Kruizinga, P.

Petkov, N.

English

The performance of two well-known texture operators (based on Gabor-energy and the cooccurrence matrix) is compared with the performance of a new, biologically motivated texture operator the grating cell operator; which was proposed elsewhere by the authors. The comparison is made using a new quantitative method, based on the Fisher criterion. Together with some classification results comparison experiments the comparison shows a clear superiority of the new operator in oriented texture problems.</p

Proceedings - University of Groningen

   University of GroningenGrating cell operator features for oriented texture segmentationKruizinga, P.; Petkov, N.Published in:FOURTEENTH INTERNATIONAL CONFERENCE ON PATTERN RECOGNITION, VOLS 1 AND 2IMPORTANT NOTE: You are advised to consult the publisher's version (publisher's PDF) if you wish to cite fromit. Please check the document version below.Document VersionPublisher's PDF, also known as Version of recordPublication date:1998Link to publication in University of Groningen/UMCG research databaseCitation for published version (APA):Kruizinga, P., & Petkov, N. (1998). Grating cell operator features for oriented texture segmentation. In AK.Jain, S. Venkatesh, & BC. Lovell (Eds.), FOURTEENTH INTERNATIONAL CONFERENCE ON PATTERNRECOGNITION, VOLS 1 AND 2 (pp. 1010-1014). (INTERNATIONAL CONFERENCE ON PATTERNRECOGNITION). University of Groningen, Johann Bernoulli Institute for Mathematics and ComputerScience.CopyrightOther than for strictly personal use, it is not permitted to download or to forward/distribute the text or part of it without the consent of theauthor(s) and/or copyright holder(s), unless the work is under an open content license (like Creative Commons).The publication may also be distributed here under the terms of Article 25fa of the Dutch Copyright Act, indicated by the “Taverne” license.More information can be found on the University of Groningen website: https://www.rug.nl/library/open-access/self-archiving-pure/taverne-amendment.Take-down policyIf you believe that this document breaches copyright please contact us providing details, and we will remove access to the work immediatelyand investigate your claim.Downloaded from the University of Groningen/UMCG research database (Pure): http://www.rug.nl/research/portal. For technical reasons thenumber of authors shown on this cover page is limited to 10 maximum.Download date: 11-10-2022Appearedin in: Proc. of the14thInt. Conf. onPatternRecognition, Brisbane,Australia,August16-20,1998,pp.1010-1014.Grating cell operator features for oriented texture segmentationP. KruizingaandN. PetkovInstituteof MathematicsandComputingScienceandCentrefor High PerformanceComputingUniversityof GroningenP.O.Box 800,9700AV Groningen,TheNetherlandspeterkr@cs.rug.nl, petkov@cs.rug.nlAbstractThe performanceof two well-knowntexture operators(basedon Gabor-energy and the cooccurrencematrix) iscomparedwith theperformanceof a new, biologically mo-tivated texture operator, the grating cell operator, whichwasproposedelsewhere by theauthors. Thecomparisonismadeusinga new quantitativemethod,basedon theFishercriterion. Togetherwith someclassificationresultscompar-isonexperimentsthecomparisonshowsa clear superiorityof thenew operator in orientedtexture problems.1. IntroductionTexture is an importantpart of the visual world of an-imals and men and their visual systemssuccessfullyde-tect,discriminateandsegmenttexture. Relatively recentlyprogresswasmadeconcerningstructuresin thebrainwhicharepresumablyresponsiblefor textureprocessing.Von derHeydt etal. [19] reportedon thediscoveryof a new typeoforientationselectiveneuronin areasV1 andV2 of thevisualcortex of monkeys which they calledgrating cell. Gratingcells respondvigorouslyto gratingsof barsof appropriateorientation,positionandperiodicity. In contrastootherori-entationselective cells, gratingcells respondvery weaklyor notatall to singlebarswhichdonotmakepartof a grat-ing. This behaviour of gratingcellscannotbeexplainedbylinearfiltering followedby half-wave rectificationasin thecaseof simplecells, neithercan it be explainedby three-stagemodelsof thetypeusedfor complex cells.Elsewherewe proposeda modelof this typeof cell anddemonstratedtheadvantagesof gratingcellswith respecto theseparationof textureandform information[9, 16].In this paperwe usetheoutputof gratingcell operatorsastexturefeaturesandcomparethemwith commonlyusedtexture featuresascooccurrencematrix andGabor-energyfeatures. For this comparisona new methodis proposedwhich enablesa quantitative evaluationof the texture dis-criminationpropertiesof featureextractionoperators.Themethoddiffersfrom thecommonlyusedtexturefeatureper-formanceevaluationmethodwhich is basedonthecompar-isonof classificationresults[1, 3, 13, 17, 20].Theproblemwith the traditionalcomparisonmethodisthat it mixestogetherthe performanceof a classifierwiththe discriminationpropertiesof the featureoperator. Fur-thermore,it doesnot give an estimationof the reliabilityof classification:for instance,two differentoperatorscangive rise to the samenumberof misclassifiedpixelswhenappliedto two different texture images,but this doesnotmeanthat they will performequallyin futureclassificationtaskswith otherimagesof thesametextures.Consequently,a methodis neededin which the performanceof a classi-fier canbeseparatedfrom thediscriminationpropertiesofthefeatureoperatorandin which thespreadin thediscrim-inationpropertiescanbequantifiedin orderto estimatethereliability of classification.2. Grating cell modelOur modelof gratingcells consistsof two stages[16].In the first stage,the responsesof so-calledgrating sub-unitsarecomputedusingasinput thecomputedresponsesof centre-onandcentre-of simplecells with symmetricalreceptivefields(for a computationalmodelof simplecells,see[15]). The modelof a gratingsubunit is conceived insucha way that the unit is activatedby a setof threebarswith appropriateperiodicity, orientationandposition.In thesecondstage,the responsesof gratingsubunits of a givenpreferredorientationandperiodicity aresummedtogetherwithin a certainareato computethe responseof a gratingcell. Thismodelis next explainedin moredetail:A quantity     	 , calledtheactivity of a gratingsub-unit with position  , preferredorientation     andpreferredgratingperiodicity  , is computedasfollows:    	! #"%$'&)( +*    	, -/.10324  5 	 "%$763( 8*    	, -/910324  5 	 (1)where ( ;:=<?>?@@@ABand 0 is a thresholdparameterwith avaluesmallerthanbutnear1 (e.g. 0   @ C ) andtheauxiliaryquantities*   5 	D -and 2    	 arecomputedasfollows:*   5 	D -  E7FDG :IH JK JK  	, LNMPO DQ3QR(  A5ST=U WVX Q <Y, 9  ([Z\   AST=U ](  A5U^`_ aVbc Q <Y 9  (PZd   AU^e_ ]f - g  (  <?>h<     (  <iA  jA B (2)whereH J J  	, LNM is theoutputof asimplecell operator1 ofpreferredorientation andperiodicity  atposition c Q  Q and 2    	'\E7FIG :*    	, - O (  <?>k@@h@A3B (3)Thequantities*    	, -  (  <?>?@@@A arerelatedto theactivities of simple cells with symmetricreceptive fieldsalong a line segmentof length >N passingthroughpointc in orientation  . This segmentis divided in inter-vals of length	 landthe maximumactivity of onesort ofsimplecells, centre-on f -    or centre-of  f -   ,is determinedin eachinterval. *  I  	,nm)o , for instance,isthemaximumactivity of centre-onsimplecellsin thecorre-spondinginterval of length	 l; *   5 	Dnm l is themaximumactivity of centre-of simplecells in the adjacentinterval,etc.Centre-onandcentre-of simplecell activitiesarealter-natelyusedin consecutive intervals. 2    	 is themaxi-mumamongtheabove interval maxima.Roughly speaking,the concernedgrating cell subunitwill beactivatedif centre-onandcentre-of cellsof thesamepreferredorientation  andspatialfrequency p	 arealter-natelyactivatedin intervalsof length	 lalongalinesegmentof length >N centredonpoint  andpassingin direction . This will, for instance,bethecaseif threeparallelbarswith spacing andorientation of thenormalto themareencountered(Fig.1). In contrast,the condition is not ful-filled by thesimplecell activity patterncausedby a singlebaror two bars,only.In the next, secondstageof the model, the responseqr   	 of a gratingcell is computedby weightedsumma-tion of the responsesof the gratingsubunits. At the same1Halfwave rectifiedconvolutionof theimagewith a2D Gaborfunction(see[15, 16] for furtherdetails).responsesinputcentre-onc)b)a)M M M-3M M M-1-2 0 21centre-offresponsesFigure 1. Luminance distribution along a nor-mal to a set of three square bars (a), andthe distribution of the computed responsesof centre-on (b) and centre-off (c) simple cellsalong this line.time themodelis madesymmetricalfor oppositedirectionsby taking the sumof gratingsubunits with orientationsand  Z  .q    	 s3tvu m?wnxy,x J{z}|j~ w}y, Jez{|| w  z |    J J  	 Z   J J 3 	 5 Q  Q a    (4)Theweightedsummationis a provision madeto modelthespatialsummationpropertiesof gratingcellswith respectothenumberof barsandtheir lengthaswell astheirunmod-ulatedresponseswith respectto the exactposition(phase)of a grating. The parameter determinesthe size of theareaover which effective summationtakesplace. A valueof   resultsin a good approximationof the spatialsummationpropertiesof gratingcells. For further detailswe refer to [16]. The gratingcell operatoris availableontheinternet[10].3. Texture features and the Fisher criterionThequantitiescomputedwith thegratingcell operatorscanbe usedastexture features.We next comparethe fol-lowing setof features: Grating cell operator features: A setof gratingcelloperatorswith eight different preferredorientationsandthreepreferredspatial-frequenciesi appliedto animage,yieldinga vectorof 24 featuresin eachpoint. Gabor-energy features: A popularsetof texturefea-tures is basedon the use of Gabor filters [7]. InT1 T2 T3 T4 T5 T6 T7 T8 T9T1 - 4.36 9.61 9.23 4.77 8.33 9.91 13.47 13.99T2 - 7.51 6.35 4.79 5.65 6.24 10.96 9.31T3 - 14.62 9.60 6.24 3.84 6.72 20.40T4 - 8.24 15.60 10.09 18.67 24.36T5 - 7.72 9.38 13.06 11.20T6 - 4.53 6.83 11.96T7 - 6.14 15.33T8 - 39.71T9 -Table 1. The Fisher criterion for pairs of texture images calculated on the basis of feature vectorsobtained with the grating cell operator.this case,an imageis filtered with a setof Gaborfil-terswith differentorientations,spatialfrequenciesandphases.Using eight orientationsand threepreferredspatial-frequenciesandcombiningtheresultsof sym-metric and anti-symmetricfilters, this multi-channelfiltering schemeyields a featurevectorof 24 Gabor-energy quantities.Thesamepreferredorientationsandspatial-frequenciesareusedastheonesof thegratingcell operators. Cooccurrence matrix features: A classicmethodfortexturesegmentationis basedon the gray-level cooc-currencematrices[6]. In eachpoint of a texture im-age,a setof gray-level cooccurrencematricesis cal-culatedfor different orientationsand inter-pixel dis-tances.From thesematrices,a numberof featuresisextractedwhichcharacterisetheneighbourhoodof theconcernedpixel. In our experimentseight gray-levelcooccurrencematriceswere calculatedin eachpointusing a neighbourhoodof size  A  A . From eachof the matricesthreefeatures(energy, inertia anden-tropy) wereextractedresultingin a vectorof 24 fea-turesin eachimagepoint.The featurevectorscomputedat differentpointsof a tex-ture usinga given operatorarenot identical. They ratherform a clusterin themulti-dimensionalfeaturespace.Thelarger thedistancebetweentwo clusterswhich correspondto two differenttypesof texture, thebetterthediscrimina-tion propertiesof the texture operatorwhich producedthefeaturevectors. The distancehas,of course,to be relatedto the size of the clusters. In order to determinethe dis-tancebetweentwo clustersof featurevectors,it is sufficientto look at theprojectionof the  -dimensionalfeaturespaceonto a one-dimensionalspace,underthe assumptionthatthis projectionmaximisestheseparabilityof theclustersintheone-dimensionalspace.A lineartransformationthatre-alizesthis projectionwasfirst introducedby Fisher[4] andis called Fisher’s linear discriminantfunction. It hasthefollowing form:    p < l %8 m p  , where  p and  larethemeansof thetwo clustersand  m p is the inverseofthe pooledcovariancematrix. Fisher’s linear discriminantfunction is invariantunderany nonsingularlinear transfor-mation.Figure 2. The nine test images of oriented tex-tures, enumerated T1 through T9 left to rightand top to bottom.Theprojectionof thefeaturevectorsontotheprojectionline maximisestheso-calledFishercriterion[5] !)j   where ¢¡ and  ¤£ arethestandarddeviationsof thedistribu-tionsof theprojectedfeaturevectorsof therespectiveclus-tersand ¥¡ and ¥,£ aretheprojectionsof themeans¦8¡ and¦£ . Sincethematrix §  ¡ is positivedefinite,thedifference¥ ¡,¨ ¥ £ is alwayspositive.TheFishercriterionexpressesthedistancebetweentwo clustersrelative to their compactnessT1 T2 T3 T4 T5 T6 T7 T8 T9T1 - 4.17 4.90 5.66 3.39 4.99 4.95 4.15 6.29T2 - 2.86 4.45 2.65 3.02 3.04 3.05 5.70T3 - 6.38 3.64 1.80 3.19 3.25 5.96T4 - 5.24 7.06 4.96 7.09 9.24T5 - 3.35 3.18 3.45 5.15T6 - 2.90 2.61 6.54T7 - 3.31 6.46T8 - 5.53T9 -Table 2. The Fisher criterion for pairs of texture images calculated on the basis of feature vectorsobtained with the Gabor-energy operator.in onesinglequantity.4. Performance evaluation and comparisonThe performanceof the grating cell operatoris evalu-atedaccordingto theFishercriterionby theseparabilityofnine test images,eachcontaininga singleorientedtexture(Fig.2). Theseparabilityis measuredin thefollowing way:asetof 24differentgratingcell operatorsis appliedto eachimage. In this way eachimagepoint is assigneda featurevectorof 24 gratingcell operatorcoefficients. Thepooledcovariancematrix is calculatedfor eachpair of imagesus-ing 1000samplefeaturevectorsfrom eachimage.Thenthefeaturevectorsareprojectedon a line usingFisher’s lineardiscriminantfunction andthe Fishercriterion is evaluatedin theprojectionspace.Table1 shows thevaluesof theFishercriterionfor eachpair of the test images. The minimum valuelisted is >@ © ,which meansthat for all imagepairs,theprojectedfeaturevectordistributionswill at mostoverlapfor about @   Iª .Thereforeall clustersof featurevectorscan be separatedlinearly. Note that the featurevectorsof eachclusteraretakenfrom animagethatcontainsmerelyonetexture.Thismeansthat it is a priori known to which clusterthefeaturevectorsamplesbelongto, resultingin agoodestimateof thecovariancematrix.The values obtainedwith the Gabor-energy features(listedin Table2) areall smallerthantheonesobtainedwiththegratingcell features.OnaveragetheFishercriterionforthe Gabor-energy featuresis morethantwo timessmallerthanfor the gratingcell features.Anyhow, the Fishercri-terion is still largeenoughto distinguishthe clusters.TheGabor-energy featuresarethereforesuitablefor theclassi-ficationof a textureimagesasa whole,i.e. classificationofanentiretextureimagebasedon thedistribution of a largenumberof projectedfeaturevectors.For thesegmentationof a textureimageinto regionscontainingthesametexture,i.e. for theclassificationof the individual pixels,the inter-clusterdistanceis notsufficiently largeascanbeseenfromFigure3. The quality of the cooccurrencematrix featuresis evenworsein comparisonto theGabor-energy features.Thoughtheinter-clusterdistanceis largeenoughfor classi-ficationof textureimagesasa whole(Table3), thefeaturesareinappropriatefor classificationof singlepixels.Figure3 shows the resultsof pixel classificationusingK-meansclusteringof thegeneratedfeaturevectors.It fur-ther demonstratesthe superiorityof grating cell operatorfeaturesto Gabor-energy andcooccurrencematrix features.In a future work, the authorswill comparethe gratingcell operatorwith the operatorsandmethodsproposedbyUnser [18], Laws [11] and Mitchell [12], the fractal di-mensionapproach[14], a methodbasedon GOP(GeneralOperationProcessor)operations[8], graylevel differences,centre-symmetricovariancefeatures,local binarypatterns[17] andMarkov randomfields[2].References[1] R. ConnersandC. Harlow. A theoreticalcomparisonof tex-turealgorithms.IEEETransactionsonPatternAnalysisandMachineIntelligence, 2(3):204–222,1980.[2] G. CrossandA. Jain. Markov randomfield texturemodels.IEEETransactionsonPatternAnalysisandMachineIntelli-gence, 5(1):25–39,1983.[3] J. Du Buf, M. Kardan, and M. Spann. Texture featureperformancefor imagesegmentation.PatternRecognition,23:291–309,1990.[4] A. Fisher. The mathematicaltheory of probabilities, vol-ume1. Macmilan,New York, 1923.[5] K. Fukunaga.Introductionto statisticalpatternrecognition.AcademicPress,1990.[6] R. Haralick,K. Shanmugam,andI. Dinstein. Textural fea-turesfor imageclassification. IEEE Transactionson Sys-tems,ManandCybernetics, 3(6):610–621,1973.T1 T2 T3 T4 T5 T6 T7 T8 T9T1 - 3.72 3.74 3.57 3.24 3.54 3.41 3.85 3.98T2 - 2.92 3.49 2.62 3.88 3.38 3.47 3.38T3 - 3.76 2.62 2.80 3.00 3.32 3.77T4 - 3.61 4.26 3.56 4.19 4.25T5 - 3.41 2.85 3.41 3.55T6 - 2.97 3.66 4.45T7 - 3.32 4.03T8 - 2.41T9 -Table 3. The Fisher criterion for pairs of texture images calculated on the basis of feature vectorsobtained with the cooccurrence matrix operator.Figure 3. Results of segmentation experiments using the K-means clustering algorithm. The left-most image shows an input image containing nine different textures. The exact segmentation ofthe input image is shown in the second image from the left. The three right-most images show thesegmentation results based on the grating cell operator features (middle column), the Gabor-energyfeatures (second column from the right) and the cooccurence matrix features (right-most column).[7] A. JainandF. Farrokhnia.Unsupervisedtexturesegmenta-tion usinggaborfilters. PatternRecognition, 24(12):1167–1186,1991.[8] H. KnutssonandG. Granlund.Textureanalysisusingtwo-dimensionalquadraturefilters. In IEEE Workshop CA-PAIDM, Pasadena,CA, 1983.[9] P. Kruizinga and N. Petkov. A computationalmodel ofperiodic-pattern-selective cells. In J. Mira andF. Sandoval,editors,Proc. IWANN’95, LectureNotesin ComputerSci-ence,vol.930,pages90–99.Springer-Verlag,1995.[10] P. Kruizinga, N. Petkov, and U. Hettema. The grat-ing cell operator interactive software implementation.http://www.cs.rug.nl/˜imaging/grcop.html.[11] K. Laws. Textured image segmentation. TechnicalRe-port USCIPI940,ImageProcessingInstitute,UniversityofSouthernCalifornia,1980.[12] O. Mitchell, C. Myers,andW. Boyne. A max-minmeasurefor imagetextureanalysis.IEEE Transactionson Comput-ing, C-2:408–414,1977.[13] P. OhanianandR. Dubes. Performanceevaluationfor fourclassesof textural features.PatternRecognition, 25(8):819–833,1992.[14] S.Peleg, J.Naor, R. Hartley, andD. Avnir. Multiple resolu-tion textureanalysisandclassification.IEEE Transactionson Pattern Analysisand Machine Intelligence, 6:514–523,1984.[15] N. Petkov. Biologicallymotivatedcomputationallyintensiveapproachesto imagepatternrecognition.FutureGenerationComputerSystems, 11:451–465,1995.[16] N. Petkov andP. Kruizinga.Computationalmodelsof visualneuronsspecialisedin the detectionof periodicandaperi-odicorientedvisualstimuli: barandgratingcells.BiologicalCybernetics, 76(2):83–96,1997.[17] O.Pichler, A. Teuner, andB. Hosticka.A comparisonof tex-ture featureextractionusingadaptive gaborfiltering, pyra-midalandtreestructuredwavelettransforms.PatternRecog-nition, 29(5):733–742,1996.[18] M. Unser. Locallineartransformsfor texturemeasurements.SignalProcessing, 11:61–79,1986.[19] R. von derHeydt, E. Peterhans,andM. Dürsteler. Periodic-pattern-selective cells in monkey visual cortex. Journal ofNeuroscience, 12:1416–1434,1992.[20] Z. Wang,A. Guerriero,andM. Desario.Comparisonof sev-eralapproachesfor thesegmentationof textureimages.Pat-ternRecognitionLetters, 17(5):509–521,1996.

Grating cell operator features for oriented texture segmentation

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Grating cell operator features for oriented texture segmentation

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