USING GRA FOR 2D INVARIANT OBJECT RECOGNITION

T.-H. Sun

, J. C. Liu

, C.-H. Tang

and F.-C. Tien

Department of Industrial Engineering and Management, Chaoyang University of Technology, Taiwan, R.O.C.

Department of Industrial Engineering and Management, National Taipei University of Technology

Section 3, Chung-Hsiao E. Road, Taipei 106, Taiwan, R.O.C.

Keywords: Invariant, KRA, GRA, K-curvature, Part recognition.

Abstract: Invariant features are vital to domain of pattern recognition. This research develops a vision-based invariant

recognizer for 2D object. We perform a recognition method which adopted KRA invariant feature extractor

and used grey relational analysis. The feature extraction is to derive translation, rotation, and scaling-free

features through the sequential boundary and is described with its K-curvature. Our work represents the

object profile with the K-curvature to obtain the position invariant property; and then the transformation of

autocorrelation is to ensure orientation-invariant property. Experimental also reveals that proposed method

with either GRA or MD methods offers distinctiveness and effectiveness for part recognition.

1 INTRODUCTION

Various working environments suggest that

automatic part recognition with invariant properties

is of priority concern issue. Khalil and Bayoumi

(2002a) developed a 2D invariant object recognition

method using continuous wavelet transform and

neural networks. After that, they defined three

invariant functions with dyadic wavelet

transformation of the object boundary to object

recognition (Khalil and Bayoumi 2002b). Zhang et

al. (2003) proposed an invariant 2D object

recognition approach by measuring the geodesic

distance between the observed object and a model in

the shape space. Cao et al. (2004) employed the

direction basis function (DBF) neural networks for

successful invariant object recognition. Kyrki et al.

(2004) utilized a Gabor filter to extract invariant

features for object recognition. Li and Lee (2004)

presented a Hopfield neural network model for

invariant object recognition using projective

transformations and the projective invariance was

embedded into the compatibility constraint for

finding point correspondences such that the problem

was formulated by minimizing the predefined

energy function through a Hopfield network. Huang

et al. (2005) proposed a scheme based on

independent component analysis (ICA) for object

recognition with affine transformation and for affine

motion estimation between video frames.

Sookhanaphibarn and Lursinsap (2006) proposed a

method for extracting the invariant features of a

color image based on the concept of principal

component analysis and a competitive learning

algorithm. Yu and Bennamoun (2007) developed

two complete sets of similarity invariant descriptors

using Fourier-Mellin transform and the analytical

Fourier-Mellin transform frameworks, and then

adopted 2D-PCA to simplify the invariant descriptor

for face recognition. Sun and Tien (2007) proposed

an invariant object recognition method by

incorporating the eigenvalue of covariance matrix

and autocorrelation with backpropagation neural

networks.

Using object profiles for object recognition is

one of the major fields in pattern recognition.

Therefore, boundary descriptor becomes an

important role to represent objects’ profiles.

Curvature, defined as the change rate of the slope,

has been widely employed in different applications

such as shape representation, feature extraction,

corner detection and object recognition. Different

numeric curvature estimation approaches have been

discussed in literature. Rosenfeld and Johnston

(1973) initially defined curvature as a K-cosine

function, where K denotes a region of support on the

boundary. Sohn et al. (1994) expressed curvature

with a formula involving its first- and second-order

directional derivatives. Tsai (1997) computed

108

Sun T., Liu J., Tang C. and Tien F. (2009).

USING GRA FOR 2D INVARIANT OBJECT RECOGNITION.

In Proceedings of the 11th International Conference on Enterprise Information Systems - Artiﬁcial Intelligence and Decision Support Systems, pages

109-112

DOI: 10.5220/0001958101090112

 SciTePress

directly the curvature by measuring the first- and

second-order derivatives of the continuous

functions. Later, Tsai et al. (1999) employed the

eigenvalue of covariance matrices to measure the

curvature and detect the sharp corners in a contour.

Tien et al. (2004) applied K-curvature to represent

the boundary of microdrills in order to detect the

defects. Sun (2008) adopted K-cosine to detect

corner of 2D digital objects in order to conduct

industrial inspection.

This study proposes a position, orientation, and

scale-invariant 2D object recognition method which

adopted a so-called KRA invariant feature extractor

and used grey relational analysis to recognize

objects.

2 GREY RELATIONAL

ANALYSIS

2.1 Grey Relational Analysis

Grey system theory (GTS) was first initiated by

Deng in 1982 (Deng, 1982; Deng, 1989). The

fundamentals of GRA can found in Chang and Yeh

(2005) and Jiang et al. (2002). The basic idea of

GRA is a ranking scheme that ranks the order of the

grey relationship among several subsystems. Jiang et

al. (2002) proposed a machine vision-based IC

marking identification using GRA. Chang and Yeh

(2005) developed a clustering algorithm based on

GRA. Song and Jamalipour (2005) developed a

network selection scheme that comprised AHP and

GRA for an integrated cellular/wireless LAN

system. Yeh and Chiang (2005) incorporated grey

relational analysis into the ART-2 network to

construct a GreyART network. Chen et al. (2007)

proposed a data-mining-based learning performance

assessment scheme by combining four

computational intelligence theories, including gray

relational analysis (GRA), K-means clustering

scheme, fuzzy association rule mining, and fuzzy

inference, in order to identify the learning

performance assessment rules using the gathered

Web-based learning portfolios of an individual

learner. Kung and Wen (2007) used six financial

indicators to classify twenty items of financial ratios

as research variables through the Globalization Grey

Relational Analysis (GRA), to find the significant

financial ratio variables and other financial

indicators affecting the financial performance of

venture capital enterprises. Hunag et al. (2008)

examined the potentials of the software effort

estimation model by integrating a genetic algorithm

(GA) to the GRA.

3 PROPOSED METHOD

The objective of this study is to develop an invariant

2D object recognition method for 2D object. The

framework of the proposed method is broadly

divided into: image acquisition and segmentation,

boundary representation and feature extraction, and

decision making, as shown in Figure 1.

Figure 1: Flow of the proposed method.

3.1 Image Acquisition

and Segmentation

Image acquisition is to acquire the digital

information of objects through a digitizer. Once

images are acquired, the image segmentation

procedure separates the digitized object from its

background. Thresholding is one of the most

commonly used methods for segmentation, in which

each pixel is converted into a binary value using a

pre-specified value (T). Pixels whose grey values are

higher than the threshold are given the binary value

255 (white), while pixels whose grey values are

lower than the threshold are given the binary value 0

(black). The thresholding process is usually

conducted using the following rule (Gonzalez and

Woods, 2003)

⎩

⎨

⎧

≥

Tjif

jif

),( if 0

),( if 255

),(

(1)

where f(i, j) is the grey value at coordinates (i, j);

(i, j) denotes the new grey value after

USING GRA FOR 2D INVARIANT OBJECT RECOGNITION

109

segmentation; and T is the specified threshold. After

that, the boundary following algorithm is used to

extract the boundary information and store them in a

sequential array.

3.2 KRA Feature Extractor

The proposed KRA feature extraction is to derive

translation, rotation, and scaling-free features

through the sequential boundary.

3.2.1 Boundary Representation using

K-Curvature

K-curvature (also called K-cosine) is a curvature-

based boundary descriptor developed by Rosenfeld

and Johnston (1973). Accordly, the K-curvature (or

say K-cosine) is defined as below.

<Definition > K-curvature

Given an object whose boundary is defined by

S={ P

| i=1, 2, 3, …, m}, the curvature (K-cosine) of

each boundary point P

is defined as

() ()

() cos

() ()

aK bK

⋅

(2)

As depicted in Figure 4,

)(Ka

i+K

−

)(Kb

i−K

−

, θ denotes the angle between

)(Ka

and

)(Kb

, and K is a natural number (N).

3.2.2 Re-sampling of K-Curvature

The boundary representation derived previously is

scale dependent. Figure 2 shows the boundary

representation of the original object (912 points)

when the size is reduced to 1/4 (428 points). The

total number of boundary point is approximately

reduced to 1/2, but its profile remains similar. Thus,

this study re-samples the boundaries of digital

objects with different scales and converts them into

the same number such that the scaling-invariant

property is obtained. This process is achieved by

simply sampling the K-curvature proportionally to

the numbers of c

(K) extracted.

Note: Totally, there are 428 boundary points (s=30)

Figure 2: Boundary representation with different scales.

3.2.3 Autocorrelation Transformation

Autocorrelations have been widely used features for

1D and 2D signal classification in a range of appli-

cations such as character recognition, texture

classification, face detection and recognition, signal

classification and so forth (Popovici and Thiran,

2004). Autocorrelation coefficient provides

important information about matching pattern in

time series data. The formula of autocorrelation

coefficient of time lag L is as follow:

(r)( r)

(r)

ttL

−

∑

(3)

where

denotes autocorrelation coefficient, L is

the length of the time lag (L =1, 2,…, n); n is the

number of observations; r

denotes the value of the

variable at time t; and

denotes the mean of r

4 IMPLEMENTATION

The proposed method was implemented on a

personal computer (PC) with a USB controlled X-Y

Table and 2D objects were digitized through a

black/white CCD connected to a frame grabber.

Fifty synthetic testing images were first scanned at

resolution 640 × 480 (pixels) as shown in Figure 4

for verification. For each standard pattern, 10 test

patterns with various positions (T

, and T

randomly), orientations (30°, 60°, 90°, 150°, 200°,

300°) and scales (S

=1/4 reduction, 50% and S

=1/8

reduction

25%) were created. Therefore, there were

500 test patterns for validation. All standard and test

patterns then were segmented with a pre-determined

threshold and stored as binary images. For the image

pre-processing such as color image thresholding and

boundary following, the library of e-Vision image

processing software (EasyAccess 6.5) was used. The

rest of the recognition processes were implemented

Figure 3: Standard part patterns and testing images.

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100

10 20 30 40 50 60 70 80 90 100

Number of Testing Images

Recognition Rat

GRA

Figure 4: Recognition trends of different methods.

in C++ language under Borland C++ Builder 6.0

environment.

An experiment was conducted to demonstrate the

effect for the proposed two classifiers when the

number of the testing objects increased from 10 to

100 to reveal the effect of number of objects.

Combining synthetic and real object images, the

study had 1000 testing images for validation. The

experimental results is shown in Figure 4.

Accordingly, the GRA-based method outperformed

minimum distance method (MD), even though the

MD method still owned 95% of recognition rate

when the number of patterns reaches 100.

5 CONCLUSIONS

Deriving invariant features is a crucial task in the

area of pattern recognition. This study proposes a

new translation, rotation, and scaling-free 2D object

recognition method, which adopts K-curvature

boundary representation to derive position-invariant

property, re-sampling to achieve scaling-invariant

property, and autocorrelation transform to obtain

orientation-invariant property. In addition, the

proposed method incorporated with Grey Relational

Analysis method to recognize the 2D digital objects

with a high recognition rate. A set of fifty synthetic

images, each of them was acquiring with ten

different positions, orientations and scales, were

used for validation, and another fifty real objects

were obtained for validation. Experimental results

also reveal that the proposed method with either

GRA or MD methods is effective and reliable for

part recognition. Conclusively, the proposed KRA

feature extractor incorporated with GRA classifier,

not only successfully obtained position, orientation,

and scaling- invariant features, but also classified the

features in an excellent performance. It is also

expected that the proposed method may be applied

to various applications such as part sorting,

automated visual inspection, robot positioning,

control and monitoring system.

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