International Journal of Scientific & Engineering Research Volume 2, Issue 10, Oct-2011 1
ISSN 2229-5518
Novel Defect Segmentation Technique in Random
Textured Tiles
Aborisade, D.O and Ojo, J. A.
Abstract— In this paper problem of detecting different type of defects on random textured tiles surfaces is addressed. Since Gabor filters allows optimal localization both in the spatial domain and in the spatial-frequency domain it is been utilized in the proposed technique to extract texture features which are useful for detecting defect edges on the tile. Kohonen’s Self-Organizing Maps (SOM) is used for reducing the feature vectors to obtain 1-dimensional feature map (scalar image). The output of the SOM is smoothed with Gaussian filtering mask and Canny’s edge edge-detection method is applied to the smoothed feature map image to obtain the edge map of the detected defect from the tile surface. The results obtained when the proposed technique is tested on various random texture tiles confirm its efficiency.
Index Terms— Detection of defect, Gabor filters, Self-Organizing Map, Canny operator.
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utomated visual inspection of industrial product has been received many attention nowadays. One of the industrial fields where an automated visual inspection for surface defect detection is most needed at the final
stage of manufacturing process is the tiles manufacturing
industry. The goal of the automatic surface defect detection
is to insure detection sensitivity with at least the same accuracy as the human visual inspectors. A lot of efforts have been made in the field of research on automatic techniques to detect various defects such as cracks, scratches, holes/ pitting, and lumps in random textured tiles. Numerous approaches to address the problem of detecting defects in ceramic, marble and granite tiles have been reported in literature [1], [2], [3], [4], [5]. All these methods have a limited range of application for some kind of tiles and defects. Recently, method based on multi-scale and multi-orientation such as Wavelet Transform and Gabor filters has been successfully and widely used in the detection of various classes of defects and related applications in textured images [6].
Following Mallat propositions on the use of pyramid structured wavelet transform for texture analysis [7], [8]
several studies have been carried out on texture analysis using wavelet transform [9], [10], [11]. As the Wavelet transforms posses only limited number of orientations, it is not commonly used in the field of defect detection for random texture images. Detection of defects in random
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Aborisade, David. O is currently a Senior Lecturer in the Department of Elect. / Elect. Engineering, LAUTECH. Ogbomoso, Nigeria. E-mail: doaborisade@yahoo.com
OJO, John Adedapo received his Ph.D. Degree in Electronic and
Electrical Engineering from LAUTECH. Ogbomoso, Nigeria in 2011. He is currently a Lecturer in the Department of Elect. / Elect. Engineering, LAUTECH., Ogbomoso, Nigeria. E-mail: dapojohn@yahoo.com
textured images requires multi-resolution decomposition of inspected image across several scales. Gabor filters can decompose an image into multiple orientations and scales. The impressive property of Gabor filters which allows optimal localization both in the spatial domain and in the spatial-frequency domain make it one of the most widely used approaches utilized for defect detection purpose in
random texture images.
Most work on the analysis of random textured tiles for defect detection is done using Wavelet transform, Gabor filters and other methods [12], [13], [14], [15], [16]. The main drawback that characterizes these approaches is there computational complexity. This paper thus find solution to the problem of real-time automatic defect detection and segmentation for textured tiles by employed multi-scale and multi-orientation Gabor filters along with Self Organizing Map (SOM). The proposed method has comparable improved performance at much faster speed than the existing methods.
The paper is organized as follows: Section 2 and 3 gives
a brief review of 2-D Gabor filter and SOM respectively
while the proposed method is discussed in Section 4. The
simulation results with different images are presented in
Section 5 to demonstrate the efficiency of the proposed algorithm. Finally, concluding remarks are given in Section 6.
Gabor filters are efficient for extracting texture features based on localized spatial frequency information, which are useful for further analysis such as edge detection and segmentation [17], [18]. The 1-D Gabor function was first defined by Gabor [19], and later extended to 2-D by Daugman [20], [21]. A 2-D Gabor filter is an oriented
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International Journal of Scientific & Engineering Research Volume 2, Issue 10, Oct-2011 2
ISSN 2229-5518
complex sinusoidal grating modulated by a 2-D Gaussian function, which is given by [18], [21], [22], [23]:
a way that topological-ordered relations are preserved [27], [28].
Basically, Kohonen’s SOM neural network consists of
hσ,ω,θ(x, y) gσ (x,y) exp2j xcos θ y sin θ
where
(1)
two layers [28]: the input buffer layer and a Kohonen layer consisting of L cells (neurons). Cells in Kohonen layer are
typically located on a regular low-dimensional grid, usually
gσ (x, y)
1
2π 2
exp[-(x2 y2 ) / 2 2 ], and j 1
(2)
1- or 2-dimensional lattice. Let x x1 , x 2 , , x n be input
is the Gaussian function (symmetric or asymmetric
vectors, and the weight of output layer j be represented by
depending on the application) with scale parameter σ . The parameters of a Gabor filter are, therefore, given by the
w w
j
, w j2
, , w jn
. When an input x is presented to
frequency ω , the orientation θ and the scale σ .
the network, the best matching unit (winning unit) is
The Gabor filter
h σ,ω,θ (x, y)
forms a complex valued
determined by
function. Decomposing it into real and imaginary parts gives
b ( x ) arg min x w j , i
j 1, 2, , N
(7)
hσ,ω,θ (x, y) Rσ,ω,θ (x, y) jIσ,ω,θ (x, y)
where
R σ,ω,θ (x, y) g σ (x, y) cos[2 (x cos y sin )]
(3)
where b ( x ) represents the index of the winning unit for the
input x and denotes the Euclidean norm.
The weights are updated as follows, once the winning unit and its topological neighbors are determined
I σ,ω,θ (x, y) g σ (x, y) sin[2 (x cos y sin )]
(t)[ x w (t)]
if j N
(t)
Gabor filters correspond to any linear filters, thus the most straightforward technique to perform the filtering
w (t 1)
j (t)
j b( x )
otherwise
(8)
operation is via the convolution in the spatial domain. The
where (t) is the learning rate at time t and N b( x ) (t) denote
Gabor-filtered output of a gray-level image
f(x,y) is
the neighborhood of the winning unit
b ( x ) . By this
obtained by the convolution of the image with the Gabor
filter hσ,ω,θ (u, v) , i.e.
learning rule, the weight vector
f(x u, y v) h
(u, v) dudv
(4)
b ( x ) moved towards the input vector x in the input space,
σ,ω,θ
and the topological ordering property emerges from this
Given a neighborhood window of size
k k
with
process.
k 2n 1
, the discrete convolutions of
f(x,y)
with
4. Defect Detection Technique
respective real and imaginary components of hσ,ω,θ(x, y) are
The proposed technique to detect defects in textured tile
n n
h (x,y)
f(x l,y m) R
(l,m)
(5a)
images commences by convolving the inspected sample
R
and
ln mn
σ,ω,θ
image
f (x, y) with each Gabor filter
hσ,ω,θ
(x, y) to obtain
n n the output
hI (x, y)
ln mn
f(x l, y m) I
σ,ω,θ
(l, m)
(5b)
I(x, y)
f(x, y) h F (x)
(9)
Energy E(x,y) at (x, y) within the window k k at a specific
frequency and at a specific orientation or direction is then
With four scales factor and image filtered in orthogonal
direction, thus 16-dimensional vectors I(x , y) are obtained
written as
E(x, y) h 2 (x, y) h 2 (x, y)
(6)
I(x, y) I
1 (x, y), , I16
(x, y)
(10)
R I Every pixel from the acquired image is characterized by
This captures the local features which are utilized for texture analysis purposes. An appropriate filter design with small convolution masks allows an efficient implementation of the Gabor filters in the spatial domain [24].
The Self-Organizing Map (SOM) algorithm proposed by Kohonen [25],[26] is a neural network model of the unsupervised class. SOM is used to visualize and interpret large high-dimensional data sets by projecting them to a
low dimensional output space, called a feature map, in such
a feature vector. A simplified characterization of texture based on relations between the pixels in restricted neighborhood is used. The gray-level values of neighboring pixels form the feature vector for every pixel. The feature vector does not pretend to provide an exhaustive characterization of texture, but they do implicitly capture certain local textural properties such as coarseness, directionality, regularity, etc.
The large dimension of feature vectors generates
computational and over-fitting problems. Now we are
faced with two conflicting goals. On one hand, it is
desirable to simplify the problem by reducing the
dimension of feature vectors. On the other hand, the
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International Journal of Scientific & Engineering Research Volume 2, Issue 10, Oct-2011 3
ISSN 2229-5518
original information content has to be preserved as much as possible. The Kohonen’s Self-Organizing Maps (SOM) offers a convenient way to control the tradeoff between simplifying the problem and loosing the information, and is
used over the vectors I(x, y) to generate a 1-dimensional
feature map . For each pixel (x, y) , the scalar index
P(x, y) of the reference vector closest to I(x, y) is assigned
In this section, the simulation results from the test database consisting of 150 textured tiles images with
256 256 pixels (8 bit grey level range) are presented.
Database images consist of 130 defective tiles in addition with 20 perfect tiles. The tiles used in our experiments were ceramic, granite, and marble of a size of at least
200 200 mm . The experiment is conducted using process
P(x, y) arg min I(x, y) w j
i
for all w j
(11)
described in Sect. 3. In the implementation, the tile images are decomposed using Gabor wavelets with the following
For each P(x, y) , eight sets of neighbors are defined as
parameters, frequency bandwidth
(ω 1.5),
four scale
shown in Fig. 1 [18]. The neighbors from the l direction are
factors (σ 1.5, 2, 2.5, and 3) , and four orientation angles
arranged as a vector [P l , , P l ],
P l N l
.To predict the
1 k k xy
(θ 0
, 45
, 90
, and 135 )
. The feature vectors for
center value
P(x, y)
from the neighbors, multilayer
training are extracted from a small image pitch of typically
perceptrons are trained with the relations,
65 65 pixels in the region of image having defect and in
the region of defect free image respectively. The
P(x, y) f l P l , , P l e l
l 1, , 8
(12)
1 k
The absolute error of prediction between P(x, y) and its
dimensions of feature vectors are substantially reduced
with the SOM. The SOM used for projecting the data
neighbors l
and sample variance of the prediction
nonlinearly onto a lower-dimensional display consists of 16
input nodes in the input layer and a 10x10 array of nodes in
errors are computed
e l (x, y) P(x, y) f l P l , , P l
(13)
the output layer. The resulting training vectors are smoothed by using a Gaussian filtering mask with σ 6.5
to reduce noise in the output image. Considering both the
8
2 (x, y) i 1
(e l (x, y)
8
(x, y)) 2
(14)
computational effort involved and the filtering quality, in
the proposed scheme, the sizes of the masks created from
the Gaussian smoothing filter and the optimal imaginary
where (x, y) is the mean of (e l (x, y)) 8 1 .
The Gaussian smoothing is performed on sample variance to remove local fluctuation effect.
U(x, y) G (x, y) 2 (x, y)
(15)
where, Gσ (x, y) denotes Gaussian filter and U denotes a smoothed variance image.
Canny’s edge-detection method is applied to the variance image U . The Canny operator works in a multi- stage process. First of all the image is smoothed by Gaussian convolution
Gabor filter are both set to 7 7 . Final edge map of the image is obtained after applying Canny’s edge detector with threshold value of 0.95.
The developed defect detection technique is run on
Pentium 450 MHz PC using a simple C program. The performance of the proposed technique is determined by visually assessing the binary output images. Figure 2 and 3 shows some of the corresponding segmentation results. The proposed scheme achieved a promising level of accuracy and robustness in textured tiles defect detection and can successfully segment the defects with different shapes,
different positions and different texture backgrounds.
where
K(x, y) Gσ (x, y) U(x, y)
(16)
1 x 2 y 2
G σ
2π 2
exp
2σ 2
(17)
Then gradient of K(x,y) is computed using Sobel operator
K 2 (x, y) K 2 (x, y)
(18)
and
x
θ (x, y) tan 1 K
y
y
(x, y) K x
(x, y)
(19)
Edge map is produced by thresholding the gradient magnitude
Figure 1: Eight sets of neighbors
M(x, y) Eτ
0
if M(x, y) τ
Otherwise
(20)
In this paper, a novel defect detection and segmentation scheme for textured tiles has been proposed. The technique combines concepts of multi-scale and multi-orientation
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International Journal of Scientific & Engineering Research Volume 2, Issue 10, Oct-2011 4
ISSN 2229-5518
Gabor filters along with SOM to locate the local surface defects on various textured tiles. In the proposed technique, Gabor filter parameters, such as, frequency bandwidth, the upper and lower center frequencies are chosen based on neurological findings, proposed in [6], [29]. The incorporation of feature extraction using SOM improves the performance and also reduces the complexity of the feature extraction and detection stages. A variety of typical defects are detected successfully and the ceramic tile defect segmentation results obtained by this method are found to be satisfactory. By the proposed method, a general improvement in the area of machine vision is achieved. The success of the proposed technique can be further improved by increasing the number of scales and orientations in Gabor decomposition and by varying the other Gabor filter parameters.
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