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Automatic Face Recognition System using P-tree and K-Nearest Neighbor

ClassifierMohammad Kabir Hossain, Abu Ahmed Sayeem Reaz, Rajibul Alam, and Dr.William Perrizo*

Department of Computer Science and Engineering, North South University, Dhaka 1217

*Department of Computer Science, North Dakota State University, Fargo, ND 58105, USA

Emails: mkhossain@northsouth.edu, sayeem_reaz@yahoo.com, rajibulalam@hotmail.com,

william.perrizo@ndsu.nodak.edu

Abstract: Face recognition has recently received

remarkable attention in both authentication and

identification systems due to high acceptability and

collectability, regardless its lower circumvention and

uniqueness than other biometric verification

technologies. The basic approach with face recognition

commences with feature set construction from the

relevant facial traits of the users, termed enrollment [1].

When a user is to be authenticated (i.e. the user's

identity is to be verified), his/her facial sample is

captured and a feature set is created. This featureset is

then compared with the enrollment feature set. But feature set search mechanism is time consuming and

sometimes exhaustive. In this paper, a very efficient and

time saving search mechanism is proposed that exploits

the advantages of Peano Count Tree and K- Nearest

Neighbor Search techniques.

Keywords: Verification, Identification, Feature set,

Image processing, P-tree, bSQ format, Quadrant ID,

Euclidean similarity function, Minkwoski similarity

function, Manhattan distance, K-nearest neighbor

classifier.

1. INTRODUCTIONWhile research towards automatic face recognition

began in the late 1960's, progress has been slow.

Recently there has been renewed interest in the problem

due in part to its numerous security applications ranging

from identification of suspects in police databases to

identity verification at automatic teller machines [1].

Though automatic face recognition systems exhibit

higher FAR (False Acceptance Rate), the probability

that a sample falsely matches the presented face

identification record or feature sets, and FRR (False

Rejection Rate), the probability that a sample of the

right person is falsely rejected, than other successful

biometric systems like fingerprint or iris recognition, it is

attractive because of its wide-spread acceptability,

universality and easier acquisition.

Recognition is a step by step process and quite time-

consuming in case it has to deal with a large problem

domain. In applications like surveillance system, airport

and banking security, database search time is

significantly huge. Thus, development of real-timeapplication is a challenging task. In this paper our prime

concern has been reduction in database search time

during face matching phase. In order to achieve that

objective we have made use of the techniques of peano

count tree and k-nearest neighbor algorithm. The rest of

the paper is organized as follows: first a review of the

technology behind such an identification system and

then the proposed system.

2. RELATED CONCEPTS

Before we go through the identifier we need to know the

approaches and problem domains involved in such

systems.

2.1 ApproachesAutomatic face recognition divides into roughly two

lines of inquiry: feature based approaches which rely on

a feature set small in comparison to the number of

pixels, and direct image methods which involve no

intermediate feature extraction stage. The later method issubstantially susceptible to lighting condition. Whereas

in principle, feature-based schemes can be made

invariant to scale, rotation and/or illumination variations

and thus we are interested in them.

2.2 Problem Domains

Face recognition system serves two problem domains-

verification and identification. When a user is to be

authenticated (i.e. the user's identity is to be verified),samples will be captured from the device and again a

feature set is created. This featureset is then compared

with the enrollment feature set. If the resulting similarityvalue is above a predefined threshold, the user is

considered to be authenticated. In contrast to the

verification use case, with identification the (claimed)

identity of the user is not known in advance, but shall be

determined based on sample images of the user's face

and a set (population) of feature sets with known

identities. The identification system takes some samples

of the user's face, generates a feature set from them and

compares this feature set with each element of this

population. The elements yielding the highest

comparison values above a certain confidence thresholdare candidates for the identity wanted. In this paper, we

proposed a system that can serve both purposes.

3. PREVIEWS OF FACE IDENTIFIER

There are three main parts of the system. They are,

Image processing, Recognition algorithm, and Database

searching mechanism.

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3.1 Image Processing: Image capture: We can use digital camera to take an

individuals photo. In surveillance system video cameracontinuously takes photos. The video signal is converted

to a series of digital pictures.

Face finding: The first problem to be solved before

attempting face recognition is to locate the face in the

image. A number of algorithms are available for the task.Many authors [2,3,4] have discussed methods of

segmenting skin-tone regions from images, particularly

for finding faces and hands. There are also several

algorithms for face detection based on the intensity

pattern of the image.

3.2 Recognition Algorithm:Two steps are involved: Feature extraction and feature

matching.

1) Feature extraction: It involves extracting specific

facial traits (e.g., relative position of nose, eyes,

chinbones, chin, etc.) and then forming a tuple or featureset of those geometric attributes. We might use distances

of facial traits instead of positions as features. Also

discrete cosine transform coefficients of an image can be

used as features. Whatever the value of the features

might be we are getting a feature set which is importantfor the proposed system.

2) Feature matching: The feature set is then matched

with the feature sets of faces stored in the database.

3.3 Database Searching:A huge number of feature sets are stored in the database.

Database search should not be exhaustive. Efficient

search algorithm limits database search space.

4. PROPOSED FACE RECOGNITION SYSTEM

4.1 Introducing P-tree:

Well try to explain p-tree, based on how it organizes

spatial data. A P-tree is a quadrant-based tree. It

recursively divides an entire image into quadrants and

records the count of 1-bits for each quadrant, thus

forming a quadrant count tree. P-trees are somewhat

similar in construction to other data structures in the

literature (e.g. Quadtrees [5] and HHCodes [6] ).

For example, given an 8-row-8-column image of single

bits, its P-tree is as shown in Figure 1.

Figure 1. 8x8 image and its p-tree

In this example, 55 is the number of 1's in the entire

image. This root level is labeled level 0. The numbers

16, 8, 15, and 16 found at next level (level 1) are the 1-bit count for the four major quadrants in raster order, or

Z order (upper left, upper right, lower left and lower

right). Since the first and last level-1 quadrants are

composed entirely of 1-bits (called pure-1 quadrants),

sub-trees are not needed, and these branches terminate.Similarly, quadrants composed entirely of 0-bits are

called pure-0 quadrants, which also cause termination of

tree branches. This pattern is continued recursively using

Peano, or Z-ordering (recursive raster ordering), of the

four sub-quadrants at each new level. Eventually, every

branch terminates (since, at the "leaf" level, all quadrants

are pure). If we were to expand all sub-trees, including

those for pure quadrants, then the leaf sequence would

be the Peano-ordering of the image. Thus we use the

name Peano Count Tree [7].

A spatial image can be viewed as a 2-dimensional array

of pixels. Associated with each pixel are variousdescriptive attributes, called bands. For example, BMP

image has 3 bands- namely, Blue, Green and Red. An

image can also be viewed as a relational table where

each pixel is a tuple and each band is an attribute. The

primary key can be expressed as x-y coordinates.

4.2 Bit Sequential Format:

Data in relational table must be mapped to bit Sequencial

(bSQ) format for p-tree generation. Suppose in spatial

data a reflectance value in a band is a number in the

range 0-255 and is represented by a byte. We split each

band into eight separate files, one for each bit position.

In figure 2 we give a very simple illustrative example of

bSQ format with only two bands in a scene having only

four pixels (two rows and two columns). P-trees are

basically z-order-run-length-compressed, representations

of each bSQ file. So, we store the database not in

relational tables but in bSQ files.

Figure 2. bSQ formats for a two-band 2x2 image

4.3 Basic P-trees:

We reorganize each bit file of the bSQ format into a

basic p-tree. The definition of basic P-tree has been

given in [7] as written below:

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Definition 1: A basic P-tree Pi,j is a P-tree for the j

thbit

of the ith

band i.

4.4 Logical Operations on P-tree

The basic P-trees defined in Section 4.3 can be

combined using simple logical operations (AND, ORand COMPLEMENT) to produce P-trees for the original

values at any level of precision.

4.5 Value and Tuple P-trees

Definition 2: A value P-tree Pi (v) is the P-tree if value v

at band i. Value v can be expressed in 1-bit upto 8-bit

precision [7].

Value p-trees can be constructed by ANDing basic P-

trees or their complements. For example,

Pi (110) = Pi,1 AND Pi,2 AND Pi,3

Definition 3: A tuple P-tree P (v1, v2, , vn), is the P-

tree of value vi at band i, for all i from 1 to n [6]. We

have,

P (v1,v2, , vn) = P1(v1) AND P2(v2) AND ANDPn(vn)

4.6 Root-Count and Quadrant ID of a P-tree

The total number of 1s in a P-tree is called the root

count. The root count of a p-tree indicates the total

number of 1s in the image from where the P-tree was

built. We will assume P-trees are coded in a depth-first

ordering of the paths to each 1-quadrant. We use a

hierarchical quadrant id scheme to identify quadrants as

delineated in figure 3. At each level we append a sub-

quadrant id number (0 means upper left, 1 means upper

right, 2 means lower left, and 3 means lower right).

Figure 3. Quadrant id (Qid)

For a spatial data set with 2n-row and 2

n-column, there is

a mapping from raster coordinates (x,y) to Peano

coordinates (called quadrant id or Qid). If x and y are

expressed as n-bit strings, x1x2xn and y1y2yn then the

mapping is (x,y) = (x1x2xn, y1y2yn) (x1y1.x2y2

.xnyn). Thus in an 8 by 8 image, the pixel at (3,6) =

(011,110) has quadrant id 01.11.10 = (1.3.2). For

simplicity we wrote Qid as 132 instead of 1.3.2 in figure

3[8].

4.7 Matching Feature Set:

Each feature set can be viewed as a tuple in a relational

tablewhere each feature represents a particular attribute.

This is just like pixel values of an image where a featurecorresponds to a band of the image. Each tuple might

have index of form (x, y).

Let S = B1 x B2 x x Bd be a d-dimensional feature

space and B1, B2, , Bd are the dimensions or features

of S. We consider each tuple of the table as d-

dimensional vector v = . Enrolled feature

vectors would correspond to a myriad number of points

in S for a large database. During authentication a d-

dimensional feature vector of the face to be

authenticated is created the enrolled feature sets are

searched for a match. A distance metric is required to

measure the closeness of vectors. Various distance areavailable. For two data points, X =

and Y = , the Euclidean similarity

function is defined as [8]. In this paper a new matching

mechanism has been proposed where k-nearest

neighbors are searched that might use any of the distancemetrics mentioned above.

Example:

This example has been taken from [10]. The following

relation table contains 4 features of 4-bit data values.

Table 1. Feature sets in relational table

Index Features

X Y B1 B2 B3 B4

0,0

0,1

0,2

0,3

0011

0011

0111

0111

0111

0011

0011

0010

1000

1000

0100

0101

1011

1111

1011

1011

1,0

1,1

1,2

1,3

0011

0011

0111

0111

0111

0011

0011

0010

1000

1000

0100

0101

1011

1011

1011

1011

2,0

2,1

2,2

2,3

0010

0010

1010

1111

1011

1011

1010

1010

1000

1000

0100

0100

1111

1111

1011

1011

3,03,1

3,2

3,3

00101010

1111

1111

10111011

1010

1010

10001000

0100

0100

11111111

1011

1011

This dataset is converted in bSQ format. The feature-1

bit-bands would be like below if we display the bSQ

format in 2- dimension:

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B11 B12 B13 B14

0000 0011 1111 1111

0000 0011 1111 11110011 0001 1111 0001

0111 0011 1111 0011

There is a constraint on bSQ formation. P-tree requires

the number of rows and columns in bSQ file be multipleof four. In case, the number of tuples in database is not a

multiple of four we need to pad zero vectors at the end;

so that it is.

Now, for feature-1, basic p-trees are as follows (tree

pointers are omitted).

P1,1 P1,2 P1,3 P1,4

5 7 16 11

0014 0403 4403

0001 0111 0111

Value P-trees can be constructed from basic p-treesapplying a series of AND and COMPLEMENT

operations. Value p-tree construction process of P1,0011

has been shown below as an example:

P1,0011 = P1,1 AND P1,2 AND P1,3 AND P1,44 11 9 16 11

4000 4430 4041 4403

1110 1000 0111

From the value p-trees, we can generate tuple p-trees.

As an example tuple p-tree of tuple

0010,1011,1000,1111 is:

3

0 0 3 0

1 1 1 0

Figure 4. Tuple p-tree P0010,1011,1000,1111

Here 3 is the root count indicating the relational table

has three such tuples. The three leaves with value 1

indicate the quadrants where these tuples are residing.

These quadrants can be trivially mapped to indexes of

the relational table. In the example, the three leaves with

value 1 has Qids 2.0, 2.1 and 2.2 as read from the left to

right. The three Qids are mapped such way:

2.0 = 10.00 10,00 = (2,0)

2.1 = 10.01 10,01 = (2,1)

2.2 = 10.10 11,00 = (3,0)

Based on this idea, to identify a person, the recognition

system works as follows:

1) Basic p-trees of the enrolled feature sets areconstructed as preprocessing. This is a one-time

job.

2) Feature vector of the person to be recognized isextracted.

3) A tuple p-tree of this feature vector is generatedbased on the basic p-trees.

4) If the root count of this tuple p-tree is more thanzero, then we have one or more matches. The

indexes of those matched tuples at the relationaldatabase can be figured out using Qid to (x,y)

co-ordinate conversion technique discussed

above.

This is a nice way of feature matching, as it doesnt need

to scan the database at all. A few algebraic operations

perform the job. Besides, the AND operation which

produce the tuple p-trees is fast [11] Thus, we have a

framework for real-time recognition system.

4.8 Some Improvements:

Feature extraction method might introduce somedistortion or addition of noise, which is unavoidable. In

such cases, some disparity between extracted and

enrolled feature vectors of the same person might occur.

The above-mentioned system expects to match feature

vectors exactly. If an exact match is not found it fails torecognize. So, we assume the feature extraction process

to be perfect or propose some improvement.

If root count of the tuple p-tree for target feature vector

is zero we know there is no exact match. But it is

possible to know what are the nearest matches. We

propose K-nearest neighbor classifier to achieve that

objective, as it is simple and effective [13].

Given an unknown sample, a k-nearest neighbor

classifier searches the pattern space for the k training

samples that are closest to the unknown sample. These k

training samples are the k nearest neighbors of the

unknown sample [12]. Closeness is defined in terms of

Euclidean distance, where Euclidean distance between

two feature vectors, X = (x1, x2, , xn) and Y = (y1, y2,

, yn) is

=

=

1

1

22 )(),(

n

i

ii yxYXd

. It can be generalized to

Minkowski similarity function,

q

n

i

q

iiiq yxwYXd

=

=

1

1||),(

. If q = 1, it gives the

Manhattan distance, which is

=

=

1

1

1 ||),(n

i

iiyxYXd

.

Any selected distance metric can be used to find the k-

nearest neighbors. More on how lazy classifier works

using p-trees is given in [13].

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5. CONCLUSION

In this paper, we have tried to show, how we can applyp-tree concept in face recognition. Though, framework

for a whole system has been developed in this paper, we

concentrated only on database search mechanism. The

proposed mechanism can be applied not only in face but

also in other recognition system successfully for real-time system development.

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