from training data instead.
The argument is that such features are more adaptive to
specific task. By learning features from a local region the
method can take advantage of more discriminative features
and save computational effort by learning each feature in-
dependently in a local region. The noises in the learned fea-
tures are suppressed by using a global regression that maps
all learned features together to give the optimal motion of
landmarks,
To learn for the local features, the method takes a region
around the lth landmarks and learns the local features φl in
the region by solving
argmin
Rk
l ,φk
l Ii
πl ◦ ∆xki
∗ − Rk
l φk
l (Ii, xk
i ) 2
2 (4)
where πl◦ denotes the operator that gets the l th element
of ∆xki
∗ . Comparing to Eq(2) in the supervised descent
method, this method jointly learns a local feature φk
l and
a local mapping Rk
l instead of using SIFT to calculate φk
for all landmark locations and learning a global mapping
Rk
directly.
The author solves the learning problem in Eq(4) using
the standard regression random forest[4]. During testing,
each sample will traverse the trees until it reaches on leaf
node for each tree. Each dimension in φk
l is 1 if the sam-
ple reaches the corresponding leaf node and 0 otherwise,
resulting in a binary local feature that is highly sparse.
To suppress noise in the local feature, the algorithm dis-
cards the local mapping function Rk
l learns in Eq(4) and
instead learns a global mapping Rk
by solving the problem
that is similar with Eq(2), except that the features used is the
learned local binary features rather than SIFT features and a
L2 regularization on Rk
is needed as the learned local fea-
tures have a dimension much higher than SIFT. However,
due to the sparse nature of the features, the problem can be
solved easily using a dual coordinate descent method[6].
2.2.2 Evaluation and results
The algorithm is evaluated on the LFPW datasets [2][12]the
same as the one used in SDM and two other datasets,
”Hellen”[8] and ”300-W”[11] that have richer images and
landmarks. The results show that the algorithm achieves
comparable accuracy on the first two datasets as compared
to other methods including SDM and higher accuracy on
the third dataset which includes the first two as well as other
challenging images. The paper shows sample results of both
SDM and LBF. SDM fails on some images due to large
pose variation while LBF detects most landmarks correctly.
However, for images with poor illumination condition or
unusual expressions (such as a widely opened mouth), both
SDM and LBF fail.
Also, the speed of different algorithms is compared and
the proposed method is the fastest method that runs at 300+
frames per second (FPS). The author further evaluates a
faster version with smaller feature size which runs at 3000
FPS while achieving comparable accuracy as compared to
other methods.
2.3. HPO:Face alignment under poses and occlusion
Both SDM and LBF treat all landmarks equally without
considering occlusions and head poses explicitly. To han-
dle occlusion, HPO [13] proposes to take the visibility of
landmarks into account and learns a model to predict the
probability of landmark visibility. Such model is then used
to assist the face alignment by adding the visibility infor-
mation to local features and shape configuration around a
landmark.It also proposes to unify pose variation and oc-
clusion by treating invisible landmarks due to pose change
as a special case of occlusion.
First, the algorithm learns a function from training
dataset as well as synthetic data that gives a prior proba-
bility of possible occlusion patterns. For example, occlu-
sion usually happens in a block manner (Fig 1 a) where an
entire block of the face is missing while it is very unlikely
to have a face image where every other pixel is occluded
(like a checkboard in Fig 1 b ). Fig 1 shows example syn-
thetic data that models possible occlusion patterns and an-
other less likely block patterns. The probability function
Loss(c), where c represents the probability of each pos-
sible occlusion patterns to occur in an image of m pixels
and it is a vector of length 2m
. After learning Loss(c), the
probability of landmark visibility is learned by optimizing
argmin
∆pk,T k
∆pk
− Tk
φ(I, xk−1
) 2
2 + λEpk [Loss(c)]
s.t. pk
= pk−1
+ ∆pk
(5)
The algorithm solves the problem in Eq(5) iteratively by
optimizing the objective function with respect to ∆p and T.
Solving for T is a simple least square problem while solving
for ∆p is more complicated and gradient descent method is
used.
Given the predicted landmark visibility probabilities, the
algorithm updates the landmark locations by learning the
descent direction Rk
that maps local image features to
movement of landmarks. For occluded landmarks, the re-
gion around them is not facial part thus the local appearance
around them should be less useful in predicting landmark
locations. Therefore, the local features around landmark xk
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(a) Natural Occlusion (b) Checkboard-like Occlusion
Figure 1: Example synthetic data shows different occlusion
patterns (gray blocks). Small numbers indicate facial land-
marks.
is weighed by the corresponding visibility probability pk
.
Mathematically, this modifies Eq(2) to
argmin
Rk,bk
Ii xi
k
∆xki
∗ − Rk
[pk
φk
i ] 2
(6)
where the operator denotes the product between the visi-
bility probability and the feature vector around each of the
landmark.
2.3.1 Evaluation and Results
The algorithm was evaluated on three datasets, the LFPW
dataset[2][12] which is used by both SDM and LBF, the
Helen dataset[8] used by LBF and a new dataset that has
more occluded faces and larger pose variations[5]. The pro-
posed algorithm achieves comparable accuracy in terms of
the distance between ground truth and detected landmarks
on the first two datasets while outperforming SDM and LBF
on the third dataset. In general, the algorithm is able to
detect occluded landmarks and handle pose variance better
than SDM . However, the algorithm still fails for extreme
head poses. Besides, example images of occlusion detec-
tion shown in the paper all have a nearly fronted pose, which
should reduce the complexity of occlusion detection. These
observations suggest that the power of the occlusion model-
ing and the idea of viewing side faces as a case of occlusion
is still limited.
In terms of computational efficiency, the algorithm is
slower than the previous two methods. The proposed al-
gorithm runs at 2 FPS while the SDM and LBF runs at 160
and 460 FPS respectively on the LFPW data base.
2.4. Discussion and Comparison
The three algorithms all aim at solving face alignment
problem using regression method and achieve promising re-
sults. Table 1 summarizes the quantitative results (mean ab-
solute error/FPS) obtained by the 3 algorithms on different
datasets, ”NA” indicates no result reported.
LFPW Helen 300-W COFW
SDM 3.49/160 5.85/21 7.52/70 6.69/NA
LBF 3.35/460 5.41/200 6.32/320 NA
HPO 3.93/2 5.49/2 NA 5.18/2
Table 1: Summary of quantitative results of different algo-
rithms
SPM proposes a general frame work to solve face align-
ment as an optimization problem without calculating the in-
verse of Hessian. The method is general to handle different
feature extraction functions as it does not impose any spe-
cific requirement such as differentiability. Also, the learn-
ing process requires solving a simple least square problem
only and appears to have a very fast convergence rate (4 or
5 steps) experimentally.
However, the underlying assumption for Rk to be the
optimal descent directions is that the entire dataset repre-
sents a set of similar functions with similar descent direc-
tions. Under this assumption, it is possible to average over
the training dataset and learn the descent directions that are
optimal for both training and testing data. If this assump-
tion does not hold, the algorithm can fail easily. Consider a
simple case where we sample two points of a function that
have opposite descent direction as training samples, aver-
aging over them will learn a 0 direction that leads the opti-
mization no where. This should also be the reason that the
algorithm fails on faces with extreme poses. Therefore, it
is very important to preprocess the dataset to make sure the
dataset is homogeneous. Details of such preprocessing will
be described in the experimental section.
LBF extends the SDM by learning local binary features,
which contributes to both computational efficiency and ac-
curacy of the algorithm. On the other hand, learning local
features also adds on model complexity and requires more
parameter tuning, such as the size of the local region for
the local feature learning process, which varies at differ-
ent training stages. The author proposes to perform cross-
validation to determine the optimal model parameters yet it
is not clear in the paper how stable the parameters are across
different datasets and how robust the method is to different
parameters.
HPO aims at resolving variation of head poses and oc-
clusions, which is a major challenge in face alignment and
proposes to view the two problems in a unified way. The
results show the method’s efficacy in detecting occluded
points and various poses yet the power still seems limited
for some extreme cases.
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3. Implementation of SDM
3.1. Face Detection with OpenCV
SDM algorithm requires predefined face location. The
face is detected with OpenCV’s Haar featured-based cas-
cade classifier. The face detection rate is 82.3% on LFPW
dataset. We discarded those images that cannot be detected
and ended up with 434 training images and 120 test im-
ages. The output from OpenCV’s face detector is a rectan-
gle which contains the region of the face. The face rectangle
will later be used as a reference to normalize the dataset and
initialize the algorithm.
3.2. Calculate Mean Face
The face detection information gathered from the previ-
ous step is used to center and normalize the face images
as well as the labeled landmarks. We normalized the face
rectangle to 200 pixels by 200 pixels and take 100 pixels
of padding from each side, since some of the labeled land-
marks is outside the face rectangle. We then used the nor-
malized landmarks position to generate the initial mean face
by calculating the mean position value of each landmark
from all images in the training dataset. This initial mean
face will be used in the initialization step of both learning
and predicting stage.
3.3. Learning Stage
3.3.1 Aligned Landmarks with the Face Position
The first step of SDM is generating the initial estimation of
facial landmarks based on the mean face shape we calcu-
lated in previous step and the variance of scale and trans-
lation of training face images. In our implementation, we
first resized the image based on the face size detected by
OpenCVs face detector; therefore initial face shape will be
the same across different images.
3.3.2 Extract HoG features from Landmarks
The next step is extracting the HoG features from patches
around the landmarks with size 32 pixels by 32 pixels. The
HoG features is equivalent to the SIFT features of fixed
scale and predefined local patch as described in the origi-
nal paper. The HoG features Given an image d ∈ m×1
of m pixels and x ∈ p×1
indexes p landmarks in the im-
age, we generated a feature vector φ(di
(x)) ∈ 128×1
per
landmark from the patch. The generated features for each
landmarks of the image is than concatenate into a vector
φ(di
(x)) ∈ 128p×1
, where p is the number of landmarks.
For the purpose of matrix calculation in MATLAB, we con-
catenate all feature vectors in the training dataset into a ma-
trix Φ ∈ n×128p
, where n is the number of images in train-
ing dataset and each row of the matrix is the transpose of
corresponding feature vector of that image.
Φ =









φ(d1
(x))T
φ(d2
(x))T
φ(d3
(x))T
...
φ(dn−1
(x))T
φ(dn
(x))T









(7)
3.3.3 Perform SDM Regression
The learning for SDM follows the Eq(2) and Eq(3). The
landmarks are predicted by a generic linear combination.
The SDM will learn a sequence of generic descent direction
Rk and bias term bk. To learn the generic descent direction
Rk and bias term bk, we minimized Eq(2), which is a well-
known linear least squares problem which can be solved in
closed form. To reformulate the equation in a matrix form,
we got
D = ΦA (8)
A =
bk
Rk (9)
D =









∆x1
∆x2
∆x3
...
∆xn−1
∆xn









, Φ =









1 φ1
1 φ2
1 φ3
...
...
1 φn−1
1 φn









(10)
where D ∈ n×2p
, Φ ∈ n×(128p+1)
and A ∈
(128p+1)×2p
. The dimension of D is n × 2p is because we
concatenate the x and y coordinate of the landmarks into a
row vectors, thus the length becomes two times the number
of landmarks. The close form solution for Eq(8) is
A = (ΦT
Φ)−1
ΦT
D (11)
One important implementation detail to notice is that to
perform the learning, the landmarks position need to be
normalized to a region of an unit square, i.e.∆ˆxk
=
∆xk
/s,where s is calculated as the distance between the
minimal and maximal coordinates among all landmarks xk
.
3.3.4 Recalculate the updated landmarks
After we learned the new Rk
and bk
, we can use these pa-
rameters to predict the new landmarks position by comput-
ing Eq(3). Since we normalized the landmark position to
a region of an unit square, we need to remapping the ∆xk
from Eq (1). back to its original dimension.
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3.3.5 Iterate the Learning Process
The new landmark position we got from 3.3.4 are now the
new initial land marks, and we can repeat the learning pro-
cess from 3.3.2 to 3.3.4 several times, and store the Rk
and
bk
value in each iteration. These values will be used in the
predicting stage later. The learning error decreases mono-
tonically, and the algorithm converges in less than five iter-
ations.
3.4. Predicting Stage
The steps in predicting stage is very similar to the learn-
ing stage. Instead of learning the R and b parameter in each
interation, we used the parameter R and b learned from
training data. The mean face we got from training data was
used to generate the initial landmark positions in the testing
stage. Eq(2) was used to compute the predicted landmark
position. Notice that the landmark positions also need to be
normalized to a region of an unit square when calculating
the ∆x.
Algorithm 1 SDM Learning Algorithm
1: function REGRESS(imgs, marks, ans)
2: marks ← normalized(marks)
3: Φ ← Features(imgs, tmpMarks)
4: ∆x ← ans − marks
5: Φ ← AddBias(Φ)
6: R ← (ΦT
Φ)−1
ΦT
∆x
7: ∆x ← ΦR
8: marks ← marks + Remap(∆x, faceRects)
9: return R, marks
10: function SDM TRAIN(imgs, marks, ans)
11: for k = 1 : 5 do
12: if First Iteration then
13: faceRects ← FaceDetect(imgs)
14: marks ← MeanFace(faceRects)
15: [R[k], marks] ←
Regress(imgs, marks, ans)
16: return R
4. Evaluation and Results
4.1. Dataset
In our experiment, we used the LFPW dataset the same
as the one in the paper. LFPW consists of 1,432 faces from
images download from the web and each image is labeled
with 35 fiducial landmarks by three MTurk workers. The 35
fiducial landmarks mark eyebrows (4 landmarks each), eyes
(5 landmarks each), nose (4 landmarks), mouse (5 land-
marks) and chin (1 landmark). We discarded the 6 land-
marks which labeled ears since ears are often covered by
Algorithm 2 SDM Predicting Algorithm
1: function REGRESS(imgs, R, marks)
2: marks ← normalized(marks)
3: Φ ← Features(imgs, tmpMarks)
4: Φ ← AddBias(Φ)
5: ∆x ← ΦR
6: marks ← marks + Remap(∆x, faceRects)
7: return marks
8: function SDM PREDICT(imge, R)
9: for cascade = 1 : 5 do
10: if First Iteration then
11: faceRects ← FaceDetect(imgs)
12: marks ← MeanFace(faceRects)
13: marks ← Regress(imgs, R[k], marks)
14: return marks
Figure 2: 29 Labeled Landmarks
hair in our dataset; therefore, 29 landmarks were used. Fig 2
shows the 29 labeled landmarks on an example image. Due
to the copyright issue, the dataset only contains URL to the
labeled images. Most of the URLs are no longer valid. We
downloaded 527 of the 1132 training images and 146 of the
300 test images.
(a) Initial mean face (b) Predicted landmarks
Figure 5: a) The initial mean face normalized using face
detector. b) The predicted landmarks after five iterations
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Figure 3: This top row shows the initial guess of the face landmarks. The bottom shows the predicted landmarks from SDM
algorithm after 5 iterations.
Figure 4: Example results on the YouTube Celebrities dataset.
4.2. Results
The author reported a mean error (×10−2
) of 3.47. Our
implementation shows a mean error(×10−2
) of 4.95. Con-
sidering that our dataset contains only one half of the im-
ages the original authors used, the difference between our
result and the original authors’ is acceptable. The smaller
dataset might make our learning model less representative
and more vulnerable to the face variance, such as the as-
pect ratio of the face, the distance between different organs,
and the orientation of the face, hence increase the alignment
error. Fig 5a shows an example of initial landmarks with
mean face normalized using the face detector and Fig 5b
shows the predicted landmarks using the SDM algorithm.
And the second row of Fig 3 demonstrates that the SDM
algorithm’s prediction is robust under different light condi-
tion, and a large variation in poses. Fig 4 shows example of
tracking result on YouTube Celebrities dataset. The result
video can be viewed at https://www.youtube.com/
watch?v=JCIR_BmhGfY. The processing time for the
SDM algorithm is around 0.055 seconds per frame.
5. Conclusion
In this paper, we summarize and compare three regres-
sion based face alignment algorithm. All three method re-
ports promising results. The first algorithm proposes a gen-
eral framework to learn regressor and the remaining two al-
gorithms extend the first one in terms of accuracy and ro-
bustness to occlusion. Our implementation of the first algo-
rithm reproduces its experiments on both image and video
data and achieves comparable result to the one reported.
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