research article a comparison of moments-based logo...

Research ArticleA Comparison of Moments-Based Logo Recognition Methods

Zili Zhang12 Xuan Wang12 Waqas Anwar123 and Zoe L Jiang12

1 Computer Application Research Center Shenzhen Graduate School Harbin Institute of Technology Shenzhen 518055 China2 Shenzhen Applied Technology Engineering Laboratory for Internet Multimedia Application Shenzhen 518055 China3Department of Computer Science COMSATS Institute of Information Technology Abbottabad 22010 Pakistan

Correspondence should be addressed to Xuan Wang wangxuaninsunhiteducn

Received 26 May 2014 Revised 26 July 2014 Accepted 26 July 2014 Published 12 August 2014

Academic Editor Sher Afzal Khan

Copyright copy 2014 Zili Zhang 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

Logo recognition is an important issue in document image advertisement and intelligent transportation Although there are manyapproaches to study logos in these fields logo recognition is an essential subprocess Among the methods of logo recognition thedescriptor is very vital The results of moments as powerful descriptors were not discussed before in terms of logo recognition Soit is unclear which moments are more appropriate to recognize which kind of logos In this paper we find out the relations betweenlogos with different transforms and moments which moments are fit for logos with different transforms The open datasets areemployed from the University of Maryland The comparisons based on moments are carried out from the aspects of logos withnoise and rotation scaling rotation and scaling

1 Introduction

Logo recognition plays an important role in the patternrecognition Logo has been widely used in intelligent trans-portation advertisement and document retrieval So itattracts the attention of many researchers

The research about logos can be classified into threecategories from the perspective of applications intelligenttransportation advertisement anddocument retrieval In theintelligent transportation the logos can be used to identifythe types of cars or to guide the cars to automaticallydrive Studying the advertisements producers can get theinformation which consumers are interested in and promoteproducts to these customers In the document retrieval fieldthe logos can be used to automatically classify the files so asto save much time and cost for people Among these workslogo recognition as a kernel subprocess cannot be ignored Sothis paper mainly focuses on the logo recognition part whilelogo location and detection are not discussed hereThe logoswhich are discussed here are used to retrieve documentsAlthough many technologies have already been employed torecognize logos moments [1] which are power descriptorshave not been used to compare their abilities in terms ofrecognizing logos

The object of this paper is to compare the representationabilities of moments as descriptors which are used to extractfeatures of logos It can be found out that one moment is veryappropriate to describe one kind of logos These conclusionsare also very useful for future researchers The remainderof this paper is organized as follows Related works arereviewed from intelligent transportation advertisement anddocument retrieval in Section 2 Some moments and theirinvariant moments are discussed in Section 3 Experimentalsetup is introduced in Section 4 The results of recognizinglogos by moments are analyzed in Section 5 Finally weconclude and outline plans for future research in Section 6

2 Related Works

Logo recognition is reviewed from intelligent transportationadvertisement and document retrieval First Dai et al [2]used the Tchebichef moment invariants and support vectormachine to recognize the vehicle logos However the compu-tation process has much computational load Psyllos et al [3]presented a new vehicle-logo recognition algorithm based onan enhanced scale-invariant feature transform- (SIFT-) basedfeature-matching scheme This method can be employed in

Hindawi Publishing CorporationAbstract and Applied AnalysisVolume 2014 Article ID 854516 8 pageshttpdxdoiorg1011552014854516

2 Abstract and Applied Analysis

real-time framework Llorca et al [4] proposed a new vehicle-logo recognition approach using histograms of oriented gra-dients and support vector machines All logos with low reso-lution were captured by traffic cameras However the slidingwindow technique would cost much more time Yu et al[5] proposed a new fast and reliable system based on bag-of-words for vehicle-logo recognition The vehicle-logo imageswere represented as histograms of visual words and classifiedby support vector machine This method processed theimages with less timeMao et al [6] proposed a novel methodto detect the vehicle logos in an image This method firstapplied the horizontal and vertical direction filters to producttwo new images and a saliency map was yielded from eachimage Then a binary image was created from the saliencymap Finally the vehicle logos were localized This methodhad an advantage of real time

Second in the advertisement application den Hollanderand Hanjalic [7] employed template matching technologyto detect and classify the logos in video stills Howeverthis method is very sensitive with logos foreground Hessonand Androutsos [8] used a five-dimensional cooccurrenceof colors and wavelet decomposition coefficients of pairs ofpixels This algorithm can exploit multiresolution analysiswith wavelets Phan and Androutsos [9] presented an algo-rithmwhich extended the color edge cooccurrence histogram(CECH) object detection scheme on compound color objectsHowever this global descriptor was not suitable to deal withincomplete information or transformed versions of the origi-nal logos and it was not proper to exactly describe the localityof logo traits Qi et al [10] proposed an effective solution fortrademark image retrieval by combining shape descriptionand feature matching This method can be generalized toother applications Sun and Chen [11] proposed a new recog-nition method on mobile phone cameras for logo images Byusing the Zernike moment phase information a new distinc-tive logo feature vector and an associated similarity measurewere presented Zhang et al [12] introduced a novel prelocat-ing algorithm for rapid logo detection in unconstrained colorimagesThe spatial connected component descriptor (SCCD)represents the logos while an effective-connected componentdescribes the pixel distribution information Roy and Garain[13] presented a probabilistic approach for logo detectionand localization in natural scene images One probabilitydistribution described the features and another computedthe shape geometry information defined by the key pointsHowever this algorithm could not handle logos which weremapped in two different affine planes Chu and Lin [14] usedthe pair-specific concept to capture relevant features betweena query logo and a test image employed the mean-shiftmethod to find candidate regions and combined the visualword histograms and visual patterns to describe logo objectsNew features can be designed in order to further improve theperformance for some logos Sahbi et al [15] designed a novelvariational frameworkwhichwas able tomatch and recognizemultiple instances of multiple reference logos in imagearchives This paper used an energy function mixing to mea-sure the quality of feature matching captured feature cooc-currencegeometry and controlled the smoothness of thematching solution Liu and Zhang [16] proposed a multiple

dictionary invariant sparse coding to automatically collectrepresentative logo images from the internet without anyhuman labeling or seed images This method could beextended to more general images by adopting SIFT-like localfeatures of HMAX-like features

Finally in the document image field Doermann et al [17]presented a multilevel staged approach to recognize logosThe global invariants were used to prune the database whilethe local affine invariants were used to obtain a more refinedmatch However this algorithm was only implemented in asmall database Doermann et al [18] presented a novel appli-cation of algebraic and differential invariants to recognizelogos By using invariants the shape descriptors could be usedfor matching the logos which were unique and independentof the point of view The algebraic invariants could be usedwhen the whole shapes of the logos were given while thedifferential invariants could be used when the logos hadonly a part Cesarini et al [19] proposed a new approachfor training autoassociator-based artificial neural networks(AANN) especially conceived for dealing with spot noiseThe proposed algorithm which was referred to as spot-backpropagation (S-BP) was significantly more robust withrespect to spot noise than classical Euclidean norm-basedbackpropagation (BP) Chen et al [20] proposed a methodbased on modified line segment Hausdorff distance Thismethod had the advantage in incorporating structural andspatial information to compute dissimilarity So this methodhad a faster computation speed than the method using setsof points Gori et al [21] proposed a new approach toimprove the performance of multilayer perceptron operatingas autoassociators to classify graphical items in presence ofspot noise on the images The weights which were replacedby Euclidean norm depended on the gradients of the imagesin order to give less importance to uniform color regionsThismethodwas time-consuming and the authors only discussedthe noisy spot Wang and Chen [22] proposed a new methodbased on the boundary extension of feature rectangles Wang[23] presented a simple and dynamic method to detect andrecognize logos in document images By applying feedbackand selecting proper features they were able to make theframework dynamic and interactive The feedback mecha-nisms made the framework more accurate Li et al [24]introduced a fast segmentation-free and layout-independentlogo detection and recognition method The recognitionperformance and running time were improved Hassanzadehand Pourghassem [25] proposed a novel approach based onspatial and structural features of logo images to solve theseproblemsThe novel features based on horizontal and verticalhistogram of the logo images and the KNN classifier werecombined together to recognize logo images Pham et al[26] presented a new approach for detecting logos by exploit-ing contour based features In the first stage the outer contourstrings (OCS) could be computed from each graphic andtext part of the documents In the second stage two typesof features were computed from each OCS In the finalstep correction helped with the wrong segmentation casesBagheri et al [27] proposed a novel multiclass classificationmethod which was applied to recognize logos due to consid-ering logo recognition as a multiclass classification problem

Abstract and Applied Analysis 3

the proposed system mainly used the nearest neighborclassification algorithm and the powerful binary classifier

3 Moments

Moments [28] as descriptors are widely used in pattern recog-nition and computer vision In this paper radial Tchebichefmoment invariants radial Tchebichef moments TchebichefKrawtchouk Krawtchoukmoment invariants Legendre [29]pseudo-Zernike [29] andZernike [29] are all used since theseorthogonal moments have promising characteristics Affinemoment invariants [30] are also used for recognizing logosDifferent moments have different properties so we want tofind the appropriate moments to describe the logos withnoise scaling rotation and rotation and scaling The follow-ing part introduces the moments and moment functions

Zernike and pseudo-Zernikemoments are defined in unitcircle The moment function of Zernike is defined in (1) andthat of pseudo-Zernike is defined in (3) respectively

119860119901119902 =119901 + 1

120587intint119863

119891 (119909 119910)119881lowast

119901119902(119909 119910) 119889119909 119889119910 (1)

where 119881lowast

119901119902(119909 119910) is complex conjugates of Zernike function

and 119881119901119902(119909 119910) is defined in

119881119901119902 (119909 119910)

=

(119901minus|119902|)2

sum

119904=0

(minus1)119904(119901 minus 119904)119903

119901minus2119904

119904 (((119901 +10038161003816100381610038161199021003816100381610038161003816) 2) minus 119904) (((119901 minus

10038161003816100381610038161199021003816100381610038161003816) 2) minus 119904)

119890119895119902120579

(2)

where119901 = 0 1 2 infin 0 le |119902| le 119901119901minus|119902| = even 119895 = radicminus1120579 = tanminus1(119910119909) 119903 = radic1199092 + 1199102

119885119901119902 =119901 + 1

120587int

2120587

0

int

1

0

119881lowast

119901119902(119903 120579) 119891 (119903 120579) 119903119889 119903119889 120579 (3)

where 119901 = 0 1 2 infin 0 le |119902| le 119901 lowast denotes complexconjugate 119881119901119902(119903 120579) is defined in (4) as

119881119901119902 (119903 120579) =

119901minus|119902|

sum

119904=0

(minus1)119896(2119901 + 1 minus 119904)119903

119901minus119904

119904 (119901 minus10038161003816100381610038161199021003816100381610038161003816 minus 119904) (119901 +

10038161003816100381610038161199021003816100381610038161003816 + 1 minus 119904)

119890119895119902120579

(4)

Legendre is similar to Zernike and pseudo-Zernikewhich are all continue orthogonal moments However Leg-endre is defined in unit square and its moment function isdefined in (5) as

119871119901119902 =(2119901 + 1) (2119902 + 1)

4∬

1

minus1

119875119901 (119909) 119875119902 (119910) 119891 (119909 119910) 119889119909 119889119910

(5)

where 119909 119910 isin [minus1 1]

119875119901 (119909) =

119901

sum

119896=0

(minus1)(119901minus119896)2 1

2119901

(119901 + 119896)119909119896

((119901 minus 119896) 2) ((119901 + 119896) 2)119896

(6)

where 119901 minus 119896 = even

Tchebichef [31] and Krawtchouk [32] moments are dis-crete orthogonal moments They have minimal informationredundancy and better reconstruction abilities The maincharacteristic of them is that they are defined in the dis-crete domain which is different from continuous orthogonalmoments This characteristic makes them free from thedilemma of conversion of coordinatesThemoment functionof Tchebichef is defined in (7) as

119879119901119902 =1

120588 (119901119873) 120588 (119902119873)

119873minus1

sum

119909=0

119873minus1

sum

119910=0

119901 (119909) 119902 (119910) 119891 (119909 119910) (7)

where 119901 119902 = 0 1 2 119873minus 1119873 is the width or height of theimage 119891(119909 119910) denotes an image intensity function

120588 (119899119873) =120588 (119899119873)

120573(119899119873)2

120588 (119899119873) = (2119899) (119873 + 119899

2119899 + 1)

(8)

where 119899 = 0 1 119873 minus 1 Consider

120573 (119899119873) = 119873119899

119899 (119909) =119905119899 (119909)

120573 (119899119873)

119905119899 (119909) = 119899

119899

sum

119896=0

(minus1)119899minus119896

(119873 minus 1 minus 119896

119899 minus 119896)(

119899 + 119896

119899)(

119909

119896)

(9)

Krawtchoukmoment can get local information by tuningthe two parameters This is different from the Tchebichefmoment Moment function of Krawtchouk is defined as

119876119899119898 =

119873minus1

sum

119909=0

119872minus1

sum

119910=0

119870119899 (119909 1199011 119873 minus 1)119870119898 (119910 1199012119872 minus 1) 119891 (119909 119910)

(10)

where 119891(119909 119910) denotes the intensity function Consider

119870119899 (119909 119901119873) = 119870119899 (119909 119901119873)radic120596 (119909 119901119873)

120588 (119899 119901119873)

119870119899 (119909 119901119873) =

119899

sum

119896=0

(minus119899)119896(minus119909)119896

(minus119873)119896

(1119901)119896

119896

(11)

119909 119899 = 0 1 2 119873 119901 isin (0 1)

120596 (119909 119901119873) = (119873

119909)119901119909(1 minus 119901)

119873minus119909

120588 (119899 119901119873) = (minus1)119899(1 minus 119901

119901)

119899119899

(minus119873)119899

(12)

119899119898 = 1 2 119873 (119886)119896 is the Pochhammer symbol asdefined in

(119886)119896 = 119886 (119886 + 1) sdot sdot sdot (119886 + 119896 minus 1) (13)


11 12 13 14 15 16 17 18 19 110 111 112 113 114 115 116 117

118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134

135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150

Figure 1 Ideal logos

Affine moment invariants [30] are features for patternrecognition computed from moments of objects on imagesthat do not change their value in affine transformationThe theory of these invariants is connected to the theoryof algebraic invariants These invariants are automaticallygenerated based on the graph theory The moment functioncan be constructed in

119868 (119891) = int

+infin

minusinfin

sdot sdot sdot int

+infin

minusinfin

119903

prod

119896119895=1

119862119899119896119895

119896119895sdot

119903

prod

119894=1

119891 (119909119894 119910119894) 119889119909119894119889119910119894 (14)

where the cross-product 119862119896119895 = 119909119896119910119895 minus 119909119895119910119896 is the orienteddouble area of the triangle whose vertices are (119909119896 119910119896)(119909119895 119910119895) and (0 0) and 119899119896119895 are nonnegative integers

4 Experimental Setup

To conduct a comprehensive comparison the open dataset(University ofMaryland Laboratory for Language andMediaProcessing (LAMP) LogoDataset httplampsrv02umiacsumdeduprojdbprojectphpid=47) from the University ofMaryland is employedThis dataset contains 106 logos in thisexperiment 50 original logos are shown in Figure 1

To evaluate the representation abilities of differentmoments four groups of logos are used The first group islogos with different noise which includes Gaussian whitenoise of mean zero and variance 01 that of mean zero andvariance 02 Poisson noise salt and pepper noise of densities002 005 008 01 015 and 02 speckle noise with mean0 and variance 005 and that with mean 0 and variance01 The second group is logos with scaling and the scalingfactors are 025 05 075 12 and 20 The third group islogos with rotation and the rotation angles are 30 60 90120 and 150 degrees The final group is logos with rotationand scaling which includes logos with rotation 30 degreesand scaling factor being 05 that with rotation 60 degrees andscaling factor being 075 and that with rotation 90 degreesand scaling factor being 12

The K-nearest neighbors are employed as a tool to recog-nize the logos The total number of logos is denoted by TNand the number of logos correctly recognized is denoted byCR The recognition rate is denoted by (CRTN)

5 Experiments

In pattern recognition and computer vision fields perfor-mance evaluation is more and more important Mikolajczykand Schmid [33] compared shape context steerable filtersPCA-SIFT differential invariant spin images complex filtersmoment invariants and cross correlation for different typesof interest regions Concerning the performances of differentmoments Tsougenis et al [34] had made comparisons interms of watermarking methods To our best knowledgethe performances about logo recognition based on momentshave not been discussed before In this section the compre-hensive comparisons are carried out The experiments areimplemented in turn according to the four groups of logosThese moments are discretely and continuously orthogonaland affinemoment which include radial Tchebichef momentinvariants (RTMIs) radial Tchebichef moments (RTMs)Tchebichef moment (TM) Krawtchouk moment (KM)Krawtchouk moment invariants (KMI) Legendre moment(LM) pseudo-Zernike moment (PZM) Zernike moment(ZM) and affine moment invariants (AMI) Some of themare standardmoments and the others aremoment invariantsFirst the logos with different noise are discussed

51 Logos with Different Noise In this subsection the ideallogo and the logos with different noise are shown in Figure 2

From the results of Table 1 we can conclude that KM andKMI get the highest recognition rate 09709 Both momentsare very robust to the salt and pepper noise and poissonnoise TM also has the same properties with KM and KMIhowever when the salt and pepper noise has a ratio of 20its recognition rate is just 09When the Gaussian white noiseis mean zero and variance 01 TM is not sensitive at allHowever all the other moments are a little sensitive to thiskind of noise When the Gaussian white noise is mean zeroand variance 02 RTMIs have the highest rate and RTMs havethe second highest rateThe standard and invariant momentshave some common characteristics when they are used torecognize some logos with noise just like the KM and KMIRTMIs and RTMs are also very robust to both speckle noiseTM KM and KMI also have some advantage in recognizingspeckle noise AMIhave the lowest recognition rateThemain


21 ideal 22 gaussian01 23 gaussian02 24 poisson 25 s and p002 26 s and p005

27 s and p008 28 s and p01 29 s and p015 210 s and p02 211 speckle005 212 speckle01

Figure 2 Logos with different noise

Table 1 Recognition rates of different moments about logos with different noise

Noise RTMIs RTMs TM KM KMI LM PZM ZM AMIGaussian01 09 052 1 096 096 08 094 072 002Gaussian02 1 088 064 074 074 048 032 014 002Poisson 1 1 1 1 1 092 1 098 016Salt and pepper002 092 034 1 1 1 074 1 098 056Salt and pepper005 088 02 1 1 1 098 1 098 032Salt and pepper008 094 016 1 1 1 094 1 098 026Salt and pepper01 092 012 1 1 1 1 098 096 026Salt and pepper015 09 01 1 1 1 082 09 074 02Salt and pepper02 088 004 09 1 1 1 074 044 012Speckle005 1 1 096 098 098 036 066 048 002Speckle01 1 1 1 1 1 054 09 068 002Average rate 094 04873 09545 09709 09709 078 08582 07327 018

reason is that it is very sensitive to all noise so that all recog-nized rates are very low RTMs have the second lowest averagerecognition rate When the salt and pepper noise has a ratioof 20 the recognition rate of RTMs is only 004 Whenthe salt and pepper noise has a great ratio ZM has difficultyin recognizing the logos In a word if the logos have mixedthese noises the most appropriate moment is KMI or KM forcompleting the recognition task

52 Logos with Scaling In this subsection the logos with sca-ling are discussedThe scale factors of logo are 025 05 07512 and 20The ideal logo and the scaling logos are shown inFigure 3

In Table 2 TM and PZM all have the highest rate 10No matter the scale factor is larger than 1 or smaller than1 both moments are very robust In the recognition contextboth moments can be used to recognize these logos Whenthe factor is moderate LM and AMI can replace the TM andPZM In most cases the recognition rates of other momentsalmost have the same lawThat is to say when the factor is too

small or too large the rate is very bad When the factorsapproach one from right or left the recognition rate is a littlehigher Of course there are two special cases ZM andRTMIsThe recognition rates of these moments have an ascendanttrend as the factors increase

53 Logos with Rotation In Figure 4 the logos are rotatedThe recognition rates are shown in Table 3

In Table 3 the average recognition rate of RTMs is thehighest When the rotation angle is 90 degrees the recogni-tion rates of RTMs and AMI are 100 The average recog-nition rate of KMI is the second highest However it canrecognize a part of logos when the rotation angle is 90degrees RTMIs and RTMs have similar properties in mostcircumstances however when recognizing the logos with 90degrees rotation they are definitely different The recognitionrates of other moments are very poor especially ZM whichgets the lowest rate only 0212 So if the logos have rotationtransformations RTMs are the best choice to recognize theselogos


Table 2 Recognition rates of different moments about logos with scaling

Noise RTMIs RTMs TM KM KMI LM PZM ZM AMIScaling025 032 018 1 01 01 078 1 034 078Scaling05 072 048 1 028 028 1 1 092 094Scaling075 074 048 1 088 088 1 1 098 098Scaling12 072 052 1 1 1 1 1 098 096Scaling20 082 046 1 06 06 1 1 098 1Average rate 0664 0424 1 0572 0572 0956 1 084 093

Table 3 Recognition rates of different moments about logos with rotation

Noise RTMIs RTMs TM KM KMI LM PZM ZM AMIRotation30 092 09 05 05 088 03 006 002 004Rotation60 072 072 036 014 07 028 006 002 006Rotation90 0 1 012 02 02 006 084 098 1Rotation120 078 074 036 014 074 02 006 002 002Rotation150 09 08 044 01 086 026 006 002 002Average rate 0664 0832 0356 0216 0676 022 0216 0212 023

31 ideal 32 scaling025 33 scaling05 34 scaling075 35 scaling12 36 scaling20

Figure 3 Logos with scaling

41 ideal 42 rotation30 43 rotation60 44 rotation90 45 rotation120 46 rotation150

Figure 4 Logos with rotation

51 ideal 52 rotation30 53 rotation60 54 rotation90 scaling12scaling075scaling05

Figure 5 Logos with rotation and scaling


Table 4 Recognition rates of different moments about logos with rotation and scaling

Noise RTMIs RTMs TM KM KMI LM PZM ZM AMIRotation30 scaling05 064 038 05 006 006 03 006 002 004Rotation60 scaling075 05 036 034 014 014 028 006 002 004Rotation90 scaling12 0 052 012 016 016 006 084 098 096Average rate 038 042 032 012 012 02133 032 034 035

Table 5 Average recognition rates of different moments

Different groups RTMIs RTMs TM KM KMI LM PZM ZM AMINoise 094 04873 09545 09709 09709 078 08582 07327 018Scaling 0664 0424 10 0572 0572 0956 10 084 093Rotation 0664 0832 0356 0216 0676 022 0216 0212 023Rotation and scaling 038 042 032 012 012 02133 032 034 035Average rate 0755 05375 076 06242 072 06292 06867 05975 037

54 Logos with Rotation and Scaling The sample logos ofrotation and scaling are presented in Figure 5 The recogni-tion rates of different moments are shown in Table 4

In Table 4 the average recognition rates of all momentsare very unsatisfactory The highest rate of RTMs is only042 So the logos with rotation and scaling are very difficultto be recognized In the first two groups RTMIsrsquo rateshave a superiority However RTMIs has some problems inrecognizing the logos with 90 degrees rotation therefore itsrate is undesirable LM also gets the lowest recognition rateon the third subgroup logos PZM ZM and AMI have someadvantages in recognizing the logos with 90 degrees rotationand 12 scaling factors ZMrsquos rate is higher than AMIrsquoswhile PZMrsquos rate is the lowest among these three momentsHowever in the first two groups ZM cannot recognize anylogo In short when one wants to recognize the logos withrotation and scaling RTMs are the suboptimal choice Theappropriate descriptor should be found out in the future

From Table 5 it is concluded that TM gets the highestrate If one dataset contains these four groups of logos TMcan be used as a proper descriptor KM and KMI have someadvantage in recognizing the logos with different noise andRTMIs and TM are the second best choice TM and PZMare good at recognizing the logos with scaling and LM andAMI can be used as a suboptimal descriptor RTMs havea superiority in identifying the logos with rotation RTMIsare the suboptimum tool When recognizing the logos withrotation and scaling among these moments RTMs are thefirst choice

6 Conclusion

In this paper we compare the performances of moments interms of logo recognition The original dataset is adoptedfrom the University of Maryland Laboratory for Languageand Media Processing The noise group rotation groupscaling group and rotation and scaling group are createdby MATLAB R2011a As we all know one descriptor can-not be appropriate to recognize all objects Nevertheless

one descriptor is good at recognizing one kind of objectsAccor-ding to this idea it is found that KM KMI TMand RTMIs are fit to identify the logos with gaussian saltand pepper poisson and speckle noise TM PZM LMand AMI are adapted to recognize the logos with scalingRTMs are suitable to discriminate the logos with rotationand they also can be used to distinguish the logos withrotation and scaling If one dataset includes all these logosTM can be used to complete recognition task To our bestknowledge there is no paper about performance evaluationof logo recognition even about comparing of moment-basedlogo recognition methods So this paper can provide theconstructive suggestions for the following researchers

Conflict of Interests

The authors declare that there is no conflict of interests regar-ding the publication of this paper

Acknowledgments

This research was supported in part by Public Service Plat-form of Mobile Internet Application Security Industry underGrants Shenzhen Development and Reform Commissionno 2012720 Research on Key Technology in DevelopingMobile Internet Intelligent Terminal ApplicationMiddlewareunder Grant no JC201104210032A and Research on KeyTechnology of Vision Based Intelligent Interaction underGrant no JC201005260112A

References

[1] H Shu L Luo and J L CoatrieuxDerivation of Moment Invar-iants Science Gate 2014

[2] SDaiHHuang ZGaoK Li and SXiao ldquoVehicle-logo recog-nition method based on Tchebichef moment invariants andSVMrdquo in Proceedings of the WRI World Congress on SoftwareEngineering (WCSE rsquo09) pp 18ndash21 IEEE Xiamen China May2009


[3] A P Psyllos C N Anagnostopoulos and E Kayafas ldquoVehiclelogo recognition using a sift-based enhancedmatching schemerdquoIEEE Transactions on Intelligent Transportation Systems vol 11no 2 pp 322ndash328 2010

[4] D Llorca R Arroyo andM Sotelo ldquoVehicle logo recognition intraffic images using hog features and svmrdquo in Proceedings of the16th International IEEE Conference on Intelligent TransportationSystems (ITSC rsquo13) pp 2229ndash2234 2013

[5] S Yu S Zheng H Yang and L Liang ldquoVehicle logo recogni-tion based on bag-of-wordsrdquo in Proceedings of the 10th IEEEInternational Conference on Advanced Video and Signal BasedSurveillance (AVSS rsquo13) pp 353ndash358 IEEE Krakow PolandAugust 2013

[6] S Mao M Ye X Li F Pang and J Zhou ldquoRapid vehicle logoregion detection based on information theoryrdquo Computers andElectrical Engineering vol 39 no 3 pp 863ndash872 2013

[7] R J den Hollander and A Hanjalic ldquoLogo recognition in videostills by string matchingrdquo in Proceedings of the InternationalConference on Image Processing (ICIP rsquo03) vol 3 pp III-517ndashIII-520 September 2003

[8] A Hesson and D Androutsos ldquoLogo and trademark detectionin images using color wavelet Co-occurrence histogramsrdquo inProceedings of the IEEE International Conference on AcousticsSpeech and Signal Processing (ICASSP rsquo08) pp 1233ndash1236 LasVegas Nev USA April 2008

[9] R Phan and D Androutsos ldquoContent-based retrieval of logoand trademarks in unconstrained color image databases usingcolor edge gradient co-occurrence histogramsrdquo Computer Vis-ion and Image Understanding vol 114 no 1 pp 66ndash84 2010

[10] H Qi K Li Y Shen and W Qu ldquoAn effective solution fortrademark image retrieval by combining shape description andfeature matchingrdquo Pattern Recognition vol 43 no 6 pp 2017ndash2027 2010

[11] S Sun and Z Chen ldquoRobust logo recognition for mobile phoneapplicationsrdquo Journal of Information Science and Engineeringvol 27 no 2 pp 545ndash559 2011

[12] Y Zhang S Zhang W Liang and HWang ldquoSpatial connectedcomponent pre-locating algorithm for rapid logo detectionrdquo inProceedings of the IEEE International Conference on AcousticsSpeech and Signal Processing (ICASSP rsquo12) pp 1297ndash1300March 2012

[13] A Roy and U Garain ldquoA probabilistic framework for logodetection and localization in natural scene imagesrdquo in Proceed-ings of the 21st International Conference on Pattern Recognition(ICPR rsquo12) pp 2051ndash2054 November 2012

[14] W Chu and T Lin ldquoLogo recognition and localization in real-world images by using visual patternsrdquo in Proceeding of the IEEEInternational Conference on Acoustics Speech and Signal Pro-cessing (ICASSP 12) pp 973ndash976 Kyoto Japan March 2012

[15] H Sahbi L Ballan G Serra and A Del Bimbo ldquoContext-dependent logo matching and recognitionrdquo IEEE Transactionson Image Processing vol 22 no 3 pp 1018ndash1031 2013

[16] X Liu and B Zhang ldquoAutomatic collecting representative logoimages from the internetrdquoTsinghua Science and Technology vol18 pp 606ndash617 2013

[17] D S Doermann E Rivlin and I Weiss ldquoLogo recognitionusing geometric invariantsrdquo inProceedings of the 2nd Internatio-nal Conference on Document Analysis and Recognition pp 894ndash897 1993

[18] D Doermann E Rivlin and I Weiss ldquoApplying algebraic anddifferential invariants for logo recognitionrdquoMachine Vision andApplications vol 9 no 2 pp 73ndash86 1996

[19] F Cesarini E Francesconi M Gori SMarinai J Q Sheng andG Soda ldquoNeural-based architecture for spot-noisy logo recog-nitionrdquo in Proceedings of the 4th International Conference onDocument Analysis and Recognition (ICDAR rsquo97) pp 175ndash179August 1997

[20] J Chen M K Leung and Y Y Gao ldquoNoisy logo recognitionusing line segment Hausdorff distancerdquo Pattern Recognitionvol 36 no 4 pp 943ndash955 2003

[21] M Gori M Maggini S Marinai J Q Sheng and G SodaldquoEdge-backpropagation for noisy logo recognitionrdquo PatternRecognition vol 36 no 1 pp 103ndash110 2003

[22] H Wang and Y Chen ldquoLogo detection in document imagesbased on boundary extension of feature rectanglesrdquo in Proceed-ings of the 10th International Conference on Document Analysisand Recognition (ICDAR rsquo09) pp 1335ndash1339 IEEE BarcelonaSpain July 2009

[23] H Wang ldquoDocument logo detection and recognition usingbayesian modelrdquo in Proceeding os the 20th International Confer-ence on Pattern Recognition (ICPR 10) pp 1961ndash1964 IstanbulTurkey August 2010

[24] Z Li M Schulte-Austum andM Neschen ldquoFast logo detectionand recognition in document imagesrdquo in Proceedings of the 20thInternational Conference on Pattern Recognition (ICPR rsquo10) pp2716ndash2719 Istanbul Turkey August 2010

[25] S Hassanzadeh and H Pourghassem ldquoA fast logo recognitionalgorithm in noisy document imagesrdquo inProceedings of the IEEEInternational conference on Intelligent Computation and Bio-Medical Instrumentation (ICBMI rsquo11) pp 64ndash67 Hubei ChinaDecember 2011

[26] T A Pham M Delalandre and S Barrat ldquoA contour-basedmethod for logo detectionrdquo in Proceedings of the 11th Inter-national Conference on Document Analysis and Recognition(ICDAR rsquo11) pp 718ndash722 Beijing China September 2011

[27] M A Bagheri and Q Gao ldquoLogo recognition based on a novelpairwise classification approachrdquo in Proceeding of the 16th CSIInternational Symposium on Artificial Intelligence and SignalProcessing (AISP 12) pp 316ndash321 Shiraz Iran May 2012

[28] G A Papakostas D E Koulouriotis E G Karakasis and V DTourassis ldquoMoment-based local binary patterns a novel des-criptor for invariant pattern recognition applicationsrdquo Neuro-computing vol 99 pp 358ndash371 2013

[29] M R Teague ldquoImage analysis via the general theory of mom-entsrdquo Journal of the Optical Society of America vol 70 no 8 pp920ndash930 1980

[30] T Suk and J Flusser ldquoAffine moment invariants generated bygraph methodrdquo Pattern Recognition vol 44 no 9 pp 2047ndash2056 2011

[31] RMukundan SHOng andPA Lee ldquoImage analysis byTche-bichefmomentsrdquo IEEETransactions on Image Processing vol 10no 9 pp 1357ndash1364 2001

[32] P Yap R Paramesran and S Ong ldquoImage analysis byKrawtchouk momentsrdquo IEEE Transactions on Image Processingvol 12 no 11 pp 1367ndash1377 2003

[33] K Mikolajczyk and C Schmid ldquoA performance evaluation oflocal descriptorsrdquo IEEE Transactions on Pattern Analysis andMachine Intelligence vol 27 no 10 pp 1615ndash1630 2005

[34] E D Tsougenis G A Papakostas D E Koulouriotis and VD Tourassis ldquoPerformance evaluation of moment-based water-marking methods a reviewrdquo Journal of Systems and Softwarevol 85 no 8 pp 1864ndash1884 2012

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MathematicsJournal of


Mathematical Problems in Engineering

Hindawi Publishing Corporationhttpwwwhindawicom

Differential EquationsInternational Journal of

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Applied MathematicsJournal of


Probability and StatisticsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of


Mathematical PhysicsAdvances in

Complex AnalysisJournal of


OptimizationJournal of


CombinatoricsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of


Operations ResearchAdvances in

Journal of


Function Spaces

Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of Mathematics and Mathematical Sciences


The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014


Algebra

Discrete Dynamics in Nature and Society



Decision SciencesAdvances in

Discrete MathematicsJournal of


Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Stochastic AnalysisInternational Journal of


real-time framework Llorca et al [4] proposed a new vehicle-logo recognition approach using histograms of oriented gra-dients and support vector machines All logos with low reso-lution were captured by traffic cameras However the slidingwindow technique would cost much more time Yu et al[5] proposed a new fast and reliable system based on bag-of-words for vehicle-logo recognition The vehicle-logo imageswere represented as histograms of visual words and classifiedby support vector machine This method processed theimages with less timeMao et al [6] proposed a novel methodto detect the vehicle logos in an image This method firstapplied the horizontal and vertical direction filters to producttwo new images and a saliency map was yielded from eachimage Then a binary image was created from the saliencymap Finally the vehicle logos were localized This methodhad an advantage of real time

Second in the advertisement application den Hollanderand Hanjalic [7] employed template matching technologyto detect and classify the logos in video stills Howeverthis method is very sensitive with logos foreground Hessonand Androutsos [8] used a five-dimensional cooccurrenceof colors and wavelet decomposition coefficients of pairs ofpixels This algorithm can exploit multiresolution analysiswith wavelets Phan and Androutsos [9] presented an algo-rithmwhich extended the color edge cooccurrence histogram(CECH) object detection scheme on compound color objectsHowever this global descriptor was not suitable to deal withincomplete information or transformed versions of the origi-nal logos and it was not proper to exactly describe the localityof logo traits Qi et al [10] proposed an effective solution fortrademark image retrieval by combining shape descriptionand feature matching This method can be generalized toother applications Sun and Chen [11] proposed a new recog-nition method on mobile phone cameras for logo images Byusing the Zernike moment phase information a new distinc-tive logo feature vector and an associated similarity measurewere presented Zhang et al [12] introduced a novel prelocat-ing algorithm for rapid logo detection in unconstrained colorimagesThe spatial connected component descriptor (SCCD)represents the logos while an effective-connected componentdescribes the pixel distribution information Roy and Garain[13] presented a probabilistic approach for logo detectionand localization in natural scene images One probabilitydistribution described the features and another computedthe shape geometry information defined by the key pointsHowever this algorithm could not handle logos which weremapped in two different affine planes Chu and Lin [14] usedthe pair-specific concept to capture relevant features betweena query logo and a test image employed the mean-shiftmethod to find candidate regions and combined the visualword histograms and visual patterns to describe logo objectsNew features can be designed in order to further improve theperformance for some logos Sahbi et al [15] designed a novelvariational frameworkwhichwas able tomatch and recognizemultiple instances of multiple reference logos in imagearchives This paper used an energy function mixing to mea-sure the quality of feature matching captured feature cooc-currencegeometry and controlled the smoothness of thematching solution Liu and Zhang [16] proposed a multiple

dictionary invariant sparse coding to automatically collectrepresentative logo images from the internet without anyhuman labeling or seed images This method could beextended to more general images by adopting SIFT-like localfeatures of HMAX-like features

Finally in the document image field Doermann et al [17]presented a multilevel staged approach to recognize logosThe global invariants were used to prune the database whilethe local affine invariants were used to obtain a more refinedmatch However this algorithm was only implemented in asmall database Doermann et al [18] presented a novel appli-cation of algebraic and differential invariants to recognizelogos By using invariants the shape descriptors could be usedfor matching the logos which were unique and independentof the point of view The algebraic invariants could be usedwhen the whole shapes of the logos were given while thedifferential invariants could be used when the logos hadonly a part Cesarini et al [19] proposed a new approachfor training autoassociator-based artificial neural networks(AANN) especially conceived for dealing with spot noiseThe proposed algorithm which was referred to as spot-backpropagation (S-BP) was significantly more robust withrespect to spot noise than classical Euclidean norm-basedbackpropagation (BP) Chen et al [20] proposed a methodbased on modified line segment Hausdorff distance Thismethod had the advantage in incorporating structural andspatial information to compute dissimilarity So this methodhad a faster computation speed than the method using setsof points Gori et al [21] proposed a new approach toimprove the performance of multilayer perceptron operatingas autoassociators to classify graphical items in presence ofspot noise on the images The weights which were replacedby Euclidean norm depended on the gradients of the imagesin order to give less importance to uniform color regionsThismethodwas time-consuming and the authors only discussedthe noisy spot Wang and Chen [22] proposed a new methodbased on the boundary extension of feature rectangles Wang[23] presented a simple and dynamic method to detect andrecognize logos in document images By applying feedbackand selecting proper features they were able to make theframework dynamic and interactive The feedback mecha-nisms made the framework more accurate Li et al [24]introduced a fast segmentation-free and layout-independentlogo detection and recognition method The recognitionperformance and running time were improved Hassanzadehand Pourghassem [25] proposed a novel approach based onspatial and structural features of logo images to solve theseproblemsThe novel features based on horizontal and verticalhistogram of the logo images and the KNN classifier werecombined together to recognize logo images Pham et al[26] presented a new approach for detecting logos by exploit-ing contour based features In the first stage the outer contourstrings (OCS) could be computed from each graphic andtext part of the documents In the second stage two typesof features were computed from each OCS In the finalstep correction helped with the wrong segmentation casesBagheri et al [27] proposed a novel multiclass classificationmethod which was applied to recognize logos due to consid-ering logo recognition as a multiclass classification problem



3 Moments



119860119901119902 =119901 + 1

120587intint119863

119891 (119909 119910)119881lowast

119901119902(119909 119910) 119889119909 119889119910 (1)

where 119881lowast


and 119881119901119902(119909 119910) is defined in

119881119901119902 (119909 119910)

=

(119901minus|119902|)2

sum

119904=0

(minus1)119904(119901 minus 119904)119903

119901minus2119904

119904 (((119901 +10038161003816100381610038161199021003816100381610038161003816) 2) minus 119904) (((119901 minus

10038161003816100381610038161199021003816100381610038161003816) 2) minus 119904)

119890119895119902120579

(2)


119885119901119902 =119901 + 1

120587int

2120587

0

int

1

0

119881lowast

119901119902(119903 120579) 119891 (119903 120579) 119903119889 119903119889 120579 (3)


119881119901119902 (119903 120579) =

119901minus|119902|

sum

119904=0

(minus1)119896(2119901 + 1 minus 119904)119903

119901minus119904

119904 (119901 minus10038161003816100381610038161199021003816100381610038161003816 minus 119904) (119901 +

10038161003816100381610038161199021003816100381610038161003816 + 1 minus 119904)

119890119895119902120579

(4)


119871119901119902 =(2119901 + 1) (2119902 + 1)

4∬

1

minus1

119875119901 (119909) 119875119902 (119910) 119891 (119909 119910) 119889119909 119889119910

(5)


119875119901 (119909) =

119901

sum

119896=0

(minus1)(119901minus119896)2 1

2119901

(119901 + 119896)119909119896

((119901 minus 119896) 2) ((119901 + 119896) 2)119896

(6)



119879119901119902 =1

120588 (119901119873) 120588 (119902119873)

119873minus1

sum

119909=0

119873minus1

sum

119910=0

119901 (119909) 119902 (119910) 119891 (119909 119910) (7)


120588 (119899119873) =120588 (119899119873)

120573(119899119873)2

120588 (119899119873) = (2119899) (119873 + 119899

2119899 + 1)

(8)


120573 (119899119873) = 119873119899

119899 (119909) =119905119899 (119909)

120573 (119899119873)

119905119899 (119909) = 119899

119899

sum

119896=0


(119873 minus 1 minus 119896

119899 minus 119896)(

119899 + 119896

119899)(

119909

119896)

(9)


119876119899119898 =

119873minus1

sum

119909=0

119872minus1

sum

119910=0

119870119899 (119909 1199011 119873 minus 1)119870119898 (119910 1199012119872 minus 1) 119891 (119909 119910)

(10)


119870119899 (119909 119901119873) = 119870119899 (119909 119901119873)radic120596 (119909 119901119873)

120588 (119899 119901119873)

119870119899 (119909 119901119873) =

119899

sum

119896=0

(minus119899)119896(minus119909)119896

(minus119873)119896

(1119901)119896

119896

(11)

119909 119899 = 0 1 2 119873 119901 isin (0 1)

120596 (119909 119901119873) = (119873

119909)119901119909(1 minus 119901)

119873minus119909

120588 (119899 119901119873) = (minus1)119899(1 minus 119901

119901)

119899119899

(minus119873)119899

(12)




11 12 13 14 15 16 17 18 19 110 111 112 113 114 115 116 117

118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134

135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150



119868 (119891) = int

+infin

minusinfin

sdot sdot sdot int

+infin

minusinfin

119903

prod

119896119895=1

119862119899119896119895

119896119895sdot

119903

prod

119894=1

119891 (119909119894 119910119894) 119889119909119894119889119910119894 (14)






5 Experiments



































6 Conclusion





Acknowledgments


References











































Volume 2014




Journal of











Journal of


Function Spaces






Algebra











3 Moments



119860119901119902 =119901 + 1

120587intint119863

119891 (119909 119910)119881lowast

119901119902(119909 119910) 119889119909 119889119910 (1)

where 119881lowast


and 119881119901119902(119909 119910) is defined in

119881119901119902 (119909 119910)

=

(119901minus|119902|)2

sum

119904=0

(minus1)119904(119901 minus 119904)119903

119901minus2119904

119904 (((119901 +10038161003816100381610038161199021003816100381610038161003816) 2) minus 119904) (((119901 minus

10038161003816100381610038161199021003816100381610038161003816) 2) minus 119904)

119890119895119902120579

(2)


119885119901119902 =119901 + 1

120587int

2120587

0

int

1

0

119881lowast

119901119902(119903 120579) 119891 (119903 120579) 119903119889 119903119889 120579 (3)


119881119901119902 (119903 120579) =

119901minus|119902|

sum

119904=0

(minus1)119896(2119901 + 1 minus 119904)119903

119901minus119904

119904 (119901 minus10038161003816100381610038161199021003816100381610038161003816 minus 119904) (119901 +

10038161003816100381610038161199021003816100381610038161003816 + 1 minus 119904)

119890119895119902120579

(4)


119871119901119902 =(2119901 + 1) (2119902 + 1)

4∬

1

minus1

119875119901 (119909) 119875119902 (119910) 119891 (119909 119910) 119889119909 119889119910

(5)


119875119901 (119909) =

119901

sum

119896=0

(minus1)(119901minus119896)2 1

2119901

(119901 + 119896)119909119896

((119901 minus 119896) 2) ((119901 + 119896) 2)119896

(6)



119879119901119902 =1

120588 (119901119873) 120588 (119902119873)

119873minus1

sum

119909=0

119873minus1

sum

119910=0

119901 (119909) 119902 (119910) 119891 (119909 119910) (7)


120588 (119899119873) =120588 (119899119873)

120573(119899119873)2

120588 (119899119873) = (2119899) (119873 + 119899

2119899 + 1)

(8)


120573 (119899119873) = 119873119899

119899 (119909) =119905119899 (119909)

120573 (119899119873)

119905119899 (119909) = 119899

119899

sum

119896=0


(119873 minus 1 minus 119896

119899 minus 119896)(

119899 + 119896

119899)(

119909

119896)

(9)


119876119899119898 =

119873minus1

sum

119909=0

119872minus1

sum

119910=0

119870119899 (119909 1199011 119873 minus 1)119870119898 (119910 1199012119872 minus 1) 119891 (119909 119910)

(10)


119870119899 (119909 119901119873) = 119870119899 (119909 119901119873)radic120596 (119909 119901119873)

120588 (119899 119901119873)

119870119899 (119909 119901119873) =

119899

sum

119896=0

(minus119899)119896(minus119909)119896

(minus119873)119896

(1119901)119896

119896

(11)

119909 119899 = 0 1 2 119873 119901 isin (0 1)

120596 (119909 119901119873) = (119873

119909)119901119909(1 minus 119901)

119873minus119909

120588 (119899 119901119873) = (minus1)119899(1 minus 119901

119901)

119899119899

(minus119873)119899

(12)




11 12 13 14 15 16 17 18 19 110 111 112 113 114 115 116 117

118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134

135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150



119868 (119891) = int

+infin

minusinfin

sdot sdot sdot int

+infin

minusinfin

119903

prod

119896119895=1

119862119899119896119895

119896119895sdot

119903

prod

119894=1

119891 (119909119894 119910119894) 119889119909119894119889119910119894 (14)






5 Experiments



































6 Conclusion





Acknowledgments


References











































Volume 2014




Journal of











Journal of


Function Spaces






Algebra










11 12 13 14 15 16 17 18 19 110 111 112 113 114 115 116 117

118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134

135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150



119868 (119891) = int

+infin

minusinfin

sdot sdot sdot int

+infin

minusinfin

119903

prod

119896119895=1

119862119899119896119895

119896119895sdot

119903

prod

119894=1

119891 (119909119894 119910119894) 119889119909119894119889119910119894 (14)






5 Experiments



































6 Conclusion





Acknowledgments


References











































Volume 2014




Journal of











Journal of


Function Spaces






Algebra








































6 Conclusion





Acknowledgments


References











































Volume 2014




Journal of











Journal of


Function Spaces






Algebra

















































Volume 2014




Journal of











Journal of


Function Spaces






Algebra









research article a comparison of moments-based logo...

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