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Manoj Kumar, Prof. Sagun Kumar sudhansu, Dr. Kasabegoudar V. G / International Journal of Engineering Research and Applications (IJERA) ISSN: 2248-9622 www.ijera.com Vol. 2, Issue 5, September- October 2012, pp.1963-1970 Wavelet Based Texture Analysis And Classification With Linear Regration ModelManoj Kumar*, Prof. Sagun Kumar sudhansu**, Dr. Kasabegoudar V. G. *** *(PG Department, Collage of Engineering Ambejogai)Abstract The Wavelet Transform is a analysis of spatial relations between neighbourhoodmultiresolution analysis tool commonly applied to pixels in a small image region. As a consequence,texture analysis and classification and also their performance is the best for the class of soWavelet based pre-processing is a very successful called micro-textures [9]. With a study on humanmethod providing proper Image Enhancement vision system, researchers begin to develop theand remove noise without considerable change in multi-resolution texture analysis models, such as theoverall intensity level. The Wavelet Transform wavelet transform and the Gabor transform.mostly used for contrast enhancement in noisy Extensive research has demonstrated that theseenvironments. In this paper we propose a texture approaches based on the multi-resolution analysisanalysis with the linear regression model based on could achieve reasonably good performance, so theythe wavelet transform. This method is motivated have already been widely applied to texture analysisby the observation that there exists a distinctive and classification. The most common multi-correlation between the samples images, resolution analysis approach is to transform abelonging to the same kind of texture, at different texture image into local spatial/frequencyfrequency regions obtained by 2-D wavelet representation by wrapping this image with a banktransform. Experimentally, it was observed that of filters with some tuned parameters.this correlation varies from texture to texture. This property coincides with the study thatThe linear regression model is employed to the human visual system can be modelled as a set ofanalyze this correlation and extract texture channels. This clearly motivates researchers to studyfeatures that characterize the samples. Our how to extract more discriminable texture featuremethod considers not only the frequency regions based on the multi-resolution techniques. Currentlybut also the correlation between these regions. In the wavelet transform and the Gabor transform arecontrast the tree structured wavelet transform the most popular multi-resolution methods.(TSWT) do not consider the correlation between Compared to the wavelet transform [10]-[13], thedifferent frequency regions. Experiments show Gabor transforms needs to select the filterthat our method significantly improves the parameters according to different texture. There is atexture classification rate in comparison with the, trade-off between redundancy and completeness inTSWT, Gabor Transform and GLCM with the design of the Gabor filters because of noneGabor and some recently proposed methods Orthogonality. The Gabor transform is also limitedderived from these. to its filtering area. Consequently, we choose the wavelet transform to obtain the spectral informationIndex Terms—Linear regression, texture of the texture image. Texture image at differentanalysis, texture classification, wavelet scales and use the statistics of the spectraltransforms. information as the texture descriptor, they ignore the texture structural information. In this paper, it isI. INTRODUCTION found that there exists a distinctive correlation Worldwide networking allows us to between some sample textures images, belonging tocommunicate, share, and learn information in the the same kind of texture, at different frequencyglobal manner. Digital library and multimedia regions obtained by 2-D wavelet packet transform.databases are rapidly increasing; so efficient search Experimentally it is demonstrated that thisalgorithms need to be developed. correlation varies from texture to texture. A new Texture provides essential information for texture classification method, in which the simplemany image classification tasks. Much research has linear regression model is employed into analyzingbeen done on texture classification during the last this correlation, is presented. Experiments show thatthree decades [1]-[4]. In the 1980s, most traditional this method significantly improves the textureapproaches included gray level co-occurrence classification rate in comparison with thematrices (GLCM) [5], second-order statistic method multiresolution methods, including TSWT, the[6], Gauss–Markov random field [7], and local Gabor transform [14]-[16], and some recentlylinear transform [8], which are restricted to the proposed methods. The most common 1963 | P a g e
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Manoj Kumar, Prof. Sagun Kumar sudhansu, Dr. Kasabegoudar V. G / International Journal of Engineering Research and Applications (IJERA) ISSN: 2248-9622 www.ijera.com Vol. 2, Issue 5, September- October 2012, pp.1963-1970multiresolution analysis approach is to transform a LL regions, whereas the 2-D wavelet packettexture image into local spatial/frequency transform decomposes all frequency regions torepresentation by wrapping this image with a bank achieve a full decomposition, as shown in Fig. 1 andof filters with some tuned parameters. This property 2, Therefore, the 2-D PSWT depicts thecoincides with the study that the human visual characteristics of the image in the LL regions and thesystem can be modelled as a set of channels. This 2-D wavelet packet trans- form describes theclearly motivates researchers to study how to extract properties of the image in all regions. Most of themore discriminable texture feature based on the research in the multiresolution analysis based on themultiresolution techniques [17-[18]. Currently, the wavelet domain focuses on directly extracting thewavelet transform and the Gabor transform are the energy values from the sub images and uses them tomost popular multiresolution methods. characterize the texture image. In this paper, the In this paper, it is found that there exists a mean of the magnitude of the sub-image coefficientsdistinctive correlation between some sample texture is used as its energy.images, belonging to the same kind of texture, at In this paper the mean of the magnitude ofdifferent frequency regions obtained by 2-D wavelet the sub image coefficients is used as its energy. ThatPacket transforms. Experimentally it is demonstrated is, if the sub image is x(m,n),with 1≤m≤Mthat this correlation varies from texture to texture. A and1≤n≤N its energy can be represented 𝑀 𝑁new texture classification method, in which the E=(1/𝑀𝑁) 𝑖=1 𝑗 =1 𝑋(𝑖, 𝑗) 1.0simple linear regression model is employed into Where x(i,j) is the pixel value of the sub image.analyzing this rate in comparison with themultiresolution methods including PSWT, TSWT,the Gabor transform, and some recently proposedmethods. This paper is organized as follows. Thebrief review about 2-D wavelet transform and anapplication of the correlation between differentfrequency regions to texture analysis are described inSection II. Several multiresolution techniques, such as, TSWT,and the Gabor and GLCM transform, and ourmethod are compared. Finally, the conclusions aresummarized in Section III.II. TEXTURE ANALYSIS WITH LINEAREGRESSION MODEL Fig.1:Flow Chart Level using Decomposition.A. Two-Dimensional Wavelet Packet Transform: The wavelet transform provides a preciseand unifying framework for the analysis andcharacterization of a signal at different scales. It isdescribed as a multiresolution analysis tool for thefinite energy function. It can be implementedefficiently with the pyramid-structured wavelettransform and the wavelet packet transform. Thepyramid-structured wavelet Performs furtherdecomposition of a signal only in the low frequencyregions. Adversely, the wavelet packet transformdecomposes a signal in all low and high frequencyregions. As the extension of the 1-D wavelettransform, the 2-D wavelet transform can be carriedout by the tensor product of two 1-D wavelet basefunctions along the horizontal and vertical directions,and the corresponding filters can be expressed as h LL(k,l) = h(k)h(l), h L H(k,l) = h(k)h(l), h H L(k,l) =g(k)h(l) and h H H(k,l) = g(k)g(l). An image can bedecomposed into four sub images by convolving theimage with these filters. These four sub images Fig.2 decomposition of image in HL, LL, HH, LHcharacterize the frequency information of the image regionin the LL, LH, HL, and HH frequency regionsrespectively. The 2-D PSWT can be constructed bythe whole process of repeating decomposition in the 1964 | P a g e
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Manoj Kumar, Prof. Sagun Kumar sudhansu, Dr. Kasabegoudar V. G / International Journal of Engineering Research and Applications (IJERA) ISSN: 2248-9622 www.ijera.com Vol. 2, Issue 5, September- October 2012, pp.1963-1970B. Analysis of Correlation between Frequency C) Linear Regression Model:channels. In the above subsection, the correlation Given that there are some sample texture between different frequency regions has beenimages from the same kind of texture, these images validated as a sort of effective texture characteristic.should have the same spatial relation between In this section, we employ the simple linearneighbourhood pixels as this texture. These images regression model to analyze the correlation. Supposeare all decomposed to obtain the same frequency that we have a set of the random dataregions by 2-D wavelet transform. The most 𝑋1 𝑌1 T…… (X_n Y_n )T, for two numericalcommon approach is to calculate all frequency variables X and Y and suppose that we regard X as aregions’ energy values of every image with the cause of Y. From the simple linear regressionenergy function and to characterize this texture by analysis, the distribution of the random datathe statistics of these energy values. This approach approximately appears a straight line in X, Y spaceignores the spatial relation of these sample texture when X and Y are perfectly related linearly. There isimages. In this study, we capture this inherent texture a linear function that captures the systematicproperty by learning a number of sample texture relationship between two variables. This lineimages. From a statistical perspective, a frequency function (also called the simple linear regressionregion of a sample texture image can be viewed as a equation) can be given as follows:random variable and the energy values of this yˆ= a * x + bfrequency region can be treated as the random values Where yˆ is called a fitted value of y.of this variable Experimentally it is found that there We exploit the simple linear regressionexists a distinctive correlation between different model to extract the texture features from thevariables (frequency regions). correlation in the frequency channel pairs. The As a powerful multiresolution analysis tool, channel-pair list includes all channel pairs with T.the2-D wavelet transform has proved useful in For two frequency channels of one channel pair intexture analysis, classification, and segmentation. the list, we take out their energy values from theThe 2-D PSWT performs further decomposition of a channel-energy matrix M and then consider thesetexture image only in the low frequency regions. energy values as the random data 𝑋1 𝑌1 T,... , (X_nConsequently it is not suitable for images whose Y_n )T, for two variables X and Y.The distributiondominant frequency information is located in the of these energy values should also represent amiddle or high frequency regions. Although the 2-D straight line in X,Y space. In general, the waveletwavelet packet transform characterizes the packet transform generates a multiresolution textureinformation in all frequency regions, this representation including all frequency channels of arepresentation is redundant. On the other hand, in texture image with the complete and orthogonalorder to generate a sparse representation, the 2-D wavelet basis functions which have a “reasonablyTSWT decomposes the image dynamically in the well controlled” spatial/frequency localizationlow and high frequency regions whose energies are property. Our method absorbs this advantage of thehigher than a predetermined threshold. However, it wavelet packet transform. The difference betweenignores the correlation between different frequency our method and other multiresolution based textureregions. We use 2-D wavelet packet transform to analysis methods are PSWT loses the middle andobtain all frequency information of a texture image high frequency information. TSWT does not takein this paper The detail is described as follow. First, into the account the correlation between differentthe original image is decomposed into four sub- frequency channels. The Gabor transform uses aimages, which can be viewed as the parent node and fixed n umber of filter masks with predeterminedthe four children nodes in a tree and named as O, A, frequency and bandwidth parameters. In contrast, ourB, C, and D respectively, as shown in Fig. 3. method not only thinks about all frequency channels but also analyzes the correlation between them with the simple linear regression model. So, it can be viewed as a very useful multiresolution method. III. EXPERIMENTAL RESULT In this section, we will verify the performance. we used 40 textures .Every original image is of size 640X640 pixels with 256 gray levels. 81 sample images of size 128 with an overlap32 pixels between vertically and horizontally adjacent images are extracted from each originalFig. 3 Tree Representation colour image and used in the experiments, and the mean of every image is removed before theThey symbolize the original image, LL, LH, HL, and processing. These 3240 texture images are separatedHH frequency regions. to two sets being used as the training set with 1600 1965 | P a g e
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Manoj Kumar, Prof. Sagun Kumar sudhansu, Dr. Kasabegoudar V. G / International Journal of Engineering Research and Applications (IJERA) ISSN: 2248-9622 www.ijera.com Vol. 2, Issue 5, September- October 2012, pp.1963-1970images and the test set with 1640 images, and the Gabor transform, and the statistic-basedrespectively. We compare our method with other methods, like GLCM, can achieve the super multi-traditional multi-resolutionion methods, such as . resolution methods because they take the textureThe tree-structured wavelet transforms and Gabor primitives into account. In particular, theand Gabor plus GLCM. combination of the wavelet transform and GLCM In the classification algorithm of TSWT, its excels our method in many textures though itsfeature is constructed by the energy of all frequency average correct rate is still slightly lower than mine.regions in the third scale and its controllable This dramatic trait can be illuminated that theparameters like decomposition constant and wavelet transform captures the frequencycomparison constant, are empirically set to 0.15 and information of the texture image at different scales10, respectively. We implement the Gabor transform and GLCM characterizes the local spatial propertiesobtained form by convolving an image with a set of of the texture. However this approach leads to spacefunctions by appropriate dilations and rotations of increase the feature dimension and brings in thethe Gabor mother function. The average retrieval rate computation complexity in classification scheme,defined in our method is different from that of other even the curse of dimensionality. Feature reductionmethods .Because we use threshold based like principle component analysis (PCA) alleviatescomparison in one dimension. All query samples are the curse to some extent at the cost of affecting theprocessed by our method and respectively assigned performance [19] our method is to take advantage ofto the corresponding texture. We count the samples the texture inherent in the learning phase. Thusof this texture, which are assigned to the right relation characteristic, our classification algorithmtexture, and get the average percentage number as simply takes the threshold comparison in onethe average retrieval rate of this texture. In view of dimension space in order to avoid the difficulty inour methods, the distance, where is the query sample choosing a distance function that is suitable for theand is a texture from the database, is firstly distributions of the multidimensional texture featurescomputed with the feature vectors discussed above. Furthermore, it is obvious that the simple thresholdThe distances are then sorted in increasing order and comparison in one dimension space greatlythe closet set of patterns is then retrieved. In the ideal diminishes the great computationcase all the top 41 retrievals are from the texture. The Complexity in comparison with the distance measuresample retrieval rate same is defined as the average similarities in high-dimensional space images,percentage number of samples belonging to the same respectively.texture as the query sample in the top 41 matches.The average retrieval rate of a texture is the average IV. CONCLUSIONnumber of all sample retrieval rates of this texture. In this paper, a new approach to textureSeveral different distances similarity measures, like analysis and classification with the simple linearEuclidean, Bayesian, Mahalanobis, can be explored regression model based on the wavelet transform isto obtain different results for other The different presented and its good performance on thedistances are applied to different methods in our classification accuracy is demonstrated in theexperiment on behalf of their reasonably good experiments. Although the traditional multi-performances Table 4 shows the retrieval accuracy of resolution methods, like TSWT, the Gaborthese different multiresolution methods for 40 transform, are suitable for some textures, ourtextures. Fig. 4 gives a graph illustrating the retrieval method is natural and effective for much moreperformance as a function of texture here Gabor textures. While the fuse of the Gabor transform andbased performance is very poor. However, the GLCM is confined to the Gabor filter, the way ofaverage accuracy of our method is still first class, combining the wavelet transform with GLCMhighly 96.86%, and much greater than other methods obtains the excellent performance very close to our94.16% (TSWT), 84.45% GLCK and Gabor), method. However, our method surpasses them in the76.429% (the Gabor transform), respectively. In classification scheme because it adopts the simplesummery TSWT keeps much more information of threshold comparison and the leave-one-outthe spectral resolution in high frequency regions, so algorithm. It is worthwhile to point out severalit can get better performance than the Gabor,GLCM distinctive characteristics of this new method. Totransform. Gabor with GLCM Excellent performance begin with, our method provides all frequentcompared to TSWT, GLCM, and Gabor. A very channels of the quasi-periodicity texture inbroad class of filters whose parameters are much comparison with PSWT, Gabor, So, it is able tomore suitable for textures in our Database. However, characterize much more spectral information of theour method considers not only all the frequency texture at different multi-resolution. Next, theinformation of the Texture but also the correlation correlation of different frequent channels can bebetween them. Therefore, it can achieve the best applied in this method through the simple linearresult in Comparison with TSWT, GLCM and regression model. In contrast, TSWT does notGabor, Transform The way of combining the consider the correlation between different frequentmultiresolution methods, like the wavelet transform regions though it also keeps more frequent 1966 | P a g e
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Manoj Kumar, Prof. Sagun Kumar sudhansu, Dr. Kasabegoudar V. G / International Journal of Engineering Research and Applications (IJERA) ISSN: 2248-9622 www.ijera.com Vol. 2, Issue 5, September- October 2012, pp.1963-1970information and employs the energy criterion to get to characterize the texture image at theover the over complete decomposition. multidimensional space, and our method employs the Therefore, this texture intrinsic correlation between different frequency regions tocharacteristic helps our method go beyond TSWT. the construct the texture feature. So, it employsFurthermore, most of the research in the multi- threshold comparison in one dimension space ratherresolution analysis directly computes the energy than some distance measures in the multidimensionalvalues from the sub images and extracts the features space. Therefore, it is very easy and fast to examineto characterize the texture image at the multi- the change of different frequent channels for texturedimension space, and, yet, our method employs the image.correlation between different frequency regions to Our current work has focused so far on theconstruct the texture feature. So, it employs the simple linear regression model which is used tothreshold comparison in one dimension space rather employ the linear correlation. More thoroughthan some distance measures in the multi-dimension theoretical analysis of the linear correlation isspace. Therefore, it is very easy and fast to examine expected in the future. In addition, the application ofthe change of different frequent channels for texture this method to texture segmentation is under ourimage. Our current work has focused so far on the current investigation. Due to our method being quitesimple linear regression model which is used to sensitive to noise, it is the urgent requirement ofemploy the linear correlation. More thorough achieving its noisy in- variance.theoretical analysis of the linear correlation isexpected in the future. In addition, the application of 1.2this method to texture segmentation is under ourcurrent investigation. Due to our method being quitesensitive to noise shown from Section, it is the 1urgent requirement of achieving its noisy invariance.In this paper, a new approach to texture analysis with OURthe simple linear regression model based on the 0.8wavelet transform is presented. Although the METHODtraditional multiresolution methods, like PSWT, WaveletTSWT, the Gabor transform are suitable for some 0.6textures, our method is natural and effective formuch more textures. GLCM and Next, the correlation of different frequent 0.4 Gaborchannels can be applied in this method through the Gaborsimple linear regression model. In contrast, TSWTdoes not consider the correlation between different 0.2frequent regions though it also keeps more frequentinformation and employs the energy criterion to getover the decomposition Therefore; this texture 0intrinsic characteristic helps our method go beyond 1 5 9 13172125293337TSWT. Furthermore, most of the research in themultiresolution analysis directly computes the energyvalues from the sub images and extracts the features Fig.4. Comparison of classification rate usingto characterize the texture image. In this paper, a new different methods.approach to texture analysis with the simple linearregression model based on the wavelet transform ispresented. Although the traditional multiresolutionmethods, like PSWT, TSWT, the Gabor transformare suitable for some textures, our method is naturaland effective for much more textures. Next, the correlation of different frequentchannels can be applied in this method through thesimple linear regression model. In contrast, TSWTdoes not consider the correlation between differentfrequent regions though it also keeps more frequentinformation and employs the energy criterion to getover the decomposition Therefore; this textureintrinsic characteristic helps our method go beyondTSWT. Furthermore, most of the research in themultiresolution analysis directly computes the energyvalues from the sub images and extracts the features 1967 | P a g e
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Manoj Kumar, Prof. Sagun Kumar sudhansu, Dr. Kasabegoudar V. G / International Journal of Engineering Research and Applications (IJERA) ISSN: 2248-9622 www.ijera.com Vol. 2, Issue 5, September- October 2012, pp.1963-1970 REFERENCES [1] Y. Rui, T. S. Huang, and S. F. Chang, “Image retrieval: Current techniques, promising directions, and open issues,” J. Vis. Common. Image Represent. vol. 10, pp. 39–62 1999. [2] R. Randen and J. H. Husøy, “Filtering for texture classification: A comparative study,” IEEE Trans. Pattern Anal. Mach. Intell., vol. 21, no. 4, pp. 291–310, Apr. [3] J. Zhang and T. Tan, “Brief review of invariant texture analysis methods,” Pattern Recognition. vol. 35, pp. 735–747, 2002. [4] C.-C. Chen and C.-C. Chen, “Filtering methods for texture discrimination,” Pattern Recognit. Lett., vol. 20, pp. 783– 790, 1999. [5] R.M.Haralick, K.Shanmugan, and I. Dinstein,“Textural features for image classification,” IEEE Trans. Syst. Man Cybern., vol. SMC-6, no. 6, pp. 610–621, Nov. 1973. [6] P. C. Chen and T. Pavlidis, “Segmentation by texture using correlation,” IEEE Trans. Pattern Anal. Mach. Intell., vol. 5, no. 1, pp. 64–69, Jan. 1983. [7] 7R. L. Kashyap and R. Chellappa, “Estimation and choice of neighbors in spatial- interaction models of images,” IEEE Trans. Inf. Theory, vol. 29, no. 1, pp. 60–72, Jan. 1983. [8] M.Unser,“Local linear transforms for texture measurements, “Signal Process. vol.11,pp.61–79,1986.-400, [9] M. Unser, “Texture classiﬁcation and segmentation using wavel Frames, M. Unser, “Texture classiﬁcation and segmentation using wavel Frames, [10] T.ChangandC.-C.J.Kuo,“A wavelet transform approach to texture analysis,” in Proc. IEEE ICASSP, Mar. 1992, vol. 4, no. 23–26, pp.661–664. [11] ChangandC.-C.J.Kuo,“Tree-structured wavelet transform for textured image Segmentation,”Proc.SPIE,vol.1770,pp.394 –405,1992. [12] T.Chang andC.-C.J.Kuo, “Texture analysisFig.6. Forty Texture used in this experiment. and classiﬁcation with tree-structured wavelet transform,”IEEE Trans.ImageACKNOWLEDGMENT Process., vol. 2,no.4,pp.429–441,Oct.1993.The authors would like to thank the editor and the [13] G.H.Wu, Y.J.Zhang, andX.G.Lin,“Waveletanonymous reviewers for their contributing transform-based texture classiﬁcationcomments, as well as Prof. Sagun kumar sudhansu Featureand Dr. Kasabegoudar V.G., PG Department collage weighting,”Proc.IEEEInt.Conf.Imageof engineering Ambejogai) and S. K. Dass. For Processing,vol.4,no.10,pp.435 439,1999.providing the software. [14] W.Y.Maand B.S.Manjunath,“A comparison of wavelet transform features for texture Image annotation,” Proc. IEEE Int. Conf. Image Processing, vol.2, no.23– 26,pp.256259,Oct.1995. 1969 | P a g e
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Manoj Kumar, Prof. Sagun Kumar sudhansu, Dr. Kasabegoudar V. G / International Journal of Engineering Research and Applications (IJERA) ISSN: 2248-9622 www.ijera.com Vol. 2, Issue 5, September- October 2012, pp.1963-1970[15] W.Y.MaandB.S.Manjunath,“Texture features and learning similarity,” Proc.IEEECVPR, .18–20,pp.425– 430,Jun.1996.[16] B. S. Manjunath and W. Y. Ma, “Texture feature for browsing and retrieval of image Data, IEEE rans. Pattern Anal .Mach. Intel vol.18,no.8,pp.837– 842,Aug.1996.[17] D.A.ClausiandH.Deng,“Desing-based texture feature fusion using gabor ﬁlters and co- occurrence probabilities,” IEEE Trans. Image. process.,vol.14,no.7,pp.925– 936,Jul.2005.[18] G. Van de Wouwer, P. Scheunders, and D. Van Dyck, “Statistical texture characterization from discrete wavelet representation,” IEEE Trans.Image,Vol 8,no.4,,pp,592- 598,Apr.1999.[19] Timothy K. Shih, Lawrence Y. Deng, Ching-Sheng Wang, and Sheng-En Yeh, “Conten- base Image Retrieval with Intensive Signature via Affine Invariant Transformation”, Dept. of Computer Science and Information Engineering Tamkang University. 1970 | P a g e
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