 Open Access
 Total Downloads : 247
 Authors : V. Thenmozhi, S. Aruljothi
 Paper ID : IJERTV2IS60641
 Volume & Issue : Volume 02, Issue 06 (June 2013)
 Published (First Online): 21062013
 ISSN (Online) : 22780181
 Publisher Name : IJERT
 License: This work is licensed under a Creative Commons Attribution 4.0 International License
A Wavelet Transform Approach To Texture Analysis And Classification With Linear Regression Model
V. Thenmozhi S. Aruljothi
Assistant professor/IT Assistant professor/CSE Srishakthi Institute of Engineering & Bharath Niketan Engineering
Technology College
Abstract
Texture analysis and classifications are ologybased on multi resolution properties of wavelet transform which is used to extract spectral information of the texture image at different scales and it ignores the structural information of the texture. A special emphasis is that a distinctive correlation exists between the different frequent regions of the sample images, belonging to the same kind of texture. Experimentally, it was shown that different regions of sample image obtained by 2D wavelet packet transform and observed that this correlation varies from texture to texture. The linear regression model is employed to analyze this correlation and extract texture features that discriminate the samples. We proposed a texture classification algorithm that considers frequency regions and also the correlation between these regions. Experiments show that our method signicantly improves the texture classication rate in comparison with other the multiresolution methods, including the Gabor transform, the pyramidstructured wavelet transform (PSWT) and the tree structured wavelet transform (TSWT) .

Introduction
Texture provides vital in order about image Classification tasks. The most conventional approaches included gray level cooccurrence matrices (GLCM) that considers second order statistical texture features, Gauss Markov random eld, which are
constrained to the analysis of spatial models and local linear transform considers relations between neighborhood pixels in a small image region[1],[4]. Recently, random set stochastic model is employed to texture classication in which texture can be analyzed by set of structuring windows and extracts structural properties dened by a neighborhood system. A texture image is transformed into a pattern map by a set of templates with principal component analysis (PCA) for characterizing texture information. The Fisher criterion is employed to optimize FIR lters[4] for texture feature extraction. The mutual information of different subbands after the multichannel decomposition is used for the sparse representation of texture image.
The most common multiresolution analysis approach is to transform a texture image into a local spatial/frequency representation by convolving this image with a bank of lters. The Gabor transform is also limited to its ltering area. Consequently, the wavelet transform to obtain the spectral information of the texture image. To make use of the texture primitives, GLCM as commonly popular structural descriptor is recently combined with the traditional multiresolution methods [24], [25]. An image texture is described by the number and types of its primitives and the spatial organization or layout of its primitives. The basic pattern and repetition frequency of a texture sample could be perceptually invisible, although quantitatively present. In the deterministic formulation texture is considered as a basic local pattern that is
periodically or quasiperiodically repeated over some area. An image texture may be defined as a local arrangement of image irradiances projected from a surface patch of perceptually homogeneous irradiances. Texture is characterized not only by the grey value at a given pixel, but also by the grey value `pattern' in a neighborhood surrounding the pixel. The unit of texture is texels, and the repetitiveness of the texels determines the type of the texture and decides the texture analysis approach.

System design
FEATURE EXTRACTION
FEATURE EXTRACTION
2.1 Preprocessing algorithm:
vector of this unknown texture image. Take one energy of two channels get the residual Remove the texture from the candidate list if the residual is larger than
ÂµÂ±3 .If there is only one texture is left in the candidate list, assign the unknown texture image to this texture.

Architecture Of The System:
Input
IMAGE ACQUISITION
PRE PROCESSING
PRE PROCESSING

The original image is decomposed into four subimages, which can be viewed as the parent node and thefour children nodes.

Calculate the energy of these subimages and the tree forms four branches from the parent node.

Repeat the decomposition of these subimages and the tree branches at the power of four until satisfying the least size of the subimage[5].

Repeat the steps for j samples and construct the channel energy matrix M .


Methodology
CLASSIFICATION
CLASSIFICATION
POST PROCESSING
POST PROCESSING
decision

Figure out the covariance matrix C.

Select the top channel pairs with the correlation coefficient p T and order them into a list as p descends.
2.2 Learning phase:
Learning phase directly extracts texture features a, b, Âµ, , two frequency channels and correlation coefficient of each top channel pair and index of this texture.Put all such features into a list and insert into a database.
2.3. Classification Phase:
Order all textures in the database into a candidate list, Pick out the parameters a, b, Âµ, of the j th channel pair
of a texture in the candidate list from its feature list, and select the energy of two frequency channels identical to that of this top channel pair from the channelenergy

Wavelet Transform
The wavelet transform provides a precise and unifying framework for the analysis and characterization of a signal at different scales. It can be implemented efficiently with the pyramidstructured wavelet transform and the wavelet packet transform. The pyramidstructured wavelet performs further decomposition of a signal only in the low frequency regions. Adversely, the wavelet packet transform decomposes a signal in all low and high frequency regions[7].

2D Wavelet Packet Transforms
As the extension of the 1D wavelet transform, the 2D wavelet transform can be carried out by the tensor product of two 1D wavelet base functions along the horizontal and vertical directions, An image can be decomposed
into four sub images by convolving the image with these filters. These four sub images characterize the frequency information of the image in the LL, LH, HL, and HH frequency regions.
LL 3
HL 3
LL 3
HL 3
LL 3
HL 3
LL 3
HL 3
L H3
H H3
L H3
H H3
LH 3
H H3
L H3
H H3
LL 3
HL 3
LL 3
HL 3
LL 3
HL 3
LL 3
HL 3
L H3
H H3
L H3
H H3
LH 3
H H3
L H3
H H3
LL 3
HL 3
LL 3
HL 3
LL 3
HL 3
LL 3
HL 3
L H3
H H3
L H3
H H3
LH 3
H3
L H3
H H3
LL 3
HL 3
LL 3
HL 3
LL 3
HL 3
LL 3
HL 3
L H3
H H3
L H3
LH 3
H H3
H H3
L H3
H H3
Fig 3.1 2D wavelet packet Decomposition
3.3. Energy Distribution:
The wavelet domain focuses on directly extracting the energy values from the sub images and uses them to characterize the texture image. The energy distribution of a sub image can be calculated by one of the three commonly used functions: the magnitude ,The squaring, and the rectified sigmoid.. The magnitude and squaring functions are similar in the effect of the nonlinearity. The rectified sigmoid function requires appropriate saturation parameter. The mean and the standard deviation of the magnitude of the sub image coefficients is used as its energy. That is, if the sub image is x[m,n] with 1mM and 1n<N its energy can be represented as
Where x(i,j) is the pixel value of the sub image.

Correlation Analysis
The wavelet (packet) transform approximately decorrelates the image using the orthogonal bases. Correlation indicates the spatial correlation between
some sample texture images, belonging to the same kind of texture, at different frequency regions obtained by 2D wavelet transform. The most common approach is to calculate all frequency regions energy values of every image with the energy function and to characterize this texture by the statistics of these energy values. This approach ignores the spatial relation of these sample texture images. From a statistical perspective, a frequency region of a sample texture image can be viewed as a random variable and the energy values of this frequency region can be treated as the random values of this variable.

Linear Regression Model
The simple linear regression model to analyze the correlation. Suppose that we have a set of the random data for two numerical variables X and Y. From the simple linear regression analysis, the distribution of the random data approximately appears a straight line in space.. This line function (also called the simple linear regression equation) can be given as follows:
Y=aÃ— x+b
exploit the simple linear regression model to extract the texture features from the correlation in the frequency channel pairs. The channelpair list includes all channel pairs with T. For two frequency channels of one channel pair in the list, we take out their energy values from the channelenergy matrix The parameters a and b of the line can be figured out through the least square method.

Texture Feature Set
The feature lists of the textures are needed to store into the database. In the feature lists, every texture feature contains the a,b,Âµ, and , two frequency channels and the correlation coefficient of one channel pair and the index of a texture. The parameters a,b and two frequency channels are used to compute the residual of an unknown texture image at a top channel pair of a texture, and the parameters ,Âµ and are used to get the
threshold ÂµÂ±3 in order to determine whether this image satisfies the correlation at this top channel pair of this texture.

Threshold Comparison
The statistics implies that a normally distributed (or Gaussian) random variable X has probability density function
P(x)=(1)/(2)exp[((xÂµ)2)/22)]
Where the parameters Âµ and of the distribution are the mean and Variance of X, respectively. It can be known that a texture always have many top channel pairs and the combination of these channel pairs is the characteristic of this texture. If a sample image meets the correlation of all top channel pairs of a texture, it can be inferred that it belongs to this texture. Therefore, the value of ÂµÂ±3 can be considered as an appropriate way to assign an unknown texture image to a texture. The estimation of mean and variance can be carried out by
The average retrieval rate defined is different from that of other methods because our classifier is threshold based comparison in one dimension. All query samples are processed by our method and respectively assigned to the corresponding texture. We count the samples of this texture, which are assigned to the right texture, and get the average percentage number as the average retrieval rate of this texture. Moreover, our method takes simply the threshold comparison in 1D space in the classification phase owing to taking advantage of the texture inherent correlation characteristic in the learning phase.


EXPERIMENTAL RESULTS
Every original image is of size 640Ã—640 pixels with 256gray levels. 81
sample images of size 128 Ã—128 with an overlap of 32 pixels between vertically and horizontally adjacent images are extracted from each original image and used in the experiments, and the mean of every image is removed before the processing.
Fig 4.1 Texture Image
Fig 4.2 First level Decomposition
Fig 4.3 Second Level Decomposition
This table illustrates the classification accuracy of different textures obtained from Brodatzs Texture album[2]. I used 40 textures and verify the performance of the classification algorithm. Each texture with its classification rate is shown in Table 4.1 and Figure 4.4
Textu re ID
Classifi cation Rate
Textur e ID
Classifi cation Rate
D3
84.42
D78
100
D4
99.65
D79
99.30
D6
99.65
D82
100
D9
99.65
D83
100
D11
99.65
D84
99.65
D16
100
D92
100
D19
92.733
D95
100
D21
99.65
D102
99.65
D24
99.65
D103
99.65
D29
100
D105
100
D34
100
D13
97.92
D36
100
D44
100
D52
100
D15
100
D53
95.15
D25
100
D55
100
D28
100
D57
100
D43
100
D65
100
D45
100
D68
100
D62
92.04
D74
100
D60
100
D77
100
D81
100
Table 4.1 Classification Rate of Different Textures without noise
Fig 4.4 Classification Rate of Different Textures without noise
Textur eID
Classifica tion Rate with Guassian noise
Textur eID
Classific ation Rate with Guassian noise
D3
87.54
D4
100
D6
98.96
D9
100
D11
100
D16
98.2
6
D19
98.26
D21
100
D24
100
D29
100
D34
100
D36
100
D52
100
D53
96.8
8
D55
100
D57
100
D65
100
D68
100
D74
100
D77
99.3
0
D78
100
D79
99.3
D82
100
D83
99.6
D84
100
D92
99.6
D95
99.65
D102
99.6
Textur eID
Classifica tion Rate with Guassian noise
Textur eID
Classific ation Rate with Guassian noise
D3
87.54
D4
100
D6
98.96
D9
100
D11
100
D16
98.2
6
D19
98.26
D21
100
D24
100
D29
100
D34
100
D36
100
D52
100
D53
96.8
8
D55
100
D57
100
D65
100
D68
100
D74
100
D77
99.3
0
D78
100
D79
99.3
D82
100
D83
99.6
D84
100
D92
99.6
D95
99.65
D102
99.6
This table illustrates the classification accuracy of different textures obtained from Brodatzs Texture album[2]. I used 40 textures and verify the performance of the classification algorithm by adding guassian noise with the sample image. Each texture and its classification rate with noise is shown in Table 4.2. and Figure 4.5.
D103
99.65
D105
99.65
D13
98.96
D44
99.65
D15
100
D25
100
D28
100
D43
100
D45
100
D62
89.27
D60
100
D81
100
D103
99.65
D105
99.65
D13
98.96
D44
99.65
D15
100
D25
100
D28
100
D43
100
D45
100
D62
89.27
D60
100
D81
100
correlation of different frequency channels. It is very easy and fast to examine the change of different frequent channels for texture image.
Table 4.2 Classification Rate of Different Textures with Guassian noisy data
Fige 4.5 Classification Rate of Different Textures with Guassian noisy data

CONCLUSION
This wavelet based approach is Effective and its Classification accuracy is good for much more Textures. It provides entire frequent channels in comparison with traditional approaches and it is capable to characterize much more spectral information of the texture at different multi resolution levels. Multiresolution analysis directly computes the energy values from the sub images and extracts the features to characterize the texture image at multidimensional space. Our method employs threshold comparison in one dimension space rather than the multidimensional space. It uses linear regression model to analyse
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