research article texture classification using scattering...

Research ArticleTexture Classification Using Scattering Statistical andCooccurrence Features

Juan Wang1 Jiangshe Zhang1 and Jie Zhao2

1School of Mathematics and Statistics Xirsquoan Jiaotong University Xirsquoan Shaanxi 710049 China2College of Science Zhongyuan University of Technology Zhengzhou Henan 450007 China

Correspondence should be addressed to Juan Wang wangjuan03022204163com

Received 2 November 2015 Revised 20 January 2016 Accepted 28 January 2016

Academic Editor Raffaele Solimene

Copyright copy 2016 Juan Wang et al This is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

Texture classification is an important research topic in image processing In 2012 scattering transform computed by iterating oversuccessive wavelet transforms and modulus operators was introduced This paper presents new approaches for texture featuresextraction using scattering transform Scattering statistical features and scattering cooccurrence features are derived from subbandsof the scattering decomposition and original images And these features are used for classification for the four datasets containing20 30 112 and 129 texture images respectively Experimental results show that our approaches have the promising results inclassification

1 Introduction

The texture is one of the main contents of the image Texturesegmentation texture classification and shape recovery fromtexture are three primary issues in texture analysis [1]Among them texture classification plays an important rolein many tasks ranging from remote sensing and medicalimaging to query by content in large image data bases andso forth [2] Texture analysis is one of the most importanttechniques when images which consist of repetition or quasirepetition of some fundamental image elements are analyzedand interpreted (eg [3]) Various feature extraction andclassification techniques have been suggested for the purposeof texture analysis in the past Since there are many variationsamong nature textures to achieve the best performancefor texture analysis or retrieval different features should bechosen according to the characteristics of texture images It iswell recognized that these texture analysis methods capturedifferent texture properties of the image

There are fourmajor stages in texture analysis that is fea-ture extraction texture discrimination texture classificationand shape from texture [4] The first stage of image textureanalysis is feature extraction Texture features obtained fromthis step are used to discriminate textures classify image

textures or determine object shape Feature extraction com-putes a characteristic that can describe texture properties ofa digital image The process that partitions a textured imageinto regions each corresponding to a perceptually homoge-neous texture is texture discrimination In the stage of textureclassification a rule which classifies a given test image ofunknown classes to one of the known classes is designedShape from texture reconstructs 3D surface geometry fromtexture information Feature extraction techniques mainlyinclude first-order histogram based features cooccurrencematrix based features and multiscale features [4] First-order histogram based features according to the shape of thehistogram of intensity levels provides a number of clews asto the character of the image The second-order histogramis considered as the cooccurrence matrix [5] Cooccurrencematrix based features are the estimate of the joint probabilitydistributions of pairs of pixels In order to calculatemultiscalefeatures many time-frequency methods are adopted [6] Thecommon methods are Wigner distributions Gabor func-tions wavelet transform and ridgelet transformWigner dis-tributions can produce inference terms which lead to wrongsignal interpretation Gabor filter results in redundant fea-tures at different scales or channels [7]Wavelet transform is alinear operation andpossesses a capability of time localisation

Hindawi Publishing CorporationMathematical Problems in EngineeringVolume 2016 Article ID 3946312 6 pageshttpdxdoiorg10115520163946312

2 Mathematical Problems in Engineering

of signal spectral features For these reasons it is interesting inapplication to texture analysis for wavelet transform Ridgelettransform can deal effectively with line singularities in 2DIt is well known that texture classification based on ridgeletstatistical features (RSFs) and ridgelet cooccurrence features(RCFs) has been done by Arivazhagan et al [8]

In the last few decades wavelet theory has been widelyused for texture classification purposes [9ndash11] Howeverwavelet transform is not translation invariant In 2012 Mallatadvanced scattering transform which is invariant to trans-lations and Lipschitz continuous relatively to deformations[12] Scattering transform can overcome the weakness ofwavelet transform that is not translation invariant The ideais that scattering transform is computed by iterating oversuccessive wavelet transforms and modulus operators Scat-tering transformmaps high frequency information of imagesto low frequency Then scattering transform can providea stationary representation Scattering transform has foundapplications in texture classification (eg [13 14]) Theseclassification tasks are based on original scattering vectors

In this paper the scattering transform is applied on aset of texture images Statistical features and cooccurrencefeatures are extracted from original images and each ofscattering subbandsThese features are used for classificationFor the sake of comparative analysis classification tasks aredone using RSFs RCFs wavelet statistical features (WSFs)and wavelet cooccurrence features (WCFs) respectively Theexperimental results show that the success rate of our featureextraction techniques is promising but unsatisfactory But itis considered as a proof of concept for scattering statisticalfeatures (SSFs) and scattering cooccurrence features (SCFs)

The rest of this paper is organized as follows In Section 2the theory of scattering transform is briefly reviewed Thefeature extraction and texture classification are explained inSection 3 In Section 4 texture classification experimentalresults are discussed in detail Finally concluding remarks aregiven in Section 5

2 Scattering Transform

Wavelet transform is a process which was applied to originalsignal by a filter [15] 119866 denotes a discrete finite rotationgroup in 119877

2 A wavelet function 120595 is a band-pass filter Thefollowing formula is rotation and dilation of 120595

120595120582(119909) = 2

2119895120595 (2119895119903minus1119909) (1)

with 120582 = 2119895119903 isin and = 119866 times 119885 and |120582| = 2

119895 119903 isin 119866 is rotationparameter 2119895 for 119895 isin 119885 is dilation parameter

A texture119883(119909) is modeled as a realization of a stationaryprocess So the wavelet transform of 119883(119909) is written asfollows

119882120582119883(119909) = 119883 lowast 120595

120582(119909) (2)

119880[120582]119883(119909) = |119883 lowast120595120582(119909)| is the wavelet modulus of119883(119909)The

high frequency coefficients of wavelet transform are mappedto the low frequency form by the modulus operator [16]

Xp = 0

U[1205821]X

p = 1

U[1205821 1205822]X

p = 2

U[1205821 1205822 1205823]X

SJ[120601]XSJ[1205821]X SJ[1205821 1205822]X

middot middot middot


Figure 1 Scattering transform It can be seen as a network whichiterates over wavelet transform and modulus operator

The result of the convolution of texture 119883(119909) and zoomfunctionΦ

119869(119909) is low frequency information that is

119860119869119883 (119909) = 119883 (119909) lowast Φ

119869(119909) (3)

where Φ119869(119909) = 2

minus2119869Φ(2minus119869119909) The resulting wavelet modulus

operator |119872| is

|119872|119883 (119909) = 119883 lowast Φ119869(119909)

1003816100381610038161003816119883 lowast 120595120582(119909)

1003816100381610038161003816 (4)

The high frequency information which is lost by thewavelet modulus operator could be recovered by next 119880 [12]resulting in the scattering propagators 119880[119901] along differentpaths 119901 = (120582

1 120582

119898) as follows

119880 [119901]119883 (119909) = 119880 [120582119898] sdot sdot sdot 119880 [120582

1]119883 (119909)

= |sdot sdot sdot |⏟⏟⏟⏟⏟⏟⏟119898

119883 lowast 1205951205821

10038161003816100381610038161003816lowast1205951205822

10038161003816100381610038161003816sdot sdot sdot

10038161003816100381610038161003816lowast120595120582119898(119909)

10038161003816100381610038161003816

(5)

In particular when 119901 = 0 119880[120601]119883(119909) = 119883(119909)

The wavelet modulus operator is iteratively applied toprogressively map the high frequency information to the lowfrequency information Thus scattering operator is definedfrom 119860

119869119883(119909) = 119883(119909) lowast Φ

119869(119909) and 119880[120582]119883(119909) = |119883 lowast 120595

120582(119909)|

[12] The information of texture is scattered to different pathsin the iterative processThe scattering operator 119878

119869implements

a sequence of wavelet convolutions andmodulus followed bya convolution with Φ

119869

119878119869[119901]119883 (119909) = 119880 [119901]119883 lowast Φ

119869(119909)

= |sdot sdot sdot |⏟⏟⏟⏟⏟⏟⏟119898

119883 lowast 1205951205821

10038161003816100381610038161003816lowast1205951205822

10038161003816100381610038161003816sdot sdot sdot

10038161003816100381610038161003816lowast120595120582119898

10038161003816100381610038161003816lowast Φ119869(119909)

(6)

If 119901 = 0 then 119878119869[120601]119883(119909) = 119883(119909) lowast Φ

119869

The scattering transform is thus computed with a cascadeof wavelet transform and modulus The scattering transformprocess could be described by a deep network architecture(see eg [17 18]) as shown in Figure 1Mallat has proved thatthe energy of the deepest layer converges quickly to zero as thelength of path increases in [12] Bruna and Mallat [19] haveillustrated that most of the energy is concentrated in |119901| le

3 Further details about scattering transform are presented in[12]

3 Feature Extraction and TextureClassification

The steps involved in texture training and texture classifica-tion are shown in Figure 2

Texture Training At the stage of the texture training theknown texture images are decomposed by using scattering

Mathematical Problems in Engineering 3

Known textureimage

Scatteringdecomposition

Featureextraction

Featureslibrary

(a)


Featureextraction

Featureslibrary

Unknown textureimage

Classifier

Classified textureimage

(b)

Figure 2 (a) Texture training steps (b) Texture classification steps

transform Then mean and standard deviation of originalimages and subbands of two layers decomposed images arecalculated as features using the formulas given in the follow-ing

mean (119898) = 1

1198732

119873

sum

119894119895=1

119901 (119894 119895) (7)

Standard deviation (sd) = 1

119873radic

119873

sum

119894119895=1

[119901 (119894 119895) minus 119898]2

(8)

where 119901(119894 119895) is the transformed valued in (119894 119895) for any imageof size119873times119873 [20]These features are stored in features libraryas scattering statistical features (SSFs) which are further usedin the texture classification phase

In addition in order to further verify the classificationrate cooccurrent matrix (119862) [21] is formed for each sub-band of scattering transform and each image respectivelyFrom the cooccurrence matrix the features such as clusterprominence cluster shade contrast and local homogeneityare given by Arivazhagan and Ganesan [9]These features areobtained by (9)ndash(12) These features are stored in the featuredatabase as scattering cooccurrence features (SCFs)

Cluster prominence (cp)

= sum

119894

sum

119895

(119894 minus 119909+ 119895 minus

119910)4

119862 (119894 119895) (9)

Cluster shade (cs)

= sum

119894

sum

119895

(119894 minus 119909+ 119895 minus

119910)3

119862 (119894 119895) (10)

Contrast (con) = sum

119894

sum

119895

(119894 minus 119895)2

119862 (119894 119895) (11)

Local homogeneity (lho)

= sum

119894

sum

119895

1

1 + (119894 minus 119895)2119862 (119894 119895)

(12)

where 119909= sum119894sum119895119894119862(119894 119895)

119910= sum119894sum119895119895119862(119894 119895) and 119862(119894 119895)

is the (119894 119895)th element of the cooccurrence matrix 119862

Texture Classification Here the unknown texture images aredecomposed using scattering transformThen SSFs and SCFsof original images and subbands of scattering decomposedimages are extracted using (7)ndash(12) respectively These fea-tures are compared with the corresponding feature valuesstored in the features library using a distance formula givenas follows

(119896) =

119899

sum

119894=1

abs [119891119894(119909) minus 119891

119894(119896)] (13)

where 119909 is an unknown texture 119899 indicates number offeatures 119891

119894(119909) represents the features of 119909 while 119896 is a known

119896th texture in the library and 119891119894(119896) is the features of known

119896th texture If the distance (119896) is minimum among alltextures which is available in the library then the knowntexture is classified as 119896th textureThis classification approachis very simple efficient and effective in many fields [22]This rule is widely used in object recognition [23] textcategorization [24] pattern recognition [25] and so on

Performance of the feature sets is tested with success rateLet 119873

119862be the number of subimages correctly classified and

let be the total number of subimages derived from eachtexture imageThen classification success rate 119878

119877is calculated

using

119878119877=119873119862

times 100 (14)

4 Experimental Results and Discussion

In this section several experiments are carried out on texturedatabases from Brodatz texture album [26] and VisTex colorimage database [27] Four experiments are conducted withonly one objective which is investigation of the textureclassification performance based on the proposed methodsof feature extraction For the purpose of comparison theclassification experiment is repeated with RSFs RCFs WSFsand WCFs respectively In order to verify performance ofour feature extraction methods on large amounts of dataand small amounts of data VisTex color image database


Table 1 Results of texture classification using scattering transform ridgelet transform and wavelet transform for 20 VisTex images (with1680 image regions Dataset-1)

Dataset-1 Feature vectorsF1 F2 F3 R1 [8] R2 [8] R3 [8] W1 [9] W2 [9] W3 [8]

Mean success rate () 9607 7899 9560 9548 7756 9869 9202 8786 9780Number of image regions correctly classified 1614 1327 1606 1604 1303 1658 1546 1476 1643F1 = SSFs (mean and standard deviation) F2 = SCFs (cluster prominence cluster shade contrast and local homogeneity) F3 = F1 + F2 R1 = RSFs (mean andstandard deviation) R2 = RCFs (cluster prominence cluster shade contrast and local homogeneity) R3 = R1 + R2W1 =WSFs (mean and standard deviation)W2 =WCFs (cluster prominence cluster shade contrast and local homogeneity) W3 =W1 +W2


Dataset-2 Feature vectorsF1 F2 F3 R1 [8] R2 [8] R3 [8] W1 W2 W3 [8]


is used thrice the first two times with a small number ofimages and the third time with a large number Furthermorethe efficiency of feature extraction approaches proposed isdemonstratedwith the average success rate and image regionscorrectly classified

Since Bruna andMallat have illustrated that most of scat-tering energy is concentrated in |119901| le 3 we mainly considerthe first three layers in the current work It is noted thatthe computing cost of the first three layers is larger thanthat of the first two layers It is a pity that the classificationperformance of the first three layers is slightly better than thatof the first two layers Therefore the maximum number ofscattering layers is 2 in our experiments In addition in orderto get optimal values of the number of orientations and themaximum scale we try to change the values of these parame-ters and do a large number of experiments Comprehensivelyconsidering the computation complexity and classificationperformance the number of scattering orientations is 4 andthe maximum scale of scattering transform is 2 There is avarious number of scattering matrices in different layers ofscattering transform As a result the resulting number ofscattering matrices in the zeroth layer of scattering transformis only one there are 8 scattering matrices in the first layer ofscattering transform and the number of scattering matricesof the second layer is 16

Firstly Dataset-1 contains 20monochrome images whichare obtained from VisTex color image database each of size512 times 512 Texture image classification is done for Dataset-1using SSFs and SCFs Here each texture image is subdividedinto sixty-four 64 times 64 sixteen 128 times 128 and four 256 times 256nonoverlapping image regions So there are a total of 1680subimages regions in the database By decomposing animage using scattering transform 25 25 and 25 subbandsare obtained for the image of size 64 times 64 128 times 128 and256 times 256 respectively SSFs and SCFs are calculated over allthe scattering decomposed subbands Furthermore SSFs andSCFs of the regions of size 64 times 64 128 times 128 and 256 times 256are also obtained

The experimental results are summarized inTable 1 FromTable 1 it is found that compared with RSFs and WSFswhen classification is carried out with statistical featuresthat is mean and standard deviation of original images andsubbands of transformdecomposed images themean successrate obtained from SSFs is the highest that is 9607 Itcan be seen that SCFs perform better than RCFs but poorerthan WCFs Using the feature vectors which contain thecombination of statistical features and cooccurrence featuresthe mean success rate for feature vectors F3 R3 and W3 is9560 9869 and 9780 respectively

Next Dataset-2 containing thirty 512 times 512 sizemonochrome images which are obtained from VisTex colorimage database is used for analysis In a similar mannerfor Dataset-2 each texture image is subdivided into four256 times 256 sixteen 128 times 128 and sixty-four 64 times 64

nonoverlapping image regions Therefore there are 2520

subimage regions respectively in the database SSFs andSCFs are extracted from original images and subbands ofscattering transform decomposed images

The classification results which are obtained for all the84 subimage regions derived from each texture image inDataset-2 are given in Table 2 Table 2 shows the following(i) using the feature vector F1 the success rate achieved is9496 (ii) using SSFs as feature vector F1 a mean successrate is about 2012 more than the average success rateusing F2 whose mean success rate is only 7484 (iii) themean success rate obtained using F3 is 9401 which isabout 095 less than the average success rate obtained usingF1

In addition our proposed approaches are compared withR1 R2 R3 W1 W2 and W3 in terms of the classificationperformance Compared with RSFs and WSFs the perfor-mance of SSFs is the best For cooccurrence features SCFs getbetter classification performance than WCFs while its meanaccuracy is slightly lower than that from RCFs From Table 2it is found that when classification is carried out withW3 andR3 the mean success rate is 9647 and 9679 respectively


Table 3 Results of texture classification using scattering transform ridgelet transform and wavelet transform for 112 Brodatz images (with2240 image regions Dataset-3)




Dataset-4 Feature vectorsF1 F2 F3 R1 [8] R2 [8] R3 [8] W1 W2 W3


But when classification is done with F3 themean success rateis slightly reduced to 9401

Then Dataset-3 containing one hundred and twelvemonochrome images obtained from Brodatz texture albumis used for analysis Size of each image in Dataset-3 is 512 times512 Each texture image is subdivided into four 256 times 256

and sixteen 128 times 128 nonoverlapping image regions Hencethe database includes a total of 2240 subimage regionsrespectivelyThe feature vectors SSFs and SCFs for each imageare calculated from the subbands of scattering transformdecomposed image and the original image

The classification results are summarized in Table 3 Themean success rate of feature vectors F1 F2 and F3 is 91347862 and 9018 respectively As shown in Table 3 forstatistical features it is noted that the highest mean successrate is obtained using SSFs ComparingwithRCFs andWCFsthe performance of SCFs is better thanWCFs and worse thanRCFs Likewise the mean classification accuracy obtainedusing F3 is higher than that achieved usingW3and lower thanthe mean score got using R3 when the performance of F3 iscompared with that of feature vectors R3 and W3

Finally Dataset-4 is created from one hundred andtwenty-nine monochrome images from VisTex color imagedatabase The database is constructed by dividing each 512 times512 image into nonoverlapping four 256 times 256 and sixteen128 times 128 image regions There are 2580 image regions inthe database SSFs and SCFs are extracted from subbandsof scattering transform decomposed image and the originalimage F1 contains mean and standard deviation F2 includesSCFs that is cluster prominence cluster shade contrast andlocal homogeneity F3 is the combination of SSFs and SCFsClassification is done using three different feature vectors (F1F2 and F3) F1 F2 and F3 are calculated from scatteringsubbands and original images

The classification results are summarized in Table 4 Theclassification is implemented using feature vector F1 and amean success rate achieved is 8581 Using F2 the mean

success rate is 7399Then using F3 the mean success rateobtained is only 8523 The mean success rate obtainedusing F1 is about 1182 more than the average success rateobtained using F2 The mean success rate obtained using F3is about 1124 more than the average success rate obtainedusing F2

Comparing with the performance of RSFs andWSFs theaverage correct classification rate achieved using SSFs is thehighest Comparing with RCFs and WCFs the performanceof SCFs is better than that of RCFs and worse than theperformance ofWCFs Likewise the mean classification gainobtained using F3 is higher than that achieved using W3 andlower than the average classification rate of R3 when theperformance of F3 is compared with that of R3 and W3

From experiment results of this section it is found that ajoint phenomenon is that F2 is much worse than F1 whilstF3 is a little bit worse than F2 we speculate that it maybe due to high variance in the estimation of cooccurrencefeaturesThrough the comparison with wavele transform andridgelet transform the classification performance based onscattering statistical features is the best in the four datasetsFor cooccurrence features the mean classification accuracyof SCFs is comparable with that of RCFs and WCFs in thisstudy When combining statistical features and cooccurrencefeatures the average classification accuracy obtained by F3is lower than that achieved by feature vectors R3 and W3for small amounts of datasets For large amounts of datasetsthe experimental results obtained by F3 are better than thatachieved using W3 but worse than the outcomes of R3

5 Conclusion

In this present work the highest mean success rate achievedusing scattering statistical and cooccurrence features is9607 9496 9134 and 8581 in Dataset-1 Dataset-2Dataset-3 and Dataset-4 respectively Our methods may not


be competitive to state-of-the-art feature extraction methodsusing significant image knowledge and heuristics Howeverwe find that these results are promising and view them asa proof of concept for SSFs and SCFs From the exhaustiveexperiments conducted with texture image datasets it isinferred that statistical features in the context of scatteringrepresentations provide a good compromise between dis-criminability and good feature properties whereas cooccur-rence features come with nonhigh discriminability

Our current work has so far focused on algorithmicdevelopment and experimental justification More thoroughtheoretical analysis of feature extraction methods proposedis expected in the future Furthermore this work can beextended for an efficient classification system design withexcellent success rate of classification

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgments

The first author would like to express gratitude to her advisorProfessor Jiangshe Zhang for his valuable comments andsuggestions which lead to a substantial improvement ofthis paper This work was supported by the National BasicResearch Program of China (973 Program) under Grantno 2013CB329404 and the Major Research Project of theNational Natural Science Foundation of China under Grantnos 91230101 11131006 11201367 and 61572393

References

[1] S Arivazhagan and L Ganesan ldquoTexture segmentation usingwavelet transformrdquo Pattern Recognition Letters vol 24 no 16pp 3197ndash3203 2003

[2] L M Kaplan ldquoExtended fractal analysis for texture classifica-tion and segmentationrdquo IEEE Transactions on Image Processingvol 8 no 11 pp 1572ndash1585 1999

[3] P P Raghu and B Yegnanarayana ldquoSegmentation of gabor-filtered textures using deterministic relaxationrdquo IEEE Transac-tions on Image Processing vol 5 no 12 pp 1625ndash1636 1996

[4] A Materka and M Strzelecki ldquoTexture analysis methodsmdasha reviewrdquo COST B11 report Technical University of LodzInstitute of Electronics Brussels Belgium 1998

[5] R M Haralick ldquoStatistical and structural approaches to tex-turerdquo Proceeding of IEEE vol 67 no 5 pp 786ndash804 1979

[6] L Cohen ldquoTime-frequency distributionsmdasha reviewrdquo Proceed-ings of the IEEE vol 77 no 7 pp 941ndash981 1989

[7] A Teuner O Pichler and B J Hosticka ldquoUnsupervised texturesegmentation of images using tuned matched Gabor filtersrdquoIEEE Transactions on Image Processing vol 4 no 6 pp 863ndash870 1995

[8] S Arivazhagan L Ganesan and T G Subash Kumar ldquoTextureclassification using ridgelet transformrdquo Pattern RecognitionLetters vol 27 no 16 pp 1875ndash1883 2006

[9] S Arivazhagan and L Ganesan ldquoTexture classification usingwavelet transformrdquo Pattern Recognition Letters vol 24 no 9-10 pp 1513ndash1521 2003

[10] T Chang and C C J Kuo ldquoTexture analysis and classificationwith tree-structured wavelet transformrdquo IEEE Transactions onImage Processing vol 2 no 4 pp 429ndash441 1993

[11] S Hatipoglu S K Mitra and N Kingsbury ldquoTexture classifica-tion using dual-tree complex wavelet transformrdquo in Proceedingsof the 7th International Conference on Image Processing and itsApplications pp 344ndash347 July 1999

[12] S Mallat ldquoGroup invariant scatteringrdquo Communications onPure and Applied Mathematics vol 65 no 10 pp 1331ndash13982012

[13] L Sifre and S Mallat ldquoRotation scaling and deformationinvariant scattering for texture discriminationrdquo in Proceedingsof the 26th IEEE Conference on Computer Vision and PatternRecognition (CVPR rsquo13) pp 1233ndash1240 Portland Ore USAJune 2013

[14] L Sifre and S Mallat Rigid-motion scattering for texture classi-fication [PhD thesis] Ecole Polytechnique CMAP 2014

[15] J Zhang B Zhang and X Jiang ldquoAnalysis of feature extractionmethods based onwavelet transformrdquo Siginal Processing vol 16pp 157ndash162 2000

[16] S Mallat ldquoRecursive interferometric representationrdquo in Pro-ceedings of the European Signal Processing Conference pp 716ndash720 Aalborg Denmark August 2010

[17] Y LeCun K Kavukcuoglu and C Farabet ldquoConvolutionalnetworks and applications in visionrdquo in Proceedings of the IEEEInternational Symposium on Circuits and Systems pp 253ndash256IEEE Paris France June 2010

[18] J Bouvrie L Rosasco and T Poggio ldquoOn invariance inhierarchical modelsrdquo in Proceedings of the Advances in NeuralInformation Processing Systems 22 (NIPS rsquo09) pp 162ndash170 2009

[19] J Bruna and S Mallat ldquoInvariant scattering convolution net-worksrdquo IEEE Transactions on Pattern Analysis and MachineIntelligence vol 35 no 8 pp 1872ndash1886 2013

[20] MKokare P K Biswas and BN Chatterji ldquoRotation-invarianttexture image retrieval using rotated complex wavelet filtersrdquoIEEE Transactions on Systems Man and Cybernetics Part BCybernetics vol 36 no 6 pp 1273ndash1282 2006

[21] R M Haralick K Shanmugam and I Dinstein ldquoTexturefeatures for image classificationrdquo IEEE Transactions on ImageProcessing vol 8 pp 1572ndash1585 1973

[22] N Bhatia ldquoSurvey of nearest neighbor techniquesrdquo Interna-tional Journal of Computer Science and Information Security vol8 no 2 pp 302ndash305 2010

[23] F Bajramovic F Mattern N Butko and J Denzler ldquoA compar-ison of nearest neighbor search algorithms for generic objectrecognitionrdquo in Proceedings of the 8th International ConferenceonAdvanced Concepts for Intelligent Vision Systems (ACIVS rsquo06)Antwerp Belgium September 2006 vol 4179 of Lecture Notes inComputer Science pp 1186ndash1197 Springer 2006

[24] Y Liao and V R Vemuri ldquoUsing text categorization techniquesfor intrusion detectionrdquo Survey Paper University of California2002

[25] S Xu and Y Wu ldquoAn algorithm for remote sensing imageclassification based on artificial immune B-cell networkrdquo TheInternational Archives of the Photogrammetry Remote Sensingand Spatial Information Sciences vol 37 pp 107ndash112 2008

[26] P Brodatz Textures A Photographic Album for Artists andDesigners Dover New York NY USA 1966

[27] VisTex Color Image Database MIT Media Lab CambridgeMass USA 1995

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of signal spectral features For these reasons it is interesting inapplication to texture analysis for wavelet transform Ridgelettransform can deal effectively with line singularities in 2DIt is well known that texture classification based on ridgeletstatistical features (RSFs) and ridgelet cooccurrence features(RCFs) has been done by Arivazhagan et al [8]

In the last few decades wavelet theory has been widelyused for texture classification purposes [9ndash11] Howeverwavelet transform is not translation invariant In 2012 Mallatadvanced scattering transform which is invariant to trans-lations and Lipschitz continuous relatively to deformations[12] Scattering transform can overcome the weakness ofwavelet transform that is not translation invariant The ideais that scattering transform is computed by iterating oversuccessive wavelet transforms and modulus operators Scat-tering transformmaps high frequency information of imagesto low frequency Then scattering transform can providea stationary representation Scattering transform has foundapplications in texture classification (eg [13 14]) Theseclassification tasks are based on original scattering vectors

In this paper the scattering transform is applied on aset of texture images Statistical features and cooccurrencefeatures are extracted from original images and each ofscattering subbandsThese features are used for classificationFor the sake of comparative analysis classification tasks aredone using RSFs RCFs wavelet statistical features (WSFs)and wavelet cooccurrence features (WCFs) respectively Theexperimental results show that the success rate of our featureextraction techniques is promising but unsatisfactory But itis considered as a proof of concept for scattering statisticalfeatures (SSFs) and scattering cooccurrence features (SCFs)

The rest of this paper is organized as follows In Section 2the theory of scattering transform is briefly reviewed Thefeature extraction and texture classification are explained inSection 3 In Section 4 texture classification experimentalresults are discussed in detail Finally concluding remarks aregiven in Section 5

2 Scattering Transform

Wavelet transform is a process which was applied to originalsignal by a filter [15] 119866 denotes a discrete finite rotationgroup in 119877

2 A wavelet function 120595 is a band-pass filter Thefollowing formula is rotation and dilation of 120595

120595120582(119909) = 2

2119895120595 (2119895119903minus1119909) (1)

with 120582 = 2119895119903 isin and = 119866 times 119885 and |120582| = 2

119895 119903 isin 119866 is rotationparameter 2119895 for 119895 isin 119885 is dilation parameter

A texture119883(119909) is modeled as a realization of a stationaryprocess So the wavelet transform of 119883(119909) is written asfollows

119882120582119883(119909) = 119883 lowast 120595

120582(119909) (2)

119880[120582]119883(119909) = |119883 lowast120595120582(119909)| is the wavelet modulus of119883(119909)The

high frequency coefficients of wavelet transform are mappedto the low frequency form by the modulus operator [16]

Xp = 0

U[1205821]X

p = 1

U[1205821 1205822]X

p = 2

U[1205821 1205822 1205823]X

SJ[120601]XSJ[1205821]X SJ[1205821 1205822]X



Figure 1 Scattering transform It can be seen as a network whichiterates over wavelet transform and modulus operator

The result of the convolution of texture 119883(119909) and zoomfunctionΦ

119869(119909) is low frequency information that is

119860119869119883 (119909) = 119883 (119909) lowast Φ

119869(119909) (3)

where Φ119869(119909) = 2

minus2119869Φ(2minus119869119909) The resulting wavelet modulus

operator |119872| is

|119872|119883 (119909) = 119883 lowast Φ119869(119909)

1003816100381610038161003816119883 lowast 120595120582(119909)

1003816100381610038161003816 (4)

The high frequency information which is lost by thewavelet modulus operator could be recovered by next 119880 [12]resulting in the scattering propagators 119880[119901] along differentpaths 119901 = (120582

1 120582

119898) as follows

119880 [119901]119883 (119909) = 119880 [120582119898] sdot sdot sdot 119880 [120582

1]119883 (119909)

= |sdot sdot sdot |⏟⏟⏟⏟⏟⏟⏟119898

119883 lowast 1205951205821

10038161003816100381610038161003816lowast1205951205822

10038161003816100381610038161003816sdot sdot sdot

10038161003816100381610038161003816lowast120595120582119898(119909)

10038161003816100381610038161003816

(5)

In particular when 119901 = 0 119880[120601]119883(119909) = 119883(119909)

The wavelet modulus operator is iteratively applied toprogressively map the high frequency information to the lowfrequency information Thus scattering operator is definedfrom 119860

119869119883(119909) = 119883(119909) lowast Φ

119869(119909) and 119880[120582]119883(119909) = |119883 lowast 120595

120582(119909)|

[12] The information of texture is scattered to different pathsin the iterative processThe scattering operator 119878

119869implements

a sequence of wavelet convolutions andmodulus followed bya convolution with Φ

119869

119878119869[119901]119883 (119909) = 119880 [119901]119883 lowast Φ

119869(119909)

= |sdot sdot sdot |⏟⏟⏟⏟⏟⏟⏟119898

119883 lowast 1205951205821

10038161003816100381610038161003816lowast1205951205822

10038161003816100381610038161003816sdot sdot sdot

10038161003816100381610038161003816lowast120595120582119898

10038161003816100381610038161003816lowast Φ119869(119909)

(6)

If 119901 = 0 then 119878119869[120601]119883(119909) = 119883(119909) lowast Φ

119869

The scattering transform is thus computed with a cascadeof wavelet transform and modulus The scattering transformprocess could be described by a deep network architecture(see eg [17 18]) as shown in Figure 1Mallat has proved thatthe energy of the deepest layer converges quickly to zero as thelength of path increases in [12] Bruna and Mallat [19] haveillustrated that most of the energy is concentrated in |119901| le

3 Further details about scattering transform are presented in[12]

3 Feature Extraction and TextureClassification

The steps involved in texture training and texture classifica-tion are shown in Figure 2

Texture Training At the stage of the texture training theknown texture images are decomposed by using scattering


Known textureimage


Featureextraction

Featureslibrary

(a)


Featureextraction

Featureslibrary


Classifier


(b)



mean (119898) = 1

1198732

119873

sum

119894119895=1

119901 (119894 119895) (7)


119873radic

119873

sum

119894119895=1

[119901 (119894 119895) minus 119898]2

(8)




= sum

119894

sum

119895

(119894 minus 119909+ 119895 minus

119910)4

119862 (119894 119895) (9)

Cluster shade (cs)

= sum

119894

sum

119895

(119894 minus 119909+ 119895 minus

119910)3

119862 (119894 119895) (10)


119894

sum

119895

(119894 minus 119895)2

119862 (119894 119895) (11)


= sum

119894

sum

119895

1

1 + (119894 minus 119895)2119862 (119894 119895)

(12)

where 119909= sum119894sum119895119894119862(119894 119895)

119910= sum119894sum119895119895119862(119894 119895) and 119862(119894 119895)



(119896) =

119899

sum

119894=1

abs [119891119894(119909) minus 119891

119894(119896)] (13)








119877is calculated

using

119878119877=119873119862

times 100 (14)



































5 Conclusion







Acknowledgments


References



































Volume 2014




Journal of











Journal of


Function Spaces






Algebra










Known textureimage


Featureextraction

Featureslibrary

(a)


Featureextraction

Featureslibrary


Classifier


(b)



mean (119898) = 1

1198732

119873

sum

119894119895=1

119901 (119894 119895) (7)


119873radic

119873

sum

119894119895=1

[119901 (119894 119895) minus 119898]2

(8)




= sum

119894

sum

119895

(119894 minus 119909+ 119895 minus

119910)4

119862 (119894 119895) (9)

Cluster shade (cs)

= sum

119894

sum

119895

(119894 minus 119909+ 119895 minus

119910)3

119862 (119894 119895) (10)


119894

sum

119895

(119894 minus 119895)2

119862 (119894 119895) (11)


= sum

119894

sum

119895

1

1 + (119894 minus 119895)2119862 (119894 119895)

(12)

where 119909= sum119894sum119895119894119862(119894 119895)

119910= sum119894sum119895119895119862(119894 119895) and 119862(119894 119895)



(119896) =

119899

sum

119894=1

abs [119891119894(119909) minus 119891

119894(119896)] (13)








119877is calculated

using

119878119877=119873119862

times 100 (14)



































5 Conclusion







Acknowledgments


References



































Volume 2014




Journal of











Journal of


Function Spaces






Algebra









































5 Conclusion







Acknowledgments


References



































Volume 2014




Journal of











Journal of


Function Spaces






Algebra














Acknowledgments


References



































Volume 2014




Journal of











Journal of


Function Spaces






Algebra
















Volume 2014




Journal of











Journal of


Function Spaces






Algebra









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