Accurate Indexing and Classification for FabricWeave Patterns Using Entropy-based Approach

Dejun Zheng, George Baciu, Jinlian Hu

Department of Computing & Institute of Textiles and ClothingThe Hong Kong Polytechnic University

Hung Hom, Kowloon, Hong KongEmail: csdzheng.csgeorge@comp.polyu.edu.hk

Abstract- In current textile design, fabric weave patternindexing and searching require extensive manual operations. Themanual weave pattern classification is not sufficient to give theaccurate and precise result and it is time-consuming. There is nosuch research to index and search for weave pattern specially. Inthis paper we propose a method to index and search weavepatterns. We use pattern clusters, transitions, entropy and FastFourier Transform (FFT) directionality as a hybrid approach forthe cognitive comparison and classification of weave pattern.There are three common patterns used in textile design. They areplain weave, twill weave and satin weave patterns. First, weclassify weave patterns into these three categories according toweave pattern definition and weave point distributioncharacteristics (weave pattern smoothness and connectivity).Second, we use the FFT to describe the weave point distribution.Finally, we use entropy method to calculate the weave pointdistribution into a significant index value. Our approach canavoid the problem of pattern duplications in the database. In ourexperiment, we select and test commonly used weave patternswith our proposed approach. Our experiment results show thatour approach can achieve substantially accurate classification.

Keywords- Weave Pattern, Content-based, Index, FFT, Entropy

I. INTRODUCTION

Weaving technology has an intrinsic relationship with theinformation science and technology. Weave patterns aredesigned to achieve aesthetic or functional features. Weavepattern perception is one of the most important fundamentalfactors in textile design process. Perception is a set ofinterpretive cognitive processes of the brain at thesubconscious cognitive function layers that detects, relates,interprets, and searches internal cognitive information in themind[I-3]. Traditional indexing and classification of fabricweave patterns requires extensively manual operation and it isalso very time-consuming for designers to manually search orcheck weave patterns one by one. Currently, the popular CADweave patterns are organized by their given names in a specificfile folder (text-based pattern retrieval method). As a result,there are many duplicated patterns (the same content) withdifferent names, which makes the unified management isdifficult to use and takes up system resources as well.

Recent years have seen a rapid increase in the applicationof digital technology to textile design and manufacturing field.This makes a series of great continuous improvements in

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357

process and efficiency. CAD (Computer Aided Design), CAM(Computer Aided Manufacturing), CAPP (Computer AidedProcess Planning), CAE (Computer Aided Engineering), ERP(Enterprise Resource Planning) systems and Web technologyhave been penetrating and expanding into nearly every aspectof textile industry. A huge amount of information is out ofthere. However, we cannot access or make use of theinformation unless it is organized so as to allow efficientbrowsing, searching, and retrieval[4]. Despite the sustainedefforts in textile design and manufacturing process in terms ofcomputerization and automation, there are few literatureswhich are dedicated to indexing and searching of basic weavepoint map in the field ofDobby and/or Jacquard fabric design.

Perception of texture is a cognitive process forclassification[5] [6]. Fabric weave pattern is a perceived featurewithout color effects which provides basic three dimensionalinterlacing structures, and as well design ideas and inspiration.There are dozens of old weaving books devoted in whole orpart to weave patterns. Oelsner [7] is the most accessible.Donat's [8] "Large Book" and Posselt's dictionary of weaves[9] are well known. Other sources include Barker [10], Brickett[11], Falcot [12], Gruner [13], Kastanek [14], Neville [15],Posselt' s book on textile design[16], Watson's [17] Textiledesign and colour, elementary weaves and figured fabrics etc[18]. The patterns are scattered, presented in a variety of ways,and organized differently. And, of course, there are manyduplicates. These books usually give defmitions to thesepatterns and organize them according to some classificationmethods in a traditional way, which is not appropriate to beread and processed by computer. Weave pattern is an importantelement in textile design. Computerization of weave patterndesign and analysis is a development trend in the informationage. The technical development and application of computerand image analysis has promoted the study on textileautomation production with creativity, efficiency and highquality.

There were some researchers who engaged in fabric weavepattern analysis and extraction by using image processingtechnologies [19, 20]. A popular method to describe thecharacteristics of the fabric pattern was based on Fouriertransform techniques [21-23]. In the power spectrum imagederived from FFT, peaks stood for frequency of directionalperiodic elements from which basic weave patterns could bediscriminated. The pattern power spectra offered a special

where, aij ={O,1};i=1,2,. ..,m;j = 1,2,... ,n; aij taking the

value °means weft point and I means warp point. We use eachcolumn to denote the warp interlacing rule in the fabric:

{ a],. . .aj , • • • an} . In this way, the interlacing rule for each warp

can be described by the following formula

c(Czoo.cx·oocp (2)a . = ------'--

J d(dZ •• • d, .. .dp

where Cx means the warp float points and d; means the weft

float points; (p + q ) is the number of interlacing timesbetween warp and weft float points.

Based on the above definitions, we can describe the threetypes of regular weave patterns: Regular Plain Weave Pattern(RPWP), Regular Twill Weave Pattern (RTWP) and RegularSatin Weave Pattern (RSWP). The value of a ij can be deduced

by the index of previous warp point position (subscript position)in the matrix. We use step in warp and weft to describe thewarp point distribution rule, Sj meaning step in warp direction

and s; meaning step in weft direction. For these regularpatterns, there is a pre-requisite condition

angle to view weave pattern types of plain, twill and satin.However, the method was still qualitative and ratherapproximate[23].

In recent years, artificial neural network [24] and fuzzy C­means algorithm [25] were adopted to study the fabric weavepatterns. Their object was at pattern recognition throughclassifying the cross states of yam points. According to thecharacteristics of these fuzzy mathematical methods, it couldbe used to classify the fabric pattern. But these methods havesome difficulties in comparing the pattern similarities [17-21].

II. PATTERN CLASSIFICATION METHOD

In textile design, we normally classify these patternsaccording to their interlacing rule by three categories: plainweave, twill weave and satin weave. The taxonomy here weuse is illustrated in Figure I.

(1)

1a] =l'(c] = I,d] =l,p=q=l),sj =sw =±l (4)

For RTWP, it can be subdivided into three categories. Thefirst one is basic twill, which can be described as

(3)

(7)

(5)

p q

m=n= ~>j +Ldjj =( j =(

For RPWP, it can be expressed as

c( da] =-,(c1 + ] ?:.3,p=q=1),sj = sw =±ld(

The second one is coarse twill, which can be given by

ca1 =...l.,(c]+d] ?:.4,c( *l,d] *l,p=q=l),

d(

Sj=sw=±l (6)

when c( > d, , technician calls it warp effect coarse twill;

c] < d( , technician refers to as weft effect coarse twill; c] = d,is the double face coarse twill.

The third type is compound twill, that is

a1 = L(c] +cz +... +cp +d1+dz...+dq)?:. 5,

m=n?:.2,s j =sw =±lFor RSWP, there are also two types, warp effect:Figure 2. Fabric and weave pattern

Figure I. Taxonomy of fabric weave pattern

A. Regular Patterns Descriptionand ClassificationFabric structure means the interlacing rule of warp and weft,

the grid plots with black and white cells as shown in Figure 2.Here, we use black cells to indicate warp point and white cellsto indicate weft point (yam draw-downs: with black cellswhere the warp is on top and white cells where the weft is ontop).

We use matrix lJ1 to describe the weave pattern asfollowing,

358

(11)

(12)

Tota lhor izontal

transitions: 6

./ _ , \

: ~

: :i f16l i1 ~ :: :: :: :: !: :: :i :: :~ :"- j

............................................., .

~~;.;~i~:~~~:n~ 1 . d I I . 1

~ ..' Tota l anti-diago nal- -:rh' ,.......,..:.. .' transitions: 3

1 1

EI(i, j) = L L ;({Ti+P,j+v :#:Ti+P,j+v})'p =- I v=- I

1 1

E2(i,j) = L L ;({Ti+P,j+v :#: Ti+p,j+v}),p =-I v=- I

ifij"""§=Gl

.hl.~. , ,, , , ,, , ,, , ,, , , . , ,, , .. , ,,, , ., ,,, ,, , - , ~ , ,-

Tota l vertical transitions: 6

Figure 4. Illustrations of transitions calculation

o 0

E3(i,j) = L L ;({Ti+P,j+v :#: Ti+P+I,j+v+I})' (13)p =-I v =-I

1 0

E4 (i , j) = L L ; ({Ti+p,j+v :#: Ti+p_I,j+v+1}), (14)p=Ov=-1

where ;(.) is an indicator function taking value from {0, 1}. An

example of broken twill weave is given in Figure 4 to illustratethe calculation of transitions in four directions . Given areference value V,2 = TlJ as plain weave category fordifferentiation of plain weave and twill weave,ifv" e(TlJ-C>,TlJ+C» , the pattern can be classified into plain

weave category (Otherwise, it is twill weave pattern) . Hereincrement l±c>l is threshold value for the judgment.

(8)

(10)

45 c touch with

the centre

90 ' touch with

the centre

Caj =..1.. ,c1 ~ 4(cl :#:5),p=q=l,

1here 1< S j < cj ' (cj + 1)and S j are relatively prime.

weft effect:

Figure 3. 45 ' and 90 ' connection

Before do the calculations of smoothness and connectivity,we use a skill to differentiate satin weave from plain and twillweaves categories . As shown in Figure 3, the centre interlacingpoint of interest has two kinds of connections with itsneighbors: toughing each other by 45 0 (i.e., (i + 1, j ±1) or

(i -1, j ±1)) or by 90 '(i.e., (i, j ±1)or (i ±1, j)). 90 ' touching

is known as four-connecti vity, and 90 ' / 45 ' touching is knownas eight-connectivity [8]. In the satin weaves, they mayor maynot have 90 ' touch with the centre. But for 45 c touch with thecentre, it is not common to have this kind of connection. Forthe reasons of simplicity, we take it as a criterion todiscriminate satins weaves from plain and twill weaves. (ifthere are exceptions, the user can adopt an enforcement rule totake this situation into consideration.)

The smoothness of the interest neighborhood around pixelTi,j is measured by the total number of horizontal , vertical,

diagonal and anti-diagonal transitions : E1 (horizontal) , E2

(vertical), E3 (diagonal) , E 4 (anti-diagonal). Ti,j is the value

of the i 'h weft and r warp in the weave pattern. In order todescribe the distributions of the four directions transitions, weuse variance of the four-direction transitionsarray {EI'E2 ,E3 ,E4 } :

V'2 =..!.i»._E;)2n i=1

1aj =--,dl ~ 5(cI :#:6),p=q=l, (9)

dj -1

Here, 1< Sw < (d j -1), dj and sware relatively prime.

B. Irregular Patterns Description and Classification

For many fabric weave patterns , their step in warp or weftis not a fixed number. In this case, we use smoothness andconnectivity to describe and classify these irregular patterns .The smoothness is measured by the horizontal, vertical anddiagonal transitions, and the connectivity is measured by thenumber of black (warp point, nominal value equals 1) andwhite (weft point, nominal value is 0) clusters.

Figure 5. Illustration of connectivity calculation

359

The square of the magnitude function is commonly referredto as power spectrum P(u) of f(x) :

For weave pattern diagram, the interlacing information onlyincludes two situations, i.e, weft point denoted as white(f(x,y)=O) and warp point denoted as black (f(x,y)=I).

In this case, Equation 15 becomes:

(20)

(17)

(18)

f(x) = .cF(u)exp(j21nJX)du

H2(Po,PI ) = r P« log, Po - PI log2PI

~~f(x,y)PI = L..J L..J M N' Po = 1- PI

M N X

where f(x) and F(u) are referred to as the Fourier transform

pair. The Fourier transform of a real function is generallycomplex, with real and imaginary components I(u) andJ(u) ,

then the magnitudeM(u) can be calculated by

F(u) = r:f(x)exp(-j21ZUX)dx (19)

where j = H The function f(x) may be reconstructed by

the inverse Fourier transform:

The calculation of a pattern's entropy involves themicroscopic essence of the pattern complexity based on theprobability of occurrence for weft or warp yam points.However, for a specific weave pattern description, entropycannot get the distribution information of the warp and weftfloat arrangement and distance. For example, theoretically,weave pattern simple plain weave and basket plain weave havethe same entropy value, but they have different spatialdistributions. Here, we use Fast Fourier Transform (FFT) toextract the information of the spatial distribution of yaminterlacing points.

If a functionf(x) in the time or spatial domain is known,

thenF(u) , the Fourier transform off(x) , can be defmed as

(15)

After the calculation of smoothness, we also useconnectivity to differentiate plain weave and twill weavepatterns. As illustrated in Figure 3 and Figure 5, theconnectivity is measured by the number of the black and whiteclusters. In order to make a differentiation between plain weaveand twill weave, we can use the 90 0 connection criterion shownin Figure 3 to describe the connectivity. In Figure 5, showinghere is an example of 4 x 4 pattern with eight white pointsforming two clusters and with eight black points forming twoclusters. The number of clusters can be automatically identifiedby traversing the graph using depth-first search strategy [26,27]. Here we use a stack-based search algorithm to calculatethe connectivity of90 degree.

Suppose that there are I' interlacing points in total and thefmal value of 8 indicates the number of clusters. Let v(k)

store the value of k" interlacing point and Vo be the interlacing

value of interest. Set up an empty stack and an P-element arrayL[·] for storing the index of the cluster that the interlacing

point belongs to; set L[k] =0 for all k =1,2,... , P; i =1;

8 = O. Step I : if L[i]"* 0 or v[i]"* vo ' go to fmal step (Step

V). Step II, 8 = 8 +1; push node- i into the stack. Step III, if

the stack is empty, go to Step V. Step IV, L[k] = 8. Find all

pixels connected with k . For each connected interlacingpoint j , if L[j] = 0 (Le. it has not been visited or pushed into

stack), let L[j] = -1, push node- j into stack (by the defmition

of connected, v[j] = vo ) ' Go back to III. Step V, i = i +1; if

i > I', stop, otherwise go to Step I . The number of clusters isused as supplementation of judgment criterion between plainpattern and twill pattern.

c. Indexing method

In information theory, for a discrete source X , the self­information of symbol x; which occurs with probability p(x;)

is defmed asI(x;) = -logp(x;). The uncertainty or entropy of

the source is defmed as

H(X) is the average information per source output. It is

related to the distribution of source probability. Indeed, theweave pattern diagram can be regarded as an image of blackand white point distribution. The distribution of differentbrightness will produce the weave pattern. The entropy of theweave pattern diagram will be different from each other. It ispossible and efficient to describe the weave pattern diagram byits entropy.

Given an image, the size is M x N and functionf(x,y) represents the brightness distribution of pixels. If

f(x,y) = {kl'k2,.··kL } and the probability of each brightness

in the image is Pf ={PI' P2"", PL} , the information entropy

for the weave pattern image can be given as

Similarly, for the discrete case, the corresponding pair ofthe two-dimensional Fourier transform ofa pattern image is

The formulation in (23) and (24) can reduce N 2 operationsin the DFT to N log, N operations in the FFT. The basic idea

of the FFT is that the DFT of N elements is the sum of the

(24)x = 0,1,2, ...M -1 , y = 0,1,2, ...N -1 .

1 M-I N-If(x,y) = -L LF(u, v)exp(j2JT(ux + lY)),

MN x=O y=O M N

1 M-I N-IF(u,v)=-L Lf(x,y)exp(-j2JT(UX + VY)),

MN x=O y=O M Nu = 0,1,2, ...M -1, v = 0,1,2, ...N -1. (23)

(16)L

HL(pl' P2" " ,PL) = LP; log, P;;=1

360

As we known, histogram equalization can also provide suchinvariance, but it is more complicated than using Equation 11.Then the spectral data can be described by the entropy, F:,vh,as

DFTs of two subsets: even-numbered points and odd-numberedpoints. The data set can be recursively split into even and odduntil the length equals one.

We can filter the Fourier transform so as to select thosefrequency components deemed to be of interest to a particularapplication, e.g. fabric density calculation and even patternrecognition [23]. Alternatively, it is convenient to collect themagnitude transform data in achieve a reduced set ofmeasurements. First, the FFT data can be normalized by thesum of the squared values of each magnitude componentinstead of histogram equalization, so that the magnitude data isinvariant to linear shifts in illumination to obtain normalizedFourier coefficients NF as

III. EXPERIMENTAL RESULTS

In order to validate the method proposed, we choose 100frequently used weave patterns to do the classification andcalculation of FFT Entropy. To improve the performance ofcompute efficiency, we use unit motifs-The smallest sub­pattern from which entire patterns can be produced byreplication. The three types ofpatterns here to classify are PlainWeave Pattern (PWP), Twill Weave Pattern (TWP) and SatinWeave Pattern (SWP). The results are shown in Figure 6, 7, 8and Figure 9.

Usually, it would be difficult to have the patterns sorted byweave type, since the taxonomy of weave patterns iscontroversial and problematical for some patterns. Many weavepatterns fall into the inevitable "miscellaneous" category. Fromour classification methods, we use pattern defmition combinedwith pattern visual description method (smoothness andconnectivity calculation). We can have a relatively satisfiedresult. In our experiment, we invited 20 designers who have atleast 3-year design experience to evaluate the classificationresults. 18 designers totally agreed with our classification. Theother two designers had different opinions on pattern p18 andp30 in plain weave pattern category. They believed that the twopatterns should be classified into twill pattern group.

From Figure 6 to Figure 8, we can fmd that the three typesof weave patterns are arranged in a rule. On the one hand, it iskeeping upward trend according to the number ofends/columns and the number ofpicks/rows. On the other hand,similar patterns are usually neighbors. By Fourier analysis, themeasures are inherently position invariant and can extract theinformation of spatial arrangement of yarns inside the image.We can see that the method is relatively immune to rotation,

IV. ApPLICATIONS

The calculation results can be used to measure the weavepattern similarity. From our experiments, the results have agood agreement with human perception judgment. When adesigner is doing fabric design, it will be very convenient tojust input a known pattern and then fmd similar patterns tomatch it. By searching the index value, we can achieve weavepattern matching. Since every pattern has a FFT Entropy value,the duplicate samples can be avoided to a large extent. Thisindexing technology can be used to build a "clean" database forwoven fabric.

Apart from searching by the FFT Entropy value, we canalso use the distribution characteristics of weave point to do asearch, i.e, by weave pattern smoothness (four-directiontransitions) and connectivity (the number of warp point and/orweft point clusters). A user can search or evaluate a patternfrom different points of view. It will be very useful to designcompound weave fabrics especially considering the balance offorce because of structure difference (yarn interlacing rule).

It might as well be a potential solution to controversialpattern classification. The fmal visual appearance is the targetof fabric design. Weave patterns are classified according tohuman visual perception. Different people have differentclassification criterion and thus have different categories. Byusing the objective description values (smoothness,connectivity, FFT Entropy value), we can have asupplementary reference to do a pattern classification for theconvenience of fabric design and the objectivity of fabricstructure evaluation.

since order is not important in their calculation. To bespecifically, in our experiments shown in Figure 9, the samplesthat equivalent under geometric transformations in 90 0

increments are close in the queue. For example, weave patternp08 and p09, p l 0 and p11, s17 and s18 etc., are neighborsrespectively. Besides, weave patterns with the same number ofwarps and picks are also very near, i.e, there are no obviousdifferences among their FFT Entropy values. For instance,weave pattern t05 and t06. The patterns with the similarnumber of warps and/or picks also have similar FFT Entropyvalue, e.g. weave pattern s16 and s17. As a result, the similarpatterns are neighbors in the queue.

V. CONCLUSIONS

By using the defmitions of weave patterns, we firstdifferentiate some simple weave patterns. For irregular weavepatterns, we use weave pattern smoothness and connectivity todiscriminate them. General pattern perception is a complexprocess which largely depends on human subjectivity, we justinvestigate 100 common weave patterns (they have beenfrequently used in wove fabric design) and classify them intothree categories: plain pattern, twill pattern, and satin pattern.We also calculate the FFT Entropy value of these weavepatterns. The results show that the proposed method is anefficient way to index and search similar weave patterns. Wealso propose solutions to search or differentiate patterns bydifferent points of view. Through the calculation of FFTEntropy for each weave pattern, we can use this value to index

(25)

(26)

1F:,vl

L Ir:,vr(u;t:O)/\(v;t:O)

M N

F:,vh = LLNF:,v log2(NF:,v)u=l v=l

NF:,v = ---;:::===:::::::::::==-

361

each pattern. In this way, we can build a weave patterndatabase without duplicates to a great degree. From ourThat will be very useful for the fabric designer to do weavepattern selection, comparison and analysis. Our work is

experimental results, the content-based indexing and searchingmethod is proved to be effective for the tested weave pattern.continuing in this direction to apply this technology in fabricCAD design system.

~rp29 p30

2p03 p04

t - --I I -~-

p07 p09 pll

:t:p25

Figure 6. Classification and FFT entropy calculation results of plain weave patterns (30 samples)

tl 8

t 11

t1 6tl 5

I-.t02

1++~t08

. .... .tl 9 t 20 U t 2 U

~~~~ ~~t 31 t 3 2 u3 t34 t35 t 3 6

I

1+~

tl 3•

Figure 7. Classification and FFT entropy calculation results of twill weave patterns (36 samples)

362

-1-1- ­_._".-

. ~s Ol

• •• • •• •• •• •s 19-. . · .s25 s30

· -· .. .• s29s28-s27

.s26

I • • - f L~_ •-.- - • • - • .--~_I ' _ _ -• - I • •• • -- I •• I • - • •s lli s03 s 04 s05 s06• • .1 . •• • • - •- • •• • II • • • • •• • - • • - • •• • • •• • I. • •• • • •

s ora s09 s 10 s l l s 12.- - .. • - - •• • • • • • • •• - - • -• • • • •• •• •• • •• • • • • •• •• - • •• • •• • •• •• • •- s 15 • s 16 • • s 18s 14 s 17- • • - • - - • - •• • • • • • • • • •• • • • • • • • - •• • • • • • • • • •• • • • • • • • • •• • • • • • • • • •s20 s2l s22 · s23 s24- -

••

••

.'• ••

•s 07•

••

•• s 13

•

FFT En t r o p y

A .5 C en ding

• Ord er

001 :>s3 l s32 s33 s34

Figure 8, Classification and FFT entropy calculation results of satin weave patterns (34 samples)

1000

900 s31 s33

800

~ 700t 36

.---<co> 600>,0.0500H+-'

cij 400t--<

& 300-+- sat i n weave patter n

200-II- t will patternweave

100 ----A- pl ain weave pa t t ern

00 5 10 15 20 25 30 35 40

weave patter ns

Figure 9, FFT Entropy value of different types ofweave patterns

363

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