Comparison of various texture classification methods using multiresolution analysis and linear regression modelling
 S. Dhanya^{1}Email authorView ORCID ID profile and
 V. S. Kumari Roshni^{2}
Received: 17 June 2015
Accepted: 17 December 2015
Published: 20 January 2016
Abstract
Textures play an important role in image classification. This paper proposes a high performance texture classification method using a combination of multiresolution analysis tool and linear regression modelling by channel elimination. The correlation between different frequency regions has been validated as a sort of effective texture characteristic. This method is motivated by the observation that there exists a distinctive correlation between the image samples belonging to the same kind of texture, at different frequency regions obtained by a wavelet transform. Experimentally, it is observed that this correlation differs across textures. The linear regression modelling is employed to analyze this correlation and extract texture features that characterize the samples. Our method considers not only the frequency regions but also the correlation between these regions. This paper primarily focuses on applying the Dual Tree Complex Wavelet Packet Transform and the Linear Regression model for classification of the obtained texture features. Additionally the paper also presents a comparative assessment of the classification results obtained from the above method with two more types of wavelet transform methods namely the Discrete Wavelet Transform and the Discrete Wavelet Packet Transform.
Keywords
Background
Image classification refers to the classification of images based on the visual content. It includes object recognition and scene classification. Important applications include industrial and biomedical surface inspection, for example for defects and disease, ground classification and segmentation of satellite or aerial imagery, segmentation of textured regions in document analysis, and contentbased access to image databases. Textures in images provide information about spatial arrangement of intensities or colour in an image. They play an important role in many image classification tasks. A fundamental issue in texture based classification tasks is how to effectively characterize the texture from the derived features. Much research has occurred in this area during the last decade (Rui et al. 1999; Randen and Husøy 1999; Zhang and Tan 2002; Chen and Chen 1999; Haralick et al. 1973; Chen and Pavlidis 1983). The traditional approaches, focusing on the analysis of spatial relations between neighborhood pixels in a small region, included Gray Level Cooccurrence Matrix (GLCM) (Kashyap and Chellappa 1983; Unser 1986), second order gray level statistics (Unser 1995),and Gauss Markov random field (Fernandez 2008). These methods perform best on microtextures. Spectral histogram is yet another commonly used texture classification method (Liu and Wang 2003). It is based on local spatial/frequency information, which provides a unified texture feature.
Extensive research has demonstrated that classification based on multiresolution analysis methods resembling the human vision system provides better performance. Hence these methods are widely used for the classification of textures. Most commonly employed multiresolution analysis techniques include the Gabor transform (Grigorescu et al. 2002) and the wavelet transform (Van de Wouwer et al. 1999; Huang and Aviyente 2008).
In these methods the texture image is transformed by the use of the respective transform to local spatial/frequency representation by wrapping the image with appropriate bandpass filters tuned to specific parameters. In the case of Gabor transform, features such as Gabor energy, complex moments, and grating cell operator are considered to characterize the texture feature while in wavelet transform analysis (Van de Wouwer et al. 1999; Huang and Aviyente 2008; Ma and Manjunath 1995; Hackmack et al. 2012; Wang and Yong 2008) the wavelet coefficients itself serve the purpose of characterizing the texture features. In (Selesnick et al. 2005) the dualtree complex wavelet transform is used to extract information on different spatial scales from structural MRI data and show its relevance for disease classification.
In this paper we apply linear regression modelling to analyse the correlation between texture samples at various frequencies, facilitated through multiresolution analysis, for the efficient classification of textures. The basic algorithm is adopted from (Wang and Yong 2008). In this work we have experimented with different multiresolution analysis tools that are used for texture classification. In addition to the miltiresolution analysis tools such as the discrete wavelet transform and the discrete wavelet packet transform that are suggested in (Wang and Yong 2008), we have employed the dual tree complex wavelet packet transform, which is the novelty adopted in this work and the performance of the three methods is compared. Our experiments show that, in most of the cases, the discrete wavelet transform outperforms the discrete wavelet packet transform and dual tree complex wavelet packet transform in terms of classification rate.
This paper is organized as follows. “Texture classification using linear regression model” provides an overview of the application of multiresolution analysis tools (Rahman et al. 2011) and linear regression modelling (Kerns 2011) for analysing correlation between frequency channels for the classification of textures. “Texture classification algorithm” explains the methodology adopted for the classification phase. The experimental results and the performance comparison with the different multiresolution analysis tools are presented in “Experimental results”. Finally the conclusions are briefed in “Conclusion”.
Texture classification using linear regression model
Multiresolution analysis tools
The level of detail within an image varies from location to location. Finer resolution for analysis is required at regions where significant information is contained. Multiresolution representation of an image provides complete detail about the extent of information present at different locations. The main concept of multiresolution analysis is that for each vector space, there is another vector space of higher resolution until the final image is obtained. The basis of each of these vector spaces is the scale function. For textures, it provides scale invariant interpretation of a texture.
 1.
Discrete wavelet transform (DWT)
 2.
discrete wavelet packet transform (DWPT)
 3.
Dual tree complex wavelet packet transform (DTCWPT)
Discrete wavelet transform (DWT) of an image provides both frequency and location information of the analyzed image. The 2D wavelet transform is carried out by the tensor product of two 1D wavelet base functions along the horizontal and vertical directions, and the corresponding filters can be expressed as h_{LL}(k, l) = h(k)h(l), h_{LH}(k, l) = h(k)g(l), h_{HL}(k, l) = g(k)h(l) and h_{HH}(k, l) = g(k)g(l). By convolving the given image with these four filters, we get four sub images and thus four channels. Further decomposition is performed only in the low—low frequency region.
For quasiperiodic signals such as speech signals and texture patterns, whose dominant frequency channels are located in the middle frequency region, DWT decomposition is proposed to be nonideal (Chang and Kuo 1993). Discrete Wavelet Packet Transform (DWPT) which allows further decomposition in all frequency regions to obtain full decomposition, is ideally suited for mid frequency regions (Chang and Kuo 1993). Thus DWPT of an image can characterize the properties of an image in all frequency regions. Wavelet packets perform better in terms of fidelity of direction but not in terms of improved directionality. The highpass coefficients will oscillate around singularities of the signal (Ana SOVIC–Damir SERSIC 2012).
Channel number and naming used for DWT
Channel no  Name  Channel no  Name 

1  OB  6  OAD 
2  OC  7  OAAA 
3  OD  8  OAAB 
4  OAB  9  OAAC 
5  OAC  10  OAAD 
Channel number and naming used for DWPT and DTCWPT
Channel no  Name  Channel no  Name 

1  OAAA  33  OCAA 
2  OAAB  34  OCAB 
3  OAAC  35  OCAC 
4  OAAD  36  OCAD 
5  OABA  37  OCBA 
6  OABB  38  OCBB 
7  OABC  39  OCBC 
8  OABD  40  OCBD 
9  OACA  41  OCCA 
10  OACB  42  OCCB 
11  OACC  43  OCCC 
12  OACD  44  OCCD 
13  OADA  45  OCDA 
14  OADB  46  OCDB 
15  OADC  47  OCDC 
16  OADD  48  OCDD 
17  OBAA  49  ODAA 
18  OBAB  50  ODAB 
19  OBAC  51  ODAC 
20  OBAD  52  ODAD 
21  OBBA  53  ODBA 
22  OBBB  54  ODBB 
23  OBBC  55  ODBC 
24  OBBD  56  ODBD 
25  OBCA  57  ODCA 
26  OBCB  58  ODCB 
27  OBCC  59  ODCC 
28  OBCD  60  ODCD 
29  OBDA  61  ODDA 
30  OBDB  62  ODDB 
31  OBDC  63  ODDC 
32  OBDD  64  ODDD 
Correlation between frequency channels
For explaining the correlation between frequency channels, decomposition using the Dual tree complex wavelet packet transform is considered here in lieu of the extensive directionality. In order to characterize the image texture, we can use the raw coefficients as such. But generally some measure derived from these values is taken as the texture feature, as handling the raw coefficients is difficult. Typical examples of these measures are mean, standard deviation, energy and so on. The energy distribution has important discriminatory properties for images as it reflects the distribution of energy along the frequency axis over scale and orientation and as such can be used as a feature for classification. In our experiments the energy values from the subimages are extracted using the mean of the magnitude of the subimage coefficients (Unser 1995). That is if (M, N) represents the size of the subimage I, and I(i, j) represents the subimage coefficient corresponding to (i, j), then its energy is given by the equation
Different samples of the same texture are taken to derive the inherent texture properties and DTCWPT decomposition is applied to each sample. Considering a three level decomposition, we get 64 real(even) and 64 imaginary(odd) components. If ah represents the real part and ag represents the imaginary part of the DTCWPT, the complex coefficients are given by ah + j ag. The magnitude of the complex coefficients is considered for further processing. Since the DTCWPT measures both the real and imaginary part of the input signal, it offers both magnitude and phase information. Hence it also characterizes the information in all frequency regions.
To arrive at the correlation between the derived channel pairs and thereby identify the significant channel pairs, we make use of a preprocessing algorithm which is detailed below.
 [Input]::

m samples of each texture
 [Output]::

channel pair list and energy matrix E for each texture
 1.
For each texture, take m samples and decompose each of the samples using three level DTCWPT.
 2.
For each sample of a given texture, we get n wavelet coefficients each for real and imaginary parts. From this we find the magnitude of the complex coefficients.
 3.
From the energy of each channel [to be found out using (1)], form the energy vector of size n for each of the texture samples.
 4.
Arrange the vectors to form energy matrix E of size m x n.
 5.
Find the correlation coefficient matrix V from E and arrange the channel pairs in the descending order of correlation coefficients.
 6.
Eliminate those channel pairs whose correlation coefficient is less than a predefined threshold value T.
Applying the DTCWPT 3level decomposition, we get 64 frequency regions. Thus the energy matrix consists of energy vectors corresponding to 64 frequency channels of m samples. This energy matrix can be viewed in statistical perspective, as each frequency channel can be considered as a random variable and the energy values corresponding to each frequency channel can be considered as the values assigned to these random variables. From the energy matrix E_{(m, 64)}, a correlation coefficient matrix V of size 64 × 64 is generated, where (i, j)th element in the matrix corresponds to the correlation coefficient between the i and jth channel. Here it is to be noted that the correlation between the same channel pairs will generate the value 1. So all the diagonal elements which have value 1 can be neglected. Due to the symmetric property of correlation matrix, the values below and to the left of the diagonal (lower triangle) will be same as the values above and to the right of the diagonal (upper triangle). Therefore the channel pairs corresponding to the upper or lower triangle need to be considered for further analysis.
Classification rate obtained for 20 brodatz textures applying DTCWPT multiresolution analysis (considering 36 samples and a threshold value of 0.65)
ID  DTCWPT ( %)  ID  DTCWPT ( %) 

D3  91.1  D77  95 
D6  96.1  D83  95 
D20  95.8  D87  95 
D21  95.3  D88  93.6 
D22  95.3  D89  94 
D67  95.3  D92  95 
D68  95.3  D93  95.3 
D71  95.3  D96  96.1 
D72  93.6  D97  93.6 
D73  95.3  D101  95.6 
Classification rate obtained for texture D3 for a threshold value of 0.45 and varrying the number of samples (applying 3 level DTCWPT multiresolution analysis)
Number of samples  Classification rate (%) 

9  90 
25  91.6 
36  93.89 
42  94.29 
64  94.22 
81  97.5 
Classification rate obtained for texture D3 by selecting 81 number of samples and varying the threshold levels (applying 3 level DTCWPT multiresolution analysis)
Threshold  Classification rate (%) 

0.45  97.5 
0.51  96.67 
0.60  95.93 
0.65  94.44 
0.75  93.21 
Thus further in this experiment for channel elimination purpose, we have choosen a threshold value of 0.45 for the selected 81 samples.
Linear regression analysis for texture classification
 [Input]::

channel pair list and energy matrix E for each texture
 [Output]::

texture feature
 1.
Each of channel pairs obtained from preprocessing algorithm, form two random variables. The energy values of corresponding channel pair taken from the channel energy matrix form the values assigned to the variables.
 2.
Compute the regression parameters \( \hat{b} \) and \( \hat{a} \) of the above values using (4) and (5).
 3.
Calculate the Predictor \( \widehat{Y}_{{\rm i}} \) using (11).
 4.
 5.
Calculate the residual between \( Y_{\rm i} \) and \( \hat{Y}_{{\rm i}} \) as \( \left {\hat{Y}_{\text{i}}  Y_{\text{i}} } \right\).
 6.
Repeat 1–5 for each texture sample
 7.
Now the channel pairs, corresponding correlation coefficient, regression parameters, mean and variance, characterize the texture features. Using these, create the database containing the feature list of each texture.
Texture classification algorithm
Classification refers to as assigning a physical object or incident into one of a set of predefined categories. In texture classification the goal is to assign an unknown sample image to one of a set of known texture classes and it is one of the four problem domains in the field of texture analysis. Texture classification process involves two phases: the learning phase and the recognition phase. In the learning phase, the target is to build a model for the texture content of each texture class present in the training data, which generally comprises of images with known class labels. The texture content of the training images is captured with the chosen texture analysis method. This yields a set of textural features for each image. These features can be scalar numbers or discrete histograms or empirical distributions. Examples are spatial structure, contrast, roughness, orientation, etc. In the recognition phase the texture content of the unknown sample is first described with the same texture analysis method. Then the textural features of the sample are compared to those of the training images with a classification algorithm, and the sample is assigned to the category with the best match. Optionally, if the best match is not sufficiently good according to some predefined criteria; the unknown sample can be rejected.
Learning phase
 [Input]::

texture samples
 [Output]::

database containing texture features
 1.
Take different samples of the given texture, apply preprocessing algorithm (as in “Correlation between frequency channels”) and derive the energy matrix and channel pair list.
 2.
Select the channel pairs with correlation coefficient greater than threshold value and arrange them in the descending order of correlation coefficients.
 3.
Apply feature extraction algorithm (as in “Linear regression analysis for texture classification”) and form the database.
 4.
Repeat steps 1–3 for all textures.
Recognition phase
 [Input]::

unknown texture
 [Output]::

unknown texture classified
 1.
Decompose the unknown texture using multiresolution analysis tool and obtain its energy vector V.
 2.
Select one texture from the database.
 3.
Choose the topmost channel pair.
 4.
Compute the regression parameters, mean and variance of the corresponding channel pair.
 5.
From energy vector V of the unknown texture, select the energies corresponding to the selected channel pair.
 6.
Consider one of the energy of two channels as \( X_{\rm i} \) and other as \( Y_{\rm i} \) and applying linear regression modelling, find predictor \( \widehat{Y}_{\rm i} \), using (11).
 7.
Compute the residue \( \left {\hat{Y}_{\text{i}}  Y_{\text{i}} } \right. \)
 8.
If the residue is greater than \( \upmu \pm 3\upsigma \), eliminate the texture from candidate list, choose the next texture and repeat steps 3–7.
 9.
Else select the next channel pair and repeat steps 4–7. If for all the channel pairs the residue is less than \( \upmu \pm 3\upsigma \), then that unknown texture is assigned to that corresponding texture class.
 10.
If there is only one texture left in the database, the unknown texture is assigned to that texture class.
Experimental results
Energy matrix obtained for texture D3 using two level DTCWPT
807  130  99  51  31  64  19  31  25  19  45  30  10  13  13  17 
794  124  104  54  29  55  19  29  33  23  54  34  10  15  14  19 
810  112  112  52  26  50  16  29  31  23  54  36  10  16  12  19 
735  125  107  57  29  62  18  30  30  21  50  33  10  15  12  20 
840  118  100  48  29  60  18  28  25  19  46  28  9  13  11  17 
826  125  100  53  29  58  19  31  27  21  46  30  10  15  13  18 
810  109  109  48  25  51  17  30  33  24  57  34  10  15  13  19 
841  117  111  52  27  59  17  30  28  19  52  32  9  13  12  19 
631  131  105  57  31  70  19  29  27  21  44  34  11  15  13  20 
807  123  110  55  29  59  19  31  26  19  50  30  10  14  13  17 
783  109  111  51  27  55  18  29  31  24  53  33  11  15  13  19 
853  104  117  52  26  51  16  30  32  22  57  33  10  15  13  19 
773  121  110  55  27  60  18  30  28  18  50  31  10  13  12  19 
758  114  112  52  32  63  19  30  26  18  52  31  9  12  12  17 
773  116  107  57  30  60  21  33  28  22  50  32  11  15  15  19 
795  114  119  51  26  53  18  30  33  24  59  37  11  15  14  19 
908  107  106  54  28  54  18  31  30  19  54  31  9  13  13  19 
682  121  113  54  31  67  19  30  28  22  49  36  11  15  13  20 
757  125  103  57  33  66  21  32  27  20  46  32  11  15  14  18 
750  121  112  54  29  59  20  32  32  25  55  36  12  17  16  21 
873  105  109  54  26  54  17  32  33  21  58  33  10  14  13  20 
850  114  108  54  31  62  19  31  30  20  55  33  10  13  13  19 
813  120  96  49  30  60  18  28  24  17  44  29  9  13  11  17 
782  124  103  55  30  61  21  31  29  22  48  32  11  16  14  20 
819  111  110  53  25  55  17  31  33  25  56  37  11  15  14  20 
936  97  101  52  27  52  17  31  30  19  54  31  9  13  12  19 
820  112  106  55  31  60  18  28  31  21  56  37  10  14  12  20 
903  99  88  50  26  47  17  28  24  18  42  29  9  13  12  18 
791  115  111  52  28  55  20  29  31  22  54  33  11  15  14  19 
883  94  108  52  23  47  15  29  31  21  55  34  9  14  12  20 
904  96  106  54  29  51  16  27  31  19  53  33  9  13  11  18 
716  109  105  51  31  54  17  26  26  20  45  33  9  13  12  18 
787  122  98  54  29  54  20  29  27  21  47  34  11  15  15  19 
823  106  113  49  24  49  16  27  32  22  58  34  10  13  12  18 
912  98  109  51  26  49  15  27  29  19  54  33  9  13  11  19 
764  101  111  54  29  53  18  28  33  23  57  37  11  15  13  20 
799  117  96  54  30  55  19  29  27  21  46  35  10  15  13  19 
790  122  107  51  27  56  18  30  31  23  56  34  12  15  14  19 
847  99  120  53  26  53  16  29  34  22  60  34  9  13  12  19 
846  113  107  49  30  58  17  28  30  19  53  30  9  13  12  18 
Correlation coefficient matrix obtained for texture D3 using 2 level DTCWPT
1  −0.671  −0.141  −0.360  −0.524  −0.664  −0.519  −0.097  0.151  −0.315  0.309  −0.293  −0.545  −0.545  −0.385  −0.233 
−0.671  1  −0.210  0.331  0.608  0.791  0.738  0.372  −0.402  0.005  −0.498  −0.147  0.439  0.391  0.437  −0.034 
−0.141  −0.210  1  0.042  −0.310  −0.074  −0.292  0.151  0.672  0.478  0.776  0.489  0.144  0.164  0.105  0.246 
−0.360  0.331  0.042  1  0.475  0.484  0.464  0.458  0.005  0.061  −0.131  0.235  0.364  0.285  0.342  0.470 
−0.524  0.608  −0.310  0.475  1  0.803  0.690  0.087  −0.522  −0.326  −0.548  −0.203  0.083  0.039  0.095  −0.157 
−0.664  0.791  −0.074  0.484  0.803  1  0.671  0.375  −0.406  −0.172  −0.438  −0.158  0.263  0.157  0.195  −0.003 
−0.519  0.738  −0.292  0.464  0.690  0.671  1  0.506  −0.347  0.052  −0.460  −0.115  0.572  0.461  0.647  0.101 
−0.097  0.372  0.151  0.458  0.087  0.375  0.506  1  0.136  0.245  0.094  0.033  0.490  0.387  0.612  0.381 
0.151  −0.402  0.672  0.005  −0.522  −0.406  −0.347  0.136  1  0.727  0.904  0.683  0.310  0.339  0.301  0.551 
−0.315  0.005  0.478  0.061  −0.326  −0.172  0.052  0.245  0.727  1  0.512  0.790  0.715  0.808  0.660  0.653 
0.309  −0.498  0.776  −0.131  −0.548  −0.438  −0.460  0.094  0.904  0.512  1  0.529  0.071  0.053  0.103  0.300 
−0.293  −0.147  0.489  0.235  −0.203  −0.158  −0.115  0.033  0.683  0.790  0.529  1  0.529  0.586  0.421  0.703 
−0.545  0.439  0.144  0.364  0.083  0.263  0.572  0.490  0.310  0.715  0.071  0.529  1  0.862  0.896  0.655 
−0.545  0.391  0.164  0.285  0.039  0.157  0.461  0.387  0.339  0.808  0.053  0.586  0.862  1  0.781  0.662 
−0.385  0.437  0.105  0.342  0.095  0.195  0.647  0.612  0.301  0.660  0.103  0.421  0.896  0.781  1  0.555 
−0.233  −0.034  0.246  0.470  −0.157  −0.003  0.101  0.381  0.551  0.653  0.300  0.703  0.655  0.662  0.555  1 
Top 5 channel pair list for texture D3 and the corresponding database values using 2 level DTCWPT
Channel pairs  Correlation coefficient  Regression parameters ‘a’ and ‘b’  Mean  Variance 

9, 11  0.9040  1.6010, 4.3901  0  2.0784 
13, 15  0.8969  1.1873, 0.7825  0  0.5145 
13, 14  0.8622  1.1725, 2.2148  0  0.6054 
10, 14  0.8087  0.4904, 4.1647  0  0.7028 
5, 6  0.8032  1.8875, 2.6717  0  3.3411 
Database created for texture D3 using 3 level DWT
Channel pairs  Correlation coefficient  Regression parameters ‘a’ and ‘b’  Mean  Variance 

1, 4  0.8013  2.7729, 3.3465  0  4.1292 
2, 5  0.7678  1.7739, 24.4591  0  2.8747 
5, 9  0.7409  2.2671, −0.7171  0  9.2205 
1, 8  0.6049  5.6742, 4.1983  0  14.8954 
2, 9  0.5941  4.2000, 50.4331  0  11.0436 
5, 10  0.5562  1.0696, −1.1920  0  7.1715 
9, 10  0.5526  0.3473, 18.0255  0  7.1920 
4, 8  0.5518  1.4957, 36.2262  0  15.6003 
1, 3  0.4722  0.1602, 6.6698  0  0.5964 
2, 3  0.4602  0.1603, 6.6910  0  0.6007 
Top 5 channel pair list for texture D3 and the corresponding database values using 3 level DTCWPT
Channel pairs  Correlation coefficient  Regression parameters ‘a’ and ‘b’  Mean  Variance 

21, 22  0.9185  0.5441, 7.7883  0  2.5157 
36, 44  0.8919  1.2642, 0.9915  0  1.8890 
37, 38  0.8903  1.1344, 0.1296  0  1.0028 
38, 40  0.8854  1.0531, 2.9983  0  1.2173 
33, 35  0.8764  1.1798, −0.6892  0  1.9534 
Top 5 channel pair list for texture D3 and the corresponding database values using 3 level DWPT
Channel pairs  Correlation coefficient  Regression parameters ‘a’ and ‘b’  Mean  Variance 

8, 20  0.8494  0.3350, 1.0720  0  0.1585 
3, 9  0.8458  0.3893, 0.8328  0  1.0266 
20, 24  0.8375  0.9267, 0.0694  0  0.1815 
6, 18  0.8344  0.4684, −1.7973  0  1.0072 
8, 24  0.8206  0.3581, 0.8022  0  0.1899 
It is noted from Fig. 4 that discrete wavelet transform provides the best texture classification rate for all the textures compared with discrete wavelet packet transform and dual tree complex wavelet packet transform. It is also observed that for some of the textures dual tree complex wavelet packet transform and discrete wavelet packet transform provides the same classification rate. Contrary to the above, it is found that for brodatz textures D6, D68, D72 and D89 dual tree complex wavelet packet provides better classification rate compared to that of discrete wavelet packet transform. In terms of the time elapsed for creating the database, it is found to be less for discrete wavelet transform. For dual tree complex wavelet packet transform the time needed for creating the database for 20 brodatz textures is 12 min, that for discrete wavelet packet transform is 5 min and 49 s while in the case of discrete wavelet transform the time expended is only 1 min and 38 s. We infer that computational complexity is also much reduced by the adoption of the multiresolution analysis tool of discrete wavelet transform. This is because of the simplicity in the application of the filters. For the DWPT and DTCWPT, applying the appropriate filter also plays a major role in the accuracy of the extracted features. Designing the filter required for the context is understood to give better response.
Conclusion
In this paper, various multiresolution analysis tools such as discrete wavelet transform, discrete wavelet packet transform or dual tree complex wavelet packet transform is combined with linear regression modelling for classification of textures. The dual tree complex wavelet packet transform (DTCWPT) which is the most advanced version of wavelet transforms is expected to produce the best classication rate. But in our experiments the discrete wavelet transform (DWT) outperforms both the dual tree complex wavelet packet transform (DTCWPT) and the discrete wavelet packet transform (DWPT) when applied for classification of textures. This work has focused on texture classification method. Application of this method to texture segmentation may be explored in future. The performance is also dependent on the filters used. Requirement specific filter can be designed and tried for better accuracy for DWPT and DTCWPT in future.
Declarations
Authors’ contributions
SD carried out the studies, design, development & testing of the work involved. Additionally she has drafted the manuscript. VSKR has made contributions to the conception, guidance to the first author for carrying out the studies, design, development and testing of the work involved. Additionally she has revised the manuscript for important intellectual content and given final approval of the version to be published. She agrees to be accountable for all aspects of the work in ensuring that questions related to the accuracy or integrity of any part of the work are appropriately investigated and resolved. All authors read and approved final manuscript.
Acknowledgements
Authors sincerely acknowledge the Centre for Development of Advanced Computing (CDAC), Thiruvananthapuram, Kerala, India for their unstinting support and infrastructural facilities provided.
Competing interests
The authors declare that they have no competing interests.
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