# Face Recognition with Local Binary Pattern and Partial Matching 1. Introduction 1.1 Motivation 1.2 Problem and Proposed Solution 1.3 Thesis Organization 2. Related Work

Τεχνίτη Νοημοσύνη και Ρομποτική

18 Νοε 2013 (πριν από 4 χρόνια και 5 μήνες)

148 εμφανίσεις

Face Recognition with Local Binary Pattern and Partial Matching

1.

Introduction

1.1

Motivation

1.2

Problem and Proposed Solution

1.3

Thesis Organization

2.

Related Work

2.1

Face
Recognition

2.2

Local Binary Pattern

2.3

Partial Matching

3.

Implementation

3.1

Local Binary Pattern

3.2

Local Derivative Pattern

3.3

Partial Matching

3.4

Clustering

3.5

Multi
-

4.

Experiment

4.1

Data_sets

4.2

Supervised Learning

4.3

Un
-
supervised Learning

5.

Conclusion

5.1

Discussion

5.2

Future Works

6.

Reference

Chapter 1

Introduction

1.1

Motivation

Face recognition is one of the most popular topics in computer vision for more
than three decades. Many people study in how to

improve the accuracy in restricted
environment, such as frontal faces with indoor lighting. However, some other people
focus on how to achieve high accuracy in uncontrolled environment, such as outdoor
lighting or slanted faces. We are the last one, and w
e focus on the photos taken by
everyday people.

When people go on vacation, they always take a lot of pictures. We want to
design a system that can be easily for them to find out who are in the pictures, or who
are always in the same photos. In this case,
we are dealing with photos taken by
everyday people, called “Home Photos”. These home photos perhaps contain a lot of
noise or occlusion, people maybe didn’t look at cameras, or the luminance may not be
consistent.

1.2

Problem and Proposed Solution

When
we get the home photos, we use the “Face Detection” algorithm to get the
face images. And then, we use the “Face Alignment” method to crop and warp each
pair of eyes to same position and each face to the same size. We only use the gray
value of each pixel.

We use Local Binary Pattern (LBP) and Local Derivative Pattern (LDP) to
present a face. These two methods can encode each pixel to integral, which contains
the information of gray value of this pixel and its neighborhood. Then, we can define
some regions,

and count the histogram of those integral. The histograms are the final
presentation of each face image. These methods are not easily affected by global
change of illuminations and slight rotation of the face.

After we get the presentation of each face,
we cluster similar faces. We use
“Complete
-
Link Clustering” method to put some faces together. Complete
-
clustering will see each face as one cluster in the beginning, and merge two of clusters
each time if the similarity of any component pair in these

two clusters is greater than a
threshold. In this method, we can support the components in the same cluster are
similar enough.

We test the LDP and LBP in three datasets, including AR dataset and two sets of
home photos taken by ourselves. The accuracies
of LDP are not worse than LBP in all
three datasets.

(a)

(b)

(c)

(d)

(e)

Fig.

1

The prepared works of our system. First, when we get the home photos,
such as (a), we use face detection to get the face image, i.e. (b). Then we
use the face
alignment to get the location of eyes and other features, and the result is showing in
(c). And we can rotate the face images according to the location of eyes, such as (d).
Finally, we crop the face image into the same size.

(a)

(b)

(c)

(d)

Fig.

2

The process of our system. First, we use the normalized face images, which
is the result of prepared work, for instance, (a). And we divide the face images into
some overlapped patches, (b). In each patch, we use (c) as a desc
riptor to describe the
features of images. And finally, we will get the metric to describe the image, such as
(d).

1.3

Thesis Organization

The remaining parts of the paper are organized as follows: Section 2 proposes
the related works of face recognition
s. Section 3 presents the algorithm of my system.
Section 4 demos our experiment result of three datasets and other algorithm. Section 5
is the conclusion.

Chapter
2

Related Works

In this chapter, we wil
l introduce some related works.
We will

introduce the following
topic separately: Face Recognition exclusive Local Binary Patterns and Local Binary
Patterns, LBP and its extension, and partial matching.

2.1

Face Recognition

Because the face recognition topic has been studied for several decade
s, the
algorithms change again and again. H. Moon, et al.[] use the PCA
-
based method to
analysis the face images.
P
CA model will extract the most distinguish parameters of
face images, and we can use it to reduce the dimension of face images and build
eige
n
-
face. So we can easily to use it to recognize which subject the image belongs to.

Yi Ma, et al.[] develop a serious of Sparse Representation and Classification
algorithm to deal with face recognition problem. In this method, they will look each
face imag
e as a vector, and the most important idea of this algorithm is that each
vector of face image can be linear combination with some other vector of image and
some error. So the procedure of Sparse Representation and Classification of classify
each face imag
e is to build a metric
A

combined by all the training image vectors first
and de
fine the vector to classify is
y
. Then, solve the linear system min ||
A
x
-
y
||,
x

can
be taken as the weight of each training vector, so the larger
x
i

is, the more likely
y

and
I
i

belong to the same subject. The same group extends Sparse Representation system
to uncontrolled environment []. In this paper, they define a warping parameter
τ
,
which is some kind of transformation
, so that

each image vector
y
0

can perform a
warping vec
tor
y

=
y
0

τ
. Sparse Representation and Classification is one of the most
robust face recognition algorithm, however, it takes a lot of time in solving the sparse
matrix. The more training data, the more time it will need.

Xiujuan Chai, et al.[] develop an
other way, called Local Linear Regression (LLR).
They use one frontal face image and some non
-
frontal face images of special pose as
training data, and get the translation or warping parameters of transform from
non
-
frontal face image into frontal image. T
hen, when the testing images, including
frontal and non
-
frontal images, they can warp the non
-
frontal image into frontal
image, and it is easy to do the face recognition. In their study, the warping result of
upper part of face is better than the lower par
t. And it will lead to some ghost effect
because of warping.

2.
2

Local Binary Pattern

Local Binary Pattern (LBP) is one of the most popular methods for face recognition.
It is used in pattern analysis originally, but () [] use it in the face recognition area.
It
can encode one pixel in a gray
-
value image into a meaningful
label

by using the gray
value as a threshold to analysis the relationship with its neighbor.
And the a
uthors
divide the input image into several regions, then, they can calculate a local histogram
of the labels for each region, and combine the local histogram into a huge special
histogram. When compare the similarity of any two images, they need only calcu
late
the similarity of the special histogram using weighted chi
-
square distance. The
executing time of this algorithm is very short, and its accuracy in AR datasets can be
over 95%.

Xiaoyung Tan and Bill Triggs [] extend LBP in other way. They focus on the

problems under difficult lighting condition. Although the Local Binary Patterns are
robust for monotonic change of illumination, the lighting focus on some part will
affect the performance. X. Tan, et al. develop a general form of LBP, called Local
Ternar
y Pattern (LTP), which will be less sensitive to noise. The LBP cares only about
the subtraction value of neighborhood pixels and the middle pixel, and if the
subtraction is positive, it will be labeled as

1

, otherwise,

0

. But the LDP has more
choices.

LDP define a threshold, that if the absolute value of subtraction is smaller
than the threshold, it will be labeled as the third
choice ‘
2

. And LDP will generate
two labels for each pixel. The first one is taking label

2

as

1

, and generates a label
l
ike LBP. Another one is taking label

2

as

0

, and generates another label. Moreover,
X. Tan et al. use gamma correction, Difference of
Gaussian

contrast equalization, which is improve the performance very much.

Baochang Zhang,

et al. [] develop an extension of LBP in another way. They think the
LBP is failed to extract more detailed information contained in the input object. B.
Zhang, et al. introduce a general framework to encode directional pattern feature
based on local deri
vative variations, called Local Derivative Pattern. It will label each
pixel according to the gradient of this pixel and its neighbors. Using different order of
derivative and different directions will lead to different labels. The author found that
the pe
rformance of second
-
order derivation and four special degrees is best. And this
method can also imply to the Gabor Filter result, called G_LDP. And the performance
of LDP is better than the LBP. However, the dimension of LDP and G_LDP is much
higher than L
BP. The authors say it maybe can solve by using LDA to reduce the
dimension.

2.3

Partial Matching

Gang

Hua, et al. [] present a robust elastic and partial matching metric for face
recognition. It is always a problem to recognize face under different poses, different
face expression and partial occlusion. The authors develop a system that will divide
each i
nput image into N overlapping patches. When calculating the distance or
similarities of any two images, they will calculate the minima distance of each patch
in one image with the mapping patches (the patch in the same position and its
neighbors) in anothe
r image first. However, they will not use the distance of all
patches, but use one predefine ranking distance. So, they will ignore the occlusion
part, or quite different patches caused by different expressions or poses.

Fig.

The procedure of partial
matching. Quote from []. G. Hua, et al. use the eye
detection to identify the location of eyes. And the f vector means the 36
-
dimention
vector of each patch, which means 4 gradient value, and 9 regions as (f) shows.

3.

Implementation

In this section, we will introduce the algorithm we used and experimented. First, we
will introduce the Local Binary Pattern (LBP),
and Local Derivative Pattern (LDP).
And then we will describe partial matching and how to combine LBP and LDP with
partial m
atching.

3.1

Local Binary Pattern

This method is original used in the texture description. It is computational efficiency
and can distinguish two monotonic gray level images. And it is proven to be one of
the best performing texture descriptor. T. Ahonen,

etc.[] use it in the face recognition.

3.1.1

Local binary pattern and its extension

The LBP operator assigned a label to every pixel of a gray level image. The label
mapping to a pixel is affected by the relationship between this pixel and its eight
neig
hbors of the pixel. If we set the gray level image is I, and Z0 is one pixel in this
image. So we can define the operator as a function of Z0 and its neighbors, Z1, …, Z8.
(seeing Fig. 1.) And it can be written as:

T = t (Z0, Z0
-
Z1, Z0
-
Z2, …, Z0
-
Z8).

Howev
er, the LBP operator is not directly affected by the gray value of Z0, so we can
redefine the function as following:

T

t (Z0
-
Z1, Z0
-
Z2, …, Z0
-
Z8).

To simplify the function and ignore the scaling of grey level, we use only the sign of

of the exact value. So the operator function will become:

T

t (s(Z0
-
Z1), s(Z0
-
Z2), …, s(Z0
-
Z8)).

Where the s(.) is a binary function, defined as following:

s
(
x
)
=

{
1
,
if

x

0
0
,
otherwise
.

And we get the LBP result in the following function:

LBP

=

s
(
Z
0

Z
p
)

2
p
8
p
=
1
.

Overview of LBP operator, it takes the gray value of the center pixel as a threshold,
and if the gray value of its eight
-
neighborhood pixels is larger than the threshold, it
will assign ‘1’, otherwise, it will assign ‘0’. So, we will get eight bits an
d can consider
it as a label of this pixel. Then the histogram of the labels can be taken as the
descriptor of the gray level image.

Fig.

1.

8
-
neighborhood around Z
0

In order to dealing with the different size of image, T. Ojala, etc.,[] develop an
extension of LBP, that uses neighborhoods of different sizes. They define the notation
(P, R), which means P samples in a circle of radius R. See Figure 2 as an example of
circular neighborhoods. And LBP operator can be rewritten in a general form:

LBP
P
,
R

=

s
(
Z
0

Z
p
)

2
p
P

1
p
=
1
.

where Z1, …, Zp are the samples we take around Z0.

Fig. 2.

An example of circular neighborhood. (P, R) in (a) is (8, 1). (P, R) in (b) is
(16, 2). And (P, R) in (c) is (8, 2).

Fig. 3.

An example of LBP code. (a) is the origin
al gray value. (b) is the
difference of each neighbor with the middle pixel. (c) use only the sign of (b). And
the final label of the middle pixel will be “11010011”.
=
=
Another extension of the original LBP operator is called “uniform patterns”. A local
bi
nary pattern called uniform pattern is that the binary string of its label contains at
most two bitwise transitions from 0 to 1 or vice versa when the binary string is
considered circular. For example, the patterns 11111111 (0 transitions) and 00001110
(2
transitions) are uniform patterns, but the patterns 01010101 (8 transitions) and
01100110 (4 transitions) are not. In the most of case, the uniform patterns occur much
more than the non
-
uniform patterns. If we calculate the non
-
uniform patterns
separately,

it will decrease the performance. So, we can put all the non
-
uniform
patterns in the same bin when calculating the histogram.

Another variation of original LBP operator is called “rotation”. It is defined as:

LBP
P
,
R
ri
=
min
{
ROR
(
LBP
P
,
R
,
i
)
|
i
=
0
,

,
P

1
}
,

ROR(c, i)
means rotate c by i bits. This operator will take the binary string as a ring,
and all the rotation results of this ring are put in the same bin. For instance, the
patterns 00110000 and 00001100 will be considered as the same, the patterns
00101000 and 101
00000 are also the same. However, the patterns 00110000 and
00101000 are not in the same bins. When implement this operator, we will rotate the
binary string, and return the minimal decimal as a result. If any two patterns can
return same minimal decimal,
they will be seen as the same patterns. Otherwise, they
will be put in the different bins.

3.1.2

Face Description with LBP

The LBP method presents a descriptor of the image. It will count a histogram of the
LBP labels like following function:

H
i
=

{
LBP
(
x
,
y
)
=
i
}
x
,
y
,
i
=
0
,

,
n

1
.

n is the number of bins. If we use the uniform patterns, n will be 59. If we use the
rotation patterns, n will be 36. And if we use both the uniform and rotation patterns, n
will be 9.

However, the face images are different with typica
l texture images. The different
subregions in different part of face such as eyes, noses, or lips are totally different
with others. And if we ignore those differences and use only one descriptor to present
a face, it tend to average over the image are, so

the performance will drop down. Also,
using local features can be more robust against variations in pose or illumination.

So, as the reason presented above, we will divide the face image into some local
regions and LBP descriptors are extracted from each

region independently. The local
regions can be rectangle or circle, and can be overlapped with others. See Figure 3 as
an example of a face image divided into rectangle regions.

If we divide the face image into m local regions, notation as R0, R1, …, Rm
-
1
, we
can calculate the histogram separately in each region. The enhance histogram,
composed by R0, R1, …, Rm
-
1, has size m x n. So the histogram will be modified as
following:

H
i
,
j
=

{
I
(
x
,
y
)
|
LBP
(
x
,
y
)
=
i

and

(
x
,
y
)

R
j
}
x
,
y
.

We can summarize the LBP system shortly: the

pixel value in the face image can
affect the LBP label nearby, the label can make up the histogram of local region, and
the histograms of all the local regions can form spatially enhanced histograms, which
is the descriptor of the face image.

Fig. 4

Examples of local regions. The local regions don’t need to be the same

=
=
=
c楧⸠.
=
䅮⁥xa浰me⁯映獰=瑩a汬y=e湨n湣e搠桩獴潧ra洮⁅mc栠hree渠扯n⁩渠⡡⤠楳⁡=

=
calc畬慴u⁴桥⁨楳=潧ra浳⁩渠nac栠汯捡氠牥g楯渠i湤npe湤e湴ny.=

=

Fig.

6

Examples of the weighted used in the weighted Chi
-
Square
Distance. The
regions in red box are the border regions of the face images, and we give them lower
weight. The regions in the green box are in the middle of the face images, so we
they are more reliable and give them higher weight.

3.1.3

Similarity

After we have the descriptors of all face images, we need to evaluate the similarity of
any two face images. In the LBP system, we use the weight Chi Square distance:

χ
ω
2
(A, B)
=

𝜔

[

(

,




,

)
2

,

+


,


=
0
,

,


1
]

=
0
,

,

1
,

A
,
B
are spatially enhanced histograms of two face images, and
ω

are the weights in
each local region. In our system, we set the weight in the local region of the border of
the image is ‘1’, and in the other regions is ‘2’, because when cropping the face
images

from the original home photos, it is easy to contain some background. We
decrease the weight in the border region, so the influence of background will
decrease.

3.2

Local Derivative Pattern

Local Derivative Pattern is a general framework to encode direc
tive pattern feature
from local derivative various. The (n
-
1)
th
-
order local derivative various can encode
the nth
-
order LDP. In this concept, LBP can be considered as first
-
order local
derivative pattern with all direction. Compared to LBP, LDP can store m
ore
information of the gray level image.

3.2.1

Second
-
order Local Derivative Pattern

As we describe above, the nth
-
order LDP can be encoded by (n
-
1)
th
-
order local
derivative various, to calculate second
-
order LDP must calculate first
-
order derivative
vari
ous. Given an image
I
(
Z
), we calculate first
-
order derivatives along 0°, 45°, 90°
and 135° directions, which is denoted as
I’
α
(
Z
) where
α
= 0°, 45°, 90° and 135°. If
Z
0

is one point in
I
(
Z
),
Z
i
,
i

= 1, …, 8, are the 8 neighboring point around
Z
0

(see Fig. 1).
So the four first
-
order derivatives at
Z
=
Z
0

are

I’

(
Z
0
) =
I
(
Z
0
)

I
(
Z
4
)

I’
45°
(
Z
0
) =
I
(
Z
0
)

I
(
Z
3
)

I’
90°
(
Z
0
)

=
I
(
Z
0
)

I
(
Z
2
)

I’
135°
(
Z
0
) =
I
(
Z
0
)

I
(
Z
1
)

And the second
-
order directional LDP can be defined as

LDP
2
α
(
Z
0
) =

{
f
(
I’
α
(
Z
0
),
I’
α
(
Z
1
)),
f
(
I’
α
(
Z
0
),

I’
α
(
Z
2
)), …,
f
(
I’
α
(
Z
0
),

I’
α
(
Z
8
))}, α= 0°, 45°,
90° and 135°.

Where
f
(., .) is a binary function describe below:

𝑓
(

,

)
=

{
0
,
if


>

0
1
,
if



0
}

And the second
-
order LDP,
LDP
2
(
Z
), is defined as 32 bits
sequence, which is
concatenated by 8
-
bit directional LDP:

LDP
2
(
Z
) = {
LDP
2
α
(
Z
) |α= 0°, 45°, 90° and 135°}.

Fig.

7.

Meanings of “0” and “1” for the second
-

Z
0
, and ref. 2 is
one of the 8
-
neighbor of
Z
0
. The arrows mean the gradient

in each point. (a) result in
both cases are “0”. (b) result in both cases are “1”.
=
=
c楧u牥‷⁩=汵獴牡瑥猠瑨t⁴=a湳楴楯渠i渠n牡y
-
sca汥⁩la来猠瑯⁢楮慲y⁣潤e⸠f映瑨e⁬潣=氠
pattern is a “gradient turning” pattern (Fig 2. b), it is labeled as a “1”. Otherwis
e, the
gradient is monotonically increasing (Fig 2. a
-
2) or decreasing (Fig 2. a
-
1) in both
Z
0

and its neighbor, the result is labeled as a “0”.

Figure 8 demos the second
-
order LDP in 0°. First we calculate the first derivation of
each pixel. And then, we
can calculate the multiple of the first derivations between
operating pixel and its neighbors. In 0°, we will get LDP0° = “01010011”. As the
same, we will get LDP45° = “10001101”, LDP90° = “11010010” and LDP135° =
“01000010”.

Fig.

8.

The example of 0° se
cond
-
order LDP. (a) is the original gray value in some
local pattern. (b) is the first derivation of each pixel in 0°. (c) is the multiple result of
I’
0
°
(
Z
0
) and
I’
0
°
(
Z
1
). So we can get LDP0° = “01010011”.
=
=
3.2.2

Nth
-
order Directional Local Derivative Pat
tern

Like the second
-
order LDP, we can easily calculate the third
-
order LDP. What we
need to do first is to calculate the second derivation of the images. We can define the
second derivation as following:

I

(
Z
0
) =
2*
I
(
Z
0
)

I
(
Z
4
)

I
(
Z
8
)

I

45°
(
Z
0
) =
2*
I
(
Z
0
)

I
(
Z
3
)

I
(
Z
7
)

I

90°
(
Z
0
)

=
2*
I
(
Z
0
)

I
(
Z
2
)

I
(
Z
6
)

I

135°
(
Z
0
) =
2*
I
(
Z
0
)

I
(
Z
1
)

I
(
Z
5
)
.

And the LDP operator will become:

L
DP
3
α
(
Z
0
) = {
f
(
I

α
(
Z
0
),
I

α
(
Z
1
)),
f
(
I

α
(
Z
0
),

I

α
(
Z
2
)), …,
f
(
I

α
(
Z
0
),

I

α
(
Z
8
))}, α= 0°, 45°,
90° and 135°.

LDP
3
(
Z
) = {
LDP
3
α
(
Z
) |α= 0°, 45°, 90° and 135°}.

Figure 9 shows the same example with second
-
order LDP. We can calculate the
second derivation of each pixel, and calculate the third
-
order LDP. In the Figure 9, we
show the third
-
order LDP in

. And as the same, we can get the third
-
order LDP in
45
°
, 90
°

and 135
°
, they are

00100000

,

11010010

,
an
d

00101100

.

Fig.

9.

The third
-
order LDP. (a) shows the same example with Fig. 8. (b) is the
second
-
order derivatives in the middle nine pixels. U
sing the function (), we can get
result in (c). So, the LDP
3
0
°

is

〱〱㄰11

.
=

As same as the second
-
order LDP

and third
-
order LDP
, if we want to calculate the
nth
-
order LDP, we need to calculate the (n
-
1)
th
-
order derivatives along 0°, 45°, 90°
and 135° directions, denoted as
I
(n
-
1)
α
(
Z
),
α
= 0°, 45°, 90° and 135°. The nth
-
order LDP,
LDP
n
α
(
Z
0
), in
α

direction at
Z
=
Z
0
, is defined as

LDP
n
α
(
Z
0
) = {
f
(
I
(n
-
1)
(
Z
0
),
I
(n
-
1)
(
Z
1
)),
f
(
I
(n
-
1)
(
Z
0
),
I
(n
-
1)
(
Z
2
)), …,
f
(
I
(n
-
1)
(
Z
0
),
I
(n
-
1)
(
Z
8
))},

And the nth
-
order LDP is a local pattern string defined as

LDP
n
(
Z
) = {
LDP
n
α
(
Z
) |
α
= 0°, 45°, 90°, 135°}.

Even though [] says function () can not be easy to affect by noise, in our experiment,
if the noise is too large, the
performance of LDP is even worse than LBP. In order to
decrease the influence by this noise, we use bilateral filter first to smooth the noise.
We have tried Gaussian Smooth, the performance is better than the noise images.

3.2.3

Histogram

We will calcula
te one histogram for each direction, so there are four histograms in
each image. And we will use the rotation pattern we have described in sec. 3.1.1. So
the number of bin in each direction is 36.

And we use the spatially enhanced histogram just like LBP o
perator.

3.2.4

Compete with LBP

-
order LDP over LBP can be briefly summarized below.

1.

LDP can provide a more detailed description for face by encode the high
-
order
derivatives. However, LBP can only describe the pattern in
gray
-
scale value, not

2.

LBP encodes only the relationship between the central point and its neighbors, but
LDP encodes the various distinctive spatial relationships in a local region and,
therefore, contains more spatial information.

3.3

Parti
al Matching

We have described the representation of face images above. However, sometimes the
face images of same subjects are not quite similar, because of the occlusion or noise.
So we consider if there is a algorithm that can ignore the occlusion Partia
l Matching is
one of these algorithm.

3.3.1

Partial Matching

If we sample a local region every s pixels, and totally we have N = K × K local
regions for one face image, we can have a descriptor for total image:

F
=
|
f

mn
|
,
1
<

,

<
𝐾
,

where
f

mn

corresponds to
the descriptor extracted from local regions located at (m

s, n

s).

Now, if we have two
images

I
(1)

and
I
(2)
, we first calculate the similarity of each local
descriptor
f

ij

in I
(1)

and its neighbors in I
(2)
as following:

d
(
f
ij
(
1
)
)
=

min
k
,
l
:
|
i

s

k

s
|

r
,
|
j

s

l

s
|

r

f
ij
(
1
)

f
kl
(
2
)

1
,

f
ij
(1)

and f
kl
(2)

represent the local descriptor in images I
(1)

and I
(2)
.
A
nd r shows the how
many neighbors we allow to match for each local region. Then, we can get the sorted
result as following:

[
d
1
,
d
2
,

,
d
α
N
,

d
N
]
=

Sort
{
d
(
f
ij
(
1
)
)
}
i
,
j
=
1
K
.

And

we can define

d
(
I
(
1
)

I
(
2
)
)
=

d
α
N

as the directional distance from I
(1)

to I
(2)
, where

α

is a control parameter for partial
matching. So, as the function we describe above, partial matching can find out some
regions that are similar or different. We can c
hange

α

to control

the similarity we use.

Similarly, we can also define the distance from I
(2
) to I
(1)
. Often, d(I
(1)

I
(2)
) is
different from d(I
(2)

I
(1)
). To make the similarity symmetric, we define the distance
between two images are

D
(
I
(
1
)
,
I
(
2
)
)
=

max
{
d
(
I
(
1
)

I
(
2
)
)
,
d
(
I
(
2
)

I
(
1
)
)
}
.

Fig.

Example of local regions. If we define the width of local region is n, and
sample the local region every s pixels, we can get the first two local regions as the
images shows. The green box shows the first local region, and we go
on right, sample
the second regions, as the red box showing.

[
f
11
f
12
f
21
f
22

f
1K
f
2K

f
K1
f
K2

f
KK
]

Fig.

Example of representation of the face image. Every local region can make
up a descriptor, and we combine those descriptors to perform a descriptor for the
face
image.

Fig.

Example of partial matching for a local region. The green boxes in the two
image are in the same location. If we want to match the green box in (a), we find
some neighbors of green box in (b), such as the yellow boxes and green boxes (b). We
can use the va
lue of r to control the size of red box in (b). And we can get the distance
between the local region in (a) and the most similar local region in (b).

3.3.2

Partial Matching with LBP

As we describe in 3.1, LBP operator will count a histogram to represent e
ach local
region. So it is easy to combine LBP and partial matching. When implement these two
methods, we will calculate the LBP labels for each pixel first. Then, in each local
region, we count a histogram independently, and take it as vector f
ij
. The fol
lowing
procedures are same with section 3.3.1. For each local region in I
(1)
, we can find the
most similar region in the I
(2)
. Then we can set the distance from I
(1)

to I
(2)

are the
α

region distance if we sort the distance of all the local region.

3.3.3

One of the most common problems we will face when dealing with the home photos
is the occlusion. Sometimes people may wear the sun
glasse
s or hats, which may
cover the eyes of the subjects. In traditional LBP and LTP, features

around eyes and
eyebrows are the impotent. And if we use partial matching, it will look for some
similar local regions. So it may ignore the influence of the occlusion.

3.4

Clustering

When we get the similarity of any two images, we can divide those imag
es into
several clusters. We have tried kNN, and complete
-
each method in this section.

3.4.1

Nearest Neighbor

In this algorithm, we manage each image sequentially. First, we define there are no
existed clusters. And when the first image comes in, we will put it into the first cluster.
Then, while the second image comes, we calculate the similarity of the first clu
ster
and the second image. If they are similar enough, says similarity is larger than a
threshold, we can add the second image into the first cluster. However, if those two
images are not quite similar, we need to build a new cluster, and add the second
im
age into this cluster. Like the procedure of the second image, the nth image is
compared to the existed clusters. If the similarity of the existed cluster and nth image
is larger than the threshold, we can add nth image to those cluster. Nevertheless, we
n
eed to build a new cluster which contains only one component, nth image. To
notice that, we assume the representation of the cluster is the average of its
components, so that we can
calculate

the similarity of the images and clusters just
like calculating
the similarity between two images.

The advantage of this algorithm is that it is the quickest algorithm in our testing. It is
no need to calculate the similarity of any two images, but only the similarity of image
and existed clusters. However, the accurac
y of this method may be affected by the
sequence of the face images.

3.4.2

KNN

KNN is one of the most popular algorithms of clustering. In this algorithm, we need
to give system the value of k. And in the initial step, we random select k images in the
tot
al N images as seeds of kNN. Then, we need to calculate the similarity between all
images and seeds. And if the similarity of ith image
an
d the jth seed is largest, than
we can assigned ith image into jth cluster. All the images can be assigned to a cluste
r.
We can take the mean of each cluster as new seed of this cluster. And repeatedly, we
need to calculate the similarity of images and seeds. We will do the above procedure
several times until the cluster contribution will not change.

algorithm is that it is quickly when calculating the similarity of
seeds and images each time. However, it might need to repeat many times to get a
converge result. Even worse, it might get the local minima of the system, not the
optimal result. And, the
result may be influent by the random selected images in the
initial step.

Fig.

I
f we sample a and f as the initial seeds, we will
get the optimal clustering result like (b). However, if we sample a and d as the
initial

seeds, w
e will only get the local minima result like (c).

3.4.3

Complete
-

The clustering
algorithm
s describe above are not the perfect algorithm. So we tried
some hierarchical clustering algorithm. We use complete
-
algor
-
link hierarchical clustering because it is too easy to merge
all the subjects into the same cluster in single
-
-
clustering, it will support all the components in the same cluster have strong
relati
onship with each other. The algorithm of complete
-
described in the following paragraph.

The main point of complete
-
link clustering is to build a tree according to each
pairwise
-
relationship between any two components in two clusters
. So, in the initial
step, we need to calculate all the similarity between any two identities in the dataset,
and sort the similarities. And also, we take each identity as a cluster and put in a leaf
node. In the first step, we check the most similar pair
of identities. Because in their
cluster content only one component, themselves, we can see all the component in
this two clusters are similar enough, and then, we can merge these two clusters
together. In the tree structure, we can build a parent node of t
hese two leaf nodes. In
the second step, we check the second similar pair of identities. If all pairs of their
clusters are checked, which means their similarities is larger than the pair we
process

now, we can merge these two clusters,
and also we will bu
ild a new parent node of
two cluster node.

Otherwise, we will do nothing. We will do the second step again
and again, until all pairs are processed. Then, we will get a tree, which root are
showing all the identities in the same cluster, and other nodes sh
ow some identities
in one cluster.

The complexity of worse case of complete
-
2
logn) if there are n
identities, because it needs to sort n
2

pairs. Except the high complexity, the
complete
-
link clustering perform better than kNN and nearest neighbor.

Fig.

Example of complete
-
link clustering. (a) is the similarity of four identities.
(b) shows the sorting results of similarity. (c) shows t
he initial tree nodes. (d)
-
(i) are
the processing step of complete
-
and D are made up a cluster themselves, we can merge them to the same cluster,
and

build a new node (red one). Second, we deal with B
D. However, AD are in the
same cluster, so we need to consider the similarity of AB, too. The similarity of AB is
small
er than BD, because it is not handled. So we do nothing in this step. Third, we
deal with AB pair. In this step, we check BD pair,
and we know
the similarity of
BD
pair

is larger than AB pair. So we can merge AD cluster and B cluster, like (f) shows.
The
following steps are just the same with second and third step
. And In the sixth
step, we can get a final result tree.

Fig.

If we
set a threshold = 5, which means only the pair whose similarity is
larger than 5 will be accepted to be the same cluster, we will get the result as (a).
ABD are in the same cluster, and C makes up a cluster itself.

3.5

Multi
-

To summarize all the st
eps in our system, it can be showing in the following.

We can find out that we need to do the first three steps for each face image, and the
result is independent to other images. And the forth step, calculating the similarity of
any two images are also

independent to other images except these two images. So, we
can use multithreads to parallel doing these steps.
In our implement, we
will

do it in
four
-
-
core system.

And it will have more than twice speed up.

4.

Experiment

4.1

Data sets

In our experiment, we mainly use three data sets. The first one is the AR dataset. We
use 7
or 14
images per subjects with different express and different light
ing
. In this
dataset, we totally use
881

images, so there are
120

individual subjects. Although
those subjects may have different express, they are still face to the camera and almost
on the same position. The other two data sets are provided by the members of our
laboratory. We ask them to provide some photos they took on vacation with friends, so
t
here might be several subjects in one photos. As we say before, we call these photos
“Home Photos”. In these home photos, subjects may locate at different part of images,
may not face to the camera, may have different position, and there might be different

lighting. To deal with those problems, the first job we do is to detecting where the
human faces are. And then, we need to do the face
-
aliment to each detected face, and
crop and warp each face images until the eyes of each face are located at almost the
same position and each face image have the same size. The first home
-
photo data
set
(Home Photos I) contains 30
9

images and there are 5 subjects, 2 males and 3 females.
The second home
-
photo data s
et (Home Photos II) contains
838

images and there are
8 sub
jects, 4 males and 4 females. In most of the experiments, we will focus on the
two home
-
photo data sets.

Different Express

Different Lighting

Fig.

Examples of AR datasets
.

Blur

Non
-
frontal
Image

Different
Express

Different
Lighting

Occlusion

Fig.

Examples of first home
-
photo dataset.

Blur

Non
-
frontal
Image

Different
Express

Different
Lighting

Occlusion

Fig.

Examples of second
home
-
photo dataset.

4.2

Supervised Learning

In this section, we introduce our experiment of supervised learning. For each data set,
we random select half of face images per subject for training, the remaining half for
testing.
The method we use to classif
y each image is k
-
nearest
-
neighborhood.
We will
do it for five times to get the average performance. The result is showing bellow.

AR

Home Photos I

Home Photos II

LBP

8
5.3521
%

92.7044%

93.1783
%

LDP

89.8113%

LBP + partial
matching

94.6479%

92.956%

95.7364%

LDP + partial
matching

85.9119%

Table.

The result of supervised learning.

AR

Home Photos I

Home Photos II

LBP

8.924s / 1.8056s

0.713s

/

2.422s

7.725s / 12.303s

LDP

3.909s

/

12.718s

LBP + partial
matching

220.840s /
11764.903s

59.941s /
1381.247s

150.352s /
4136.810s

LDP + partial
matching

364.938s /
9033.929s

Table.

Executing time of supervised learning.

T
he previous one is training
time, and the last one is the testing time.

One can see that the accuracy

using LDP
with

partial matching is higher than
all
other
method
s
. Furthermore, if
one

compare
s

the result of

LBP with and without partial
matching,
one

can find that the accuracy with partial matching is higher than the
accuracy without.
Especially, one can notice that
the accuracy of AR is improved the
most.
It was told us that the partial matching is useful in face recognition. However,
the calculating time of LBP with partial matching is much longer than the pure LBP,
even we use the multithread to compute the LBP and

the similarity.
In our experiment,
the ex
e
cuting time of pure LBP is about
200 minutes.
It is because the time to
compute the distance between two representations of images is 250ms in LBP with
partial matching, and 10ms in pure LBP.
It is a disadvantage if we want to implement
the partial matching in the real
-
time projects.

4.3 Unsupervised Learning

In this section, we will show some results of unsupervised learning. We mainly use
the clustering algorithm, such as complete
-
archical clustering algorithm or
kNN algorithm,
which we have described before.

LBP with partial matching performs better than pure LBP (as Figure ). And if r is
more than 0, the performance is much better than LBP.

It is because that our face
alignment is

not perfect. Sometimes, it will have one or two pixels error, and
sometimes, even we fix the location of eyes, the locations of noses or mouths are not
the same.

If we check the similarity of the neighbor local patches, maybe we will find
the correct mapp
ing patch of each patch. And the r value constrains the size of
neighborhood. If one patch locates at the middle of the face image, and another
locates at the border area, they must be not the same part of face.
However, partial
matching takes more

time

wh
en computing the similarity of two face images.

Fig.

The comparison of LBP, LDP with and without Partial Matching.

0
0.2
0.4
0.6
0.8
1
1.2
0
0.1
0.2
0.3
0.4
0.5
0.6
LBP
LDP
LBP+PartialMatching
LDP+PartialMatching

Fig.

The result of LBP with and without partial matching in unsupervised
learning using home photos II. The x
-
axle is the pair
-
wise recall and the y
-
axle is the
precision.

And we can change the parameter of alpha. Alpha value controls the similarity of the
pa
rtial matching. If we define alpha to 0, it means that we use the most similar patch
to define the similarity of two images. However, if we define alpha value to 1, it
means that we use the most different patch to calculate the similarity of two images.
To

under stand how alpha value affects our exam, we do the experiments with
different alpha values (see Fig.). As the result shows, if the alpha value is 0.5, the
performance is a little worse than 0.2 and 0.1. It is similar to the result of (partial
0
0.2
0.4
0.6
0.8
1
1.2
0
0.05
0.1
0.15
0.2
0.25
LBP+r0alpha0.2
LBP+r1alpha0.2
LBP+r2alpha0.2
LBP+r3alpha0.2
LBP+r4alpha0.2
LBP
0
0.2
0.4
0.6
0.8
1
1.2
0
0.1
0.2
0.3
0.4
LBP + PM (r=0)
LBP + PM (r=1)
LBP + PM (r=2)
LBP + PM (r=3)
LBP + PM (r=4)
LBP
matchin
g

). We think it is more reliable of more similar patches. If we set
alpha value to be 0, it might be the most similar patches. However, it might be the
chip with no information of who the subject is. If we set the alpha value to be 1, it will
indicate
the most different patch, and they are not reliable. So the alpha value is
smaller, the similarity is more reliable.

And we also try some other experiments. We wonder the descriptor of the local
patches will affect the performance or not. In the original
local binary pattern and
local derivative pattern, we used to describe a local patch with only one histogram.
However, when (partial matching

) describing their way to do the partial
matching, they use a concentric circle. So we imitate their way to use 9

histograms to
describing each local patch. The result is showing in Figure. The performance of
concentric circle descriptor is much better than the plant one. Maybe it is because
there are more spatial information if we use the concentric circle structure

to describe
each local patch. And if we use the plant structure, the label in the middle of a local
patch or in the edge could be look as the same.

Fig.

Example of different alpha value of partial matching.

Fig.

An example of different descripto
rs of local patches. The blue line uses the
concentric circle, similar with []. The red one uses no special structure to describe
local patches.

0
0.2
0.4
0.6
0.8
1
1.2
0
0.1
0.2
0.3
r3+alpha0
r3+alpha0.1
r3+alpha0.2
r3+alpha0.5
r3+alpha1
0
0.2
0.4
0.6
0.8
1
1.2
0
0.1
0.2
0.3
0.4
alpha=0
alpha=0.1
alpha=0.2
alpha-0.5
alpha=1
0
0.2
0.4
0.6
0.8
1
1.2
0
0.1
0.2
0.3
PM (r=3,sub-9)
PM (r=3,sub=1)
0
0.2
0.4
0.6
0.8
1
1.2
0
0.1
0.2
0.3
0.4
PM (r=4 sub=9)
PM (r=4 sub=1)

#Clusters

#Single
-
component
Clusters

precision

Time

Picasa Online

253

150

100%

< 1 second

Picasa PC

LBP

LDP

LBP + Partial
Matcing

LDP + Partial
Matching

(a)

#Clusters

#Single
-
component
Clusters

precision

Time

Picasa Online

99

75

100
%

< 10 seconds

Picasa PC

99

75

100
%

3 minutes

LBP

100

31

90.378%

3.641s

LDP

100

36

95.8221

11.797s

LBP + Partial
Matcing

100

39

99.4602%

1461.078s

LDP + Partial
Matching

100

59

81.5476%

8144.985s

(b)

Table.

The comparison of our result and Picasa web album.

And if we compare our result with Picasa web album, we can get the result
as
following. We put the same photos to Picasa Web album, but it can only find out part
of face. However, the Picasa almost don

t make mistakes, so the precision is very high,
and the executing time is very short in web version. And if we take a look at ou
r
result, we can find out that although we still make some mistakes. But the number of
clusters which contain only one component is much less than Picasa.

5.

Conclusion

5.1

Discussion

In this paper, we use both Local Binary Pattern and Pa
rtial Matching algorithm to deal
with face recognition problem. These two algorithms are both used in face recognition
before. However, they are not the perfect algorithms. So, in this paper, we try to
merge these two methods. We use the labels of local bi
nary pattern as the feature of
the face images. And then, we follow the partial matching algorithm to calculating the
similarity of any two face images. And as we demo before, the accuracy of our system
is better than previous works, including the Local Bi
nary Pattern and Partial Matching
algorithm. It is novel to combine these two algorithms.

To summarize the advantage of our system, it is suitable to use in the face recognition
problem of home photos. We use more dimensions to describe each patch than
ori
ginal Partial Matching algorithm. It will preserve more details than original one.
And compared to the Local Binary Pattern, we ignore some patches that are not
distinguished enough. We use a parameter alpha to control the similarity of two
images. This pa
rameter is usually set to 0.2, which means we use the patches that are
not so similar which may be in the cheek and contain less information, and we don’t
use the patches that are quite different, which are not reliable. So, to deal with home
photos, it wi
ll ignore the problem of different pose, or partial occlusion.

5.2

Future Work

Even though we have improved the accuracy of face recognition system, there are still
some problems. The biggest problem of our system is time
-
consuming. Because the
dimension
of each LBP histogram is about 59, and there are more than 3000 patches
in each image when calculating the partial match distance. Now we use 4 threads in
quar
-
code system, however, it takes about two hours in calculating the distances of
any two images of

514 images. We can apply the algorithms of this paper to the cloud
computing system in the future. The steps we use multithreads now are easily to apply
to cloud computing systems. And we can expect it will take less than one minute to
complete all the wo
rks.

Reference

[1]

T. Ahonen, A. Hadid, and M. Pietikainen. Face Recognition with Local Binary
Patterns. In
Proc
.

ECCV, 2004.

[2]

Gang Hua, Amir Akbarzadeh. A Robust Elastic and Partial Matching M
e
tric
for Face Recognition. In
Proc.

ICCV, 2009

[3]

Baochang Zhang, Yongsheng Gao. Local Derivative Pattern Versus Local
Binary Pattern: Face Recognition With High
-
Order Local Pattern Descriptor. In
IEEE Transactions on
Image

Processing, VOL. 19, No. 2, February 2010.