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Dictionary learning framework for fabric defect
detection
ab
b
b
ac
Jian Zhou , Dimitri Semenovich , Arcot Sowmya & Jun Wang
a
College of Textiles, Donghua University, Shanghai, China.
b
School of Computer Science and Engineering, University of New South Wales, Sydney,
Australia.
c
Key Laboratory of Textile Science & Technology, Ministry of Education, Shanghai, China.
Published online: 30 Sep 2013.
To cite this article: Jian Zhou, Dimitri Semenovich, Arcot Sowmya & Jun Wang (2014) Dictionary learning framework for
fabric defect detection, The Journal of The Textile Institute, 105:3, 223-234, DOI: 10.1080/00405000.2013.836784
To link to this article: http://dx.doi.org/10.1080/00405000.2013.836784
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The Journal of The Textile Institute, 2014
Vol. 105, No. 3, 223–234, http://dx.doi.org/10.1080/00405000.2013.836784
Dictionary learning framework for fabric defect detection
Jian Zhoua,b, Dimitri Semenovichb, Arcot Sowmyab and Jun Wanga,c*
a
College of Textiles, Donghua University, Shanghai, China; bSchool of Computer Science and Engineering, University of New South
Wales, Sydney, Australia; cKey Laboratory of Textile Science & Technology, Ministry of Education, Shanghai, China
Downloaded by [The University of Manchester Library] at 00:08 12 November 2014
(Received 16 May 2013; accepted 9 August 2013)
We present a new approach using dictionary learning framework to address textile fabric defect detection. Textile fabrics
are textured materials whose images exhibit high periodicity among the repeated sub-patterns determined by weaving
structure. Inspired by the image de-noising using the learned dictionary, we learn a dictionary from patches of textile
fabric images, such a dictionary is able to approximate training samples well through a linear summation of its elements.
Fabric defects can be regarded as a local anomaly against the relatively homogeneous texture. When modelling new
samples with the dictionary learned from only the examples containing normal fabrics, the approximated version of an
abnormal or defective sample will no longer contain defective region, resulting in a larger dissimilarity than a normal
one, since the learned dictionary has been tuned to normal fabric structural features. Therefore, simply measuring the
similarity between the original and its approximation is able to efficiently discriminate defective samples from normal,
and a recently developed novelty detection algorithm, the support vector data description, is used to handle classification
task. Experimental results show that the proposed algorithm can control both false alarm rate and missing detection rate
within 5%, and extensions are also conducted.
Keywords: fabric defect detection; dictionary learning; novelty detection; image approximation
Introduction
In modern textile industry, defect detection on raw
woven fabrics is quite important for visual quality control, as the presence of defects has a great impact on
costs and grading of the final product. Suffering from
both low efficiency and high labour intensity with manual inspection, automated inspection using computer
vision has drawn a considerable attention in recent decades, and numerous algorithms have been proposed to
address the problem of fabric defect detection. Some survey work can be found in Kumar (2008) and Ngan,
Pang, and Yung (2011).
Fabric defects are mainly caused by unplanned
machine malfunctions or faulty yarns during weaving
process. Due to the characteristics of the weaving process used in fabric formation, images of normal textile
fabrics are dominated by texture, exhibiting high periodicity in warp and weft directions. If there is a defect
occurring in a fabric, the local regularity (periodicity) of
the fabric will be disrupted, causing a local anomaly
against its homogeneous texture background. Such
anomaly manifests in various ways, e.g. local structure
or intensity change, and in a broad sense, a defect
(anomalous region) in a fabric image can be defined as
any abnormality deriving from the homogeneous texture.
*Corresponding author. Email: junwang@dhu.edu.cn
Ó 2013 The Textile Institute
Therefore, the fabric defect detection can be considered
as a problem of identifying anomalous pixels/blocks in
image samples.
In terms of detection strategy, fabric defect
detection schemes can be loosely categorised into
feature-extraction-based and non-feature-extraction-based.
In the first approach, feature extraction is of great importance in fabric detection, which involves extracting efficient textural features in spatial and/or spectral domains
that are capable of robustly characterising background
fabric textures and sensitive to the abnormal regions
caused by defects. In the spatial domain, some commonly used texture features for detecting defects include
neighbouring information (Kumar, 2003), grey-level cooccurrence matrix (Wen, Chiu, Hsu, & Hsu, 2001) and
fractal dimensions (Bu & Huang, 2008; Sari-Sarraf &
Goddard, 1999); and in spectral domain, Fourier spectral
features (Chan, 2000), wavelet transform coefficients
(Kim & Kang, 2007; Yang, Pang, & Yung, 2004), Gabor
wavelet features (Hou & Parker, 2007) and auto-regressive spectral features (Bu, Huang, Wang, & Chen, 2010)
are used. However, feature extraction approach always
confronts feature selection problems, since there is no
straightforward way to guarantee the optimality of
features used in case of the absence of negative samples
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J. Zhou et al.
(defects) involving in training process. Of the non-feature extraction detection scheme, Gabor filter is considered to be the most successful approach for detecting
fabric defects (see Arivazhagan, Ganesan, & Bama,
2006; Escofet, Navarro, & Pladellorens, 1998; Kumar &
Pang, 2002) in that it does not need an explicit feature
extraction stage but utilises a set of optimised Gabor filters and segment defects from the filtered images
straightforwardly. However, the choice of filter parameters is a quite complicated task, since the detection
performance heavily relies on how the filters can match
or be tuned to the property of a specific defect, e.g. the
scale and orientation of a defect. Although several methods have been developed for optimisation of filter banks
(Bodnarova, Bennamoun, & Latham, 2002; Hou &
Parker, 2007; Kumar & Pang, 2002; Mak & Peng, 2008;
Srikaew, Attakitmongcol, Kumsawat, & Kidsang, 2011),
a prior knowledge (e.g. templates or defects) is still
required for optimising filters, e.g. artificial defects were
involved in training filters (Hou & Parker, 2007); limited
defect types were used to optimise filter parameters
(Kumar & Pang, 2002); non-defective samples were
required to optimise filters using a Gabor wavelet
network (Mak & Peng, 2008; Srikaew, Attakitmongcol,
Kumsawat, & Kidsang, 2011).
Ideally, if a normal fabric has homogeneous
sub-pattern and stable cycle, template-matching will
likely offer a good solution to the defect detection
problem. However, with the significant degree of
stochastic variation in normal fabric samples, choosing
suitable matching template and alignment render the
simple template-matching method a challenging task for
detecting defects, leaving little work has been done.
Inspired by the image de-noising techniques using
learned dictionaries and sparse representation (Elad &
Aharon, 2006), we present a fabric defect detection
framework via dictionary learning. The proposed method
is quite similar to template matching but using an adaptive template. In the image de-noising application, the target images are usually natural images and a small patch
size (e.g. 8 8) is used to capture local image features.
On contrary, textile fabric images are essentially synthetic
texture images with repetitive spatial structures (not random), whereby learning a dictionary from patches of
large size (e.g. 36 36) is effective for approximating
training samples well even with a very small dictionary.
The proposed detection framework involves learning
a dictionary from defect-free samples – such a dictionary
admits a linear representation of the training patches as a
summation of its elements. When modelling unknown
samples with the learned dictionary, normal patches can
be approximated well, since it has captured the key
features of normal samples, allowing for their natural
variation. On the other hand, any anomalous patches
(patches with defects) containing structural features not
found in normal samples cannot be modelled well, i.e.
causing substantial difference between the original and
its approximated version. The classifier adopted in this
paper is the support vector data description (SVDD), a
recently developed novelty detection algorithm. There
are some advantages of the proposed method:
(1) Taking advantage of repetitive texture, the
learned dictionary can efficiently model the natural variation of fabric textures.
(2) Using learned dictionary for approximation,
complex fabric defect can be converted to template-matching problem, and the defects can be
identified in a more natural way, not needing to
consider defect and fabric types, alleviating the
feature selection problem in some sense.
(3) Computational simplicity in detection stage
(online) makes it suitable for real-time applications.
Dictionary learning
The basic idea of approximating a signal is to find the
basic functions or vectors (called dictionary) whose linear combination can approximate the signal as close as
possible subject to certain constraints. Basically, finding
such a dictionary can be viewed as an optimisation problem measuring the quality of the approximation, e.g.
most useful l2 norm. Suppose that there is an M N data
matrix X ¼ ½x1 ; x2 ; . . . ; xN ; xi 2 RM that contains N
vectors of dimension M in its columns. Then, when l2
norm is used, the problem of finding such a specific dictionary can be generally formulated as follows:
min
D; a
N
X
2
kxi Dai k2 ;
s:t: 8j; kdj k 6 1;
ð1Þ
i¼1
where D ¼ ½d1 ; d2 ; . . . ; dK ; dj 2 RM , is the dictionary
needing to be learned, and ai 2 RK is the coefficient
vector for xi 2 X , and the constraint to dj is to prevent D
from having arbitrarily large values. In this work, since
we only use the data point xi obtained from normal
fabric images to learn dictionary with Equation (1), the
learned dictionary D will only capture the structural
features of the normal fabrics.
In Equation (1), both D and α are unknown, and how
to find D is referred as a dictionary learning problem
(Mairal, Bach, Ponce, & Sapiro, 2010), which is associated with matrix factorisation. This can be made more
explicit, when rewriting Equation (1) in matrix fashion:
2
min kX DAkF ;
D; A
ð2Þ
where A ¼ ½a1 ; a2 ; . . . ; aN ; ai 2 RK , is the coefficient
matrix. Generally, Equation (2) is a generic matrix
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The Journal of The Textile Institute
factorisation problem, which is also related to singular
value decomposition (SVD), independent components
analysis (ICA) and non-negative matrix factorisation
(NMF), depending on different constraints or/and objective functions imposed. SVD aims to constrain basis
functions of D to be orthogonal and ICA to constrain the
basic functions of D to be statistically independent.
NMF enforces all elements in both D and A to be nonnegative.
Since dictionary learning can be easily extended to
solve the matrix factorisation problem, e.g. NMF and
sparse coding (Mairal et al., 2010), the aforementioned
problems can be formulated with some extra constraints
as follows:
Singular value decomposition
min
D; a
N
X
kxi Dai k22 ; s:t: DT D ¼ I;
225
justified to handle defect detection as a novelty detection
task (Markou & Singh, 2003a, 2003b). Novelty
detection, also called one-class classification or outliers
detection, involves learning a model that can describe
normal data or normal status, and therefore can reject
any potential anomalous events against normality.
Novelty detection is quite useful to deal with those
applications which have plenty of normal samples, while
the negative samples (e.g. all possible types of defects)
are quite small or difficult to obtain.
SVDD is an effective algorithm for novelty detection
(Tax, 2001). The underlying idea of SVDD is to find
a minimal volume hyper-sphere which can enclose a
certain proportion of the training samples. Given a
training set of interest fxi g16i6n with n the total number
of training samples, the primal SVDD problem is defined
as follows (Tax, 2001):
ð3Þ
min R2 þ vN1
P
R;a;n
i¼1
ni
i
ð6Þ
2
where dictionary elements are orthogonal to each other.
Non-negative matrix factorisation
min
D; a
N
X
2
kxi Dai k2 ; s:t: D P 0; 8i; ai P 0;
ð4Þ
i¼1
where non-negative constraint is imposed on D and α.
Sparse representation
Sparse representation (SP) (Elad, 2010) can be seen as
an extension of Equation (1), which has recently led to
state of the art results in signal-processing task such as
image de-noising (Elad & Aharon, 2006) and classification tasks (Yang, Yu, Gong, & Huang, 2009; Yang,
Wang, & Huang, 2011). In this case, an over-complete
dictionary (K > M) is involved in representing a signal
in a sparse fashion, i.e. using as few elements as possible to achieve best approximation. To create sparse representation, an additional penalty measuring sparseness
of the coefficient αi is introduced, which can be formulated as:
min
D; a
N
X
2
ðkxi Dai k2 þ kkai k1 Þ; s:t: 8j; kdj k 6 1;
ð5Þ
i¼1
where k is a regularisation parameter controlling the
trade-off of approximation error and sparsity.
s:t:kxi ak 6 R2 þ ni ; ni P 0; 8i;
where R and a are the hyper-sphere radius and centre,
respectively; v 2 ð0; 1Þ is the parameter controlling the
trade-off between sphere volume and the errors; and ni
are slack variables to allow the possibility of outliers.
Since Equation (6) can only create a spherical boundary which is restrictive for many applications, kernel
functions are usually introduced to create a more flexible
data description, e.g. the Gaussian kernel function
jðx; yÞ ¼ expðckx yk2 Þ. The kernelised version of
Equation (6) can be obtained via its dual:
min
P
a
ai aj jðxi ; xj Þ P
ij
P
s:t:
i
ai jðxi ; xi Þ
i
ai ¼ 1; 0 6 ai 6 vN1 ; 8i;
ð7Þ
where jð; Þ is the kernel function and αi are the
Lagrange multipliers. This is a quadratic programming
problem and can be solved by standard algorithms. Let
a 2 Rn be a solution of Equation (7) then, heuristically,
the majority of its entries will be zero (the constraints in
this problem are analogous to an l1-norm penalty term).
The data points xi with a[0 are then called the support
vectors. Supposing that y is an unlabelled sample; then,
y will be classified as an outlier if its distance from the
centre a exceeds the hyper-sphere radius R:
jðy; yÞ 2
X
i
ai jðxi ; yÞ þ
X
ai aj jðxi ; xj Þ[R2 :
ð8Þ
i;j
Novelty detection using SVDD
Since fabric defects are quite different in their characteristics and scale, it is impossible to collect all potential
types of defects to train an algorithm, so it may then be
Considering the simplicity and flexibility of Gaussian
kernel, in this paper we also employ Gaussian kernel
2
function jðx; yÞ ¼ eckxyk . When Gaussian kernel is
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J. Zhou et al.
Figure 1. Image patch extraction and column vector formation.
used, there are two parameters v and c needing to be
determined before training SVDD according to Equation
(7). v 2 ð0; 1Þ is a user-specified parameter referring to
the rejection fraction of training samples, which can be
used to control the false alarm rate (FAR) (Bu, Wang, &
Huang, 2009).
Fabric defect detection using learned dictionary
Image patch extraction
The proposed framework is based on image patches,
which means any image patches containing defective
regions will be identified as defects. Image patches are
obtained from both overlapping and non-overlapping
ways, and the patch division with overlapping is
illustrated in Figure 1. Non-overlapping division means
the patches are divided sequentially without overlapping
in the image samples. In this paper, non-overlapping
division only appears in SVDD training stage (see in the
following Section). To apply Equation (1) to learn
dictionary for patch representation, each image patch is
converted into column vectors by concatenating columns
of patch, which is shown in Figure 1. Thereafter, image
patch equals to column vector without additional
specification.
Proposed approach
The whole detection framework is illustrated in Figure 2,
consisting of the following stages:
Dictionary learning stage
In this step, non-defective fabric images are partitioned
into small overlapping patches of w w pixels, allowing
for including a wider range of fabric structures into the
training data. Dictionary can be learned from the matrix
whose columns are image patches by Equation (1) (or
Equations (3)–(5)). Since the dictionaries are learned
from the normal fabrics, the learned dictionary will only
capture the normal structural features. Two groups of the
dictionary elements learned from a twill fabric and a
plain fabric are shown in Figure 3. Note that all the dictionary elements shown in Figure 3 are reshaped back
into w w patches for displaying.
SVDD training stage
Still obtaining a collect of w w pixels image patches
from defect-free images (non-overlapping), the learned
dictionary is used to approximate these patches, extracting similarity-based features to train SVDD classifier.
Testing stage
To perform defect detection, overlapping patches are
collected from the newly acquired fabric images and
features are computed as above. The patches are then
labelled with the trained SVDD classifier.
Figure 2. Overview of defect detection framework.
Feature extraction
To better understand how the proposed detection framework can discriminate defects from normal samples,
some of approximation examples using dictionary
learned from Equation (1) are presented in Figure 4.
Figure 4(a) is the defect-free patches and Figure 4(d) is
The Journal of The Textile Institute
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the defective versions of (a). Note the residual images
presented in Figure 4(c) and (f) show the difference
between originals and their approximated versions. For
227
defect-free patches, their approximated versions exhibit a
high degree of similarity to their originals (see light differences in Figure 4(c)); for the defective patches, the
defective regions do not appear in their approximated
versions, causing lower similarity to their originals (see
large differences in Figure 4(f)). This is because the
dictionaries have been tuned to normal structural
features, and imposing the error caused by the defective
regions not found in learning stage spreads the whole
approximation in order to pursue as small error as it can
provide. This motivates us to use the similarity between
the original and its approximated version as a feature to
discriminate defects.
Let y be a column vector representing one of these
patches and its approximation ^y can be computed by
solving the following least-square problem:
a ¼ arg min ky Dak2 ;
2
a
ð9Þ
^y ¼ Da :
In our framework, it is possible to measure the similarity between y and its approximation ^y. We select
Euclidean distance and correlation coefficient as similarity measurements, which are expected to capture intensity variation and structural disparities between y and ^y.
Then the two features can be calculated as,
Figure 3. Dictionary elements of normal fabric samples: (a)
and (c) are a twill fabric and a plain fabric images,
respectively; (b) and (d) 12 dictionary elements learned from
(a) and (c), respectively.
Feature 1: Euclidean distance F1 ¼ ky ^yk2 and
Feature 2: Correlation coefficient F2 ¼
ðyly ÞT ð^yl^y Þ
:
w2 ry r^y
Figure 4. Eight approximation examples. (a) defect-free patches; (b) approximated patches corresponding to (a); (c) residual images;
(d) defective patches; (e) approximated patches corresponding to (d); (f) residual images.
228
J. Zhou et al.
where ly , l^y and ry , r^y are the means and standard deviations of the vectors y and ^y, respectively.
Note that all the features are normalised onto [0, 1]
using Softmax scaling (Theodoridis & Koutroumbas,
2008) which is given by:
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x0 ¼
1
ðx lx Þ
1 þ exp
qrx
ð10Þ
where lx and rx are the mean and standard deviation of
x, respectively, and q is a constant set to 5 in this work.
The normalised features are then used to train the SVDD
classifier with Gaussian kernel.
Dictionary size
Before using learned dictionary to approximate image
patches, the cardinality K of dictionary D is the key
input to our method and needs to be determined beforehand. The parameter K directly controls the magnitude
of approximation error, which decreases monotonically
for all patches as K increases. To achieve effective defect
detection, we wish to find such a dictionary size that the
“normal” patches are able to be approximated well,
while anomalous patches are not. To be more specific,
the choice of a large value of K increases the undesired
possibility of capturing the appearance of anomalous
regions, lowering the discriminative power for identifying defective patches, while K taken to be too small will
result in under-fitting of normal patches, leading to a
high FAR.
Since negative samples are not available for optimising the parameter K, we can only rely on the positive
samples to find its value. In this work, we determine the
dictionary size heuristically, based on the marginal reduction in the approximation error. To quantify the quality of
an approximation, we define a metric, termed approximation index (AI) with the following formulation:
MA
AI ¼ M
100%;
O
PN
PN
r^xi
rx
i¼1 i
;
M
¼
;
MA ¼ i¼1
O
N
N
ð11Þ
where rxi and r^xi denote the standard deviations of
intensities of original image patches xi and their approximations ^xi ; with N being the total number of patches.
Approximation index will lie in the range of 1–100%
attaining the value of 100 when the approximated
patches are identical to the originals.
To evaluate the efficiency of defined metric in quantifying approximation, we compute the AI of three fabric
types with varied regularity (see Figure 5(a)–(c)) using
different patch sizes. It can be readily observed that the
Figure 5. Plots of AI: (a) a twill fabric; (b) and (c) are plain fabrics; (d), (e) and (f) are AI plots of (a), (b) and (c).
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229
Figure 6. Approximation results of a defective image: rows from top to bottom using patch size 16 16, 26 26 and 36 36,
respectively.
twill fabric exhibiting the highest regularity of texture can
be approximated well with only a small dictionary size,
while the two plain fabrics need more dictionary elements
to capture stochastic variations. In addition, using the
smaller patch sizes (e.g. 16 16) results in larger AI, as
smaller patches contain fewer variations and are easier to
approximate with a small number of dictionary elements.
Approximation results for a defective sample using different values of K and patch sizes are shown in Figure 6. It
can be seen that the smaller patches (16 16) can model
the original image more efficiently than larger ones
(26 26 or 36 36) for the same dictionary size, e.g.
given K = 20, Figure 6(e) accounts for more particulars of
the defective region than Figure 6(k) or (q).
In this work, we chose K accounting for around 60%
of the AI, which was found empirically to be robust and
perform well for various fabric textures and defect types.
To prevent the selection of too small a K, e.g. some twill
fabrics can achieve 60% of AI with only two elements,
we set the lower bound on K to be 4 and the upper
bound to be 16.
Experiments
Data-set
All textile fabric images used in this work were captured
from a production line, and each individual image has
the size of 512 512 with 256-grey levels. We chose
nine different types of textile fabric images (referred to
as D1 through to D9). Since the defects such as dirt and
holes which cause significant changes in recorded intensity are easy to identify, this study only focuses on those
defect types that manifest through structural changes or
slight grey-level changes, such as miss pick, slack end,
double filling, thread ends, etc. Each data-set (D1-D9)
consists of 12 defect-free images and three images containing anomalies. Two normal images of each type were
used for learning dictionary; one half of the remainder is
used for training the SVDD classifier, the other half
together with the images containing anomalies were used
for testing.
In the dictionary learning stage, the number of dictionary elements K for Equation (1) is determined and chosen according to the AI criterion as discussed previously.
To acquire training samples, we use two 512 512
defect-free images which are subdivided into w w
patches with the w/2 overlap in both vertical and horizontal directions. We randomly selected 500 image
patches from each image and a total of 1000 image
patches are used to learn the dictionary.
In the SVDD training stage, image patches are collected from the five defect-free images without overlapping. We employ the SVDD classifier with the Gaussian
kernel function which jðx; yÞ ¼ expðckx yk2 Þ can be
solved as an OCSVM (Schlkopf, Platt, Shawe-Taylor,
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J. Zhou et al.
Smola, & Williamson, 2001) problem with LIBSVM
(Chang & Lin, 2011).
The parameter c was estimated by the method
proposed in Khazai, Homayouni, Safari, and Mojaradi
(2011), which can be formulated by:
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c¼
lnðN ð1 vÞ þ 1Þ
2
maxðjjxi xj jj Þ
;
All experiments are implemented in Matlab (R2010a)
on a Linux machine, and Equation (3) is solved with
inline function svd() in Matlab; Equations (1), (4) and
(5) are solved by SPAMS devised by Mairal et al.
(2010).
ð12Þ
where N is the number of training samples. As
mentioned before, v 2 ð0; 1Þ is the parameter that can be
used to control the FAR and we evaluated performance
with different values of v. The image patches used for
training SVDD are sampled without overlapping.
To prevent defects from occurring at the boundary of
adjacent patches, in testing stage, we also divide image
samples into w w patches with the w/2 overlap in both
vertical and horizontal directions.
Evaluation criteria
We adopt receiver-operating characteristics curves (ROCs)
Fawcett (2006) to evaluate detection performance. For
this, the FAR is defined as Nf /Nnt, where Nf is the number
of samples that are incorrectly labelled as defects and Nnt
is the number of normal samples; and the correct detection
rate (CDR) is similarly defined as Nm/Ndt, where Nm is the
number of anomalous samples that are correctly labelled
as defects and Ndt is the total number of anomalous
samples.
Figure 7. The ROC curves for all datasets D1-D9 using patch size 16 16, 26 26 and 36 36.
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Results and discussion
Effect of the patch size
Since the proposed method is based on the image patch
strategy for defect detection, the size of patch has
straightforward effect on proposed algorithm performance, e.g. AI mentioned in Section Dictionary size. To
show the effect using different patch sizes for detection
performance, we tested all data-sets with patch sizes of
16 16, 26 26 and 36 36. Figure 7 presents the
detection results using the dictionary learned from
Equation (1), and its ROC curves are computed for each
data-set (D1-D9) on the hold-out sample under v ¼ 0:01;
0:03; 0:05; 0:07; 0:09.
From Figure 7, it can be seen that small size patches
generally perform better than larger patches with an
exception of datasets D5 and D8. Specifically, larger
patch sizes (e.g. 36 36) have the worst performance on
231
average, while the medium patch size of 26 26
achieves the best performance, controlling both the FAR
and MDR (missing detection rate, MDR = 1-CDR) less
than 5%. The possible explanation is that the smaller
patches are quite sensitive to subtle texture changes yet
as a consequence are prone to a high FAR on less regular plain fabrics. Furthermore, our algorithm generally
performs better on twill fabrics than on plain fabrics,
since the twill fabrics exhibit relatively higher regularity
than plain fabrics, resulting in a lower FAR.
We note that the size of the defect also has an impact
on algorithm performance. By examining the defects
present in each of the data-sets, we note that D3 and D6
have defects at a relatively small scale and are of lower
contrast, making large image patches comparatively less
efficient at their identification. Meanwhile, defects in D5
are likely to occur at scales which make larger patches
more suitable.
Figure 8. Detection results of DL, SVD, NMF and SP under patch size 26 26 and v = 0.05.
J. Zhou et al.
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232
Figure 9. Figurative examples of detection results for D1-D9.
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The Journal of The Textile Institute
The above results indicate that our algorithm is more
robust in adapting to different fabric textures than defect
types and that the performance partly depends on the
types of defects likely to be present. Hence, in practical
applications, we recommend using different patch sizes
depending on specific process requirements, e.g. if monitoring of small-scale defects is important, a 16 16
patch size is to be preferred even though patches that are
too small may suffer from a loss of relevant information.
According to Figure 7, the medium patch size of 26 26
seems to be a good compromise.
Some figurative examples of detection results are
given in Figure 9. They were obtained using the dictionary learned from Equation (1), patch size 26 26 and
setting v = 0.05.
233
approximation index, resulting in an inefficiently modelling texture and losing discriminative power for minor
defects. On the other hand, despite the orthogonal constraint imposed on SVD, it still allows arbitrary signs for
its dictionary and coefficient vectors, leaving as small
approximation error as the unconstrained dictionary
learned from Equation (1) in a certain dictionary size.
Different from DL, SVD and NMF, the extra sparsity
constraint imposes SP to approximate image patches
using as few as its dictionary elements. Such ability to
select only a few dictionary elements for each sample
means that SP is capable of restoring the globe textural
structure, but ignores the small detail regions such as
defects, which somehow increase the discriminative
power for some subtle intensity or/and structural changes
defects, e.g. data-sets D3, D6 and D9.
Extensions
As mentioned early, dictionary learning can be easily
extended to handle matrix factorisation problem. We
extend the proposed method to learn dictionaries for
defect detection from SVD, NMF and SP. Here, the
dictionaries of SVD and NMF are learned from
Equations (3) and (4), and other procedures are identical
to that of Equation (1).
For SP, the K and λ of Equation (5), our experiments
show that using dictionary size K = 16 is adequate for a
“sparse” representation. Sparsity parameter λ yielding
about 11 zero coefficients on average for each training
sample was found to result in the best performance. In
addition, considering the object function of Equation (5)
does not focus on pursuing least-squared error, the
feature Euclidean distance is replaced with another
feature called Residual dispersion, which is given by:
; R¼
Feature 1: Residual dispersion F1 ¼ jjR Rjj
2
jy ^yj;
is mean of
where j j is absolute value operator and R
vector R.
The detection results for the dictionaries learned from
Equations (1), (3), (4) and (5) (referred as DL, SVD,
NMF and SP) are presented in Figure 8, in which the
ROC curves are also computed by testing each data-set
under m ¼ 0:01; 0:03; 0:05; 0:07; 0:09 and a medium
patch size 26 26.
From Figure 8, it can be seen that DL and SVD
exhibit a quite close detection performance, while NMF
has the worst detection performance, especially for D1
and D9. The poorer performance gap for NMF compared
to SVD and DL could be mainly due to the nonnegativity constraint imposed in the NMF problem with
the fact that known solution methods do not guarantee
global optimality also playing a role, since NMF only
permits additive combination of it elements (no subtraction can occur), which needs larger K to achieve required
Conclusions
We propose a dictionary learning framework for textile
fabric defect detection. A dictionary is learned from
defect-free fabric images; such dictionary is able to
approximate training samples well through a linear summation of its elements. Benefiting from the flexibility of
dictionary learning, the major features of a specific fabric
type can be incorporated into the learned dictionary,
which ensures that the typical structural variation can be
effectively modelled. Our algorithm resembles the classic
template-matching methods, but using adaptive templates
modelled by the learned dictionary and not needing to
consider the alignment between the templates and sample
images, alleviating feature selection problem.
Experimental results show that our method can achieve
as high as 95% CDR with less than FAR of 5%. The
extensions to SVD, NMF and SP demonstrate that our
algorithm has quite close performance as SVD, and SP
shows more advantageous in finding minor defects than
DL, since the use of sparsity constraint helps to maintain
discriminative power while reducing approximation error.
This also guides us to find more discriminative dictionary
to improve performance across defect types further.
Acknowledgement
This research was supported by the Fundamental Research
Funds for the Central Universities. This work was supported by
the National Natural Science Foundation of China (Grant No.
61379011).
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