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\title{Texture Analysis and Classification Based on Fuzzy Triangular Greylevel Pattern and Run-Length Features}
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             \author[1]{U Ravi  Babu}

             \affil[1]{  Research Schalor AN University}

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\date{\small \em Received: 12 February 2012 Accepted: 1 March 2012 Published: 15 March 2012}

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\begin{abstract}
        


Your Texture analysis is one of the most important techniques used in the analysis and interpretation of images, consisting of repetition or quasi repetition of some fundamental image elements. The present paper derived Fuzzy Triangular Greylevel Pattern (FTGP) to overcome the disadvantages of LBP and other local approaches. The FTGP is a 2 x 2 matrix that is derived from a 3 x 3 neighborhood matrix. The proposed FTGP scheme reduces the overall dimension of the image while preserving the significant attributes, primitives, and properties of the local texture. From each 3 x 3 matrix a Local Grey level Matrix (LGM) is formed by subtracting local neighborhoods by the gray value of its center. The 2 x 2 FTGP is generated from LGM by taking the average value of the Triangular Neighbor Pixels (TNP) of the 3 x 3 LGM. A fuzzy logic is applied to convert the Triangular Neighborhood Matrix (TNM) in to fuzzy patterns with 5 values {0, 1, 2, 3 and 4} instead of patterns of LBP which has two values {0, 1}. On these fuzzy patterns a set of Run Length features are evaluated for an efficient classification. The proposed method is experimented with wide variety of textures, and exhibited with a high classification rate. The proposed FTGP with run length features shown its supremacy and efficacy over the various existing methods in classification of textures.

\end{abstract}


\keywords{run length features, fuzzy triangular greylevel pattern (ftgp), triangular neighbor pixels local greylevel matrix (lgm).}

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\let\tabcellsep& 	 	 		 
\section[{Introduction}]{Introduction}\par
nalysis of textures is a fundamental research topic in the area of computer vision and has many potential applications, for example, in industrial surface inspection, remote sensing, and biomedical image analysis. Classification refers to as assigning a physical object or incident into one of a set of predefined categories. Many texture classification problems usually require the computation of a large amount of texture features in order to characterize their associated patterns. This implies that texture classifiers frequently combine big sets of features without taking into account their relevance and redundancy. Thus, lowering the dimensionality of a feature set is necessary for preserving the most relevant features and it reduces the computational cost derived from unnecessary features \hyperref[b0]{[1,}\hyperref[b1]{2,}\hyperref[b2]{3,}\hyperref[b34]{34,}\hyperref[b35]{35]}.\par
Numerous algorithms of textural features extraction have been presented during the past decades \hyperref[b3]{[4,}\hyperref[b4]{5]}. Textures are classified recently by various methods: preprocessed images \hyperref[b34]{[34]}, long linear patterns \hyperref[b35]{[35]}, edge direction movements \hyperref[b21]{[21]}, avoiding complex patterns \hyperref[b9]{[10]}, marble texture description \hyperref[b36]{[36]}, skeleton extraction of texture \hyperref[b6]{[7]}, long linear patterns using wavelets \hyperref[b7]{[8]} wavelet transform \hyperref[b7]{[8,}\hyperref[b8]{9,}\hyperref[b9]{10]}. and Gabor filters \hyperref[b11]{[11]}. More recently, the local-binary-pattern (LBP) operator \hyperref[b12]{[12,}\hyperref[b13]{13,}\hyperref[b14]{14]} is used for texture classification. LBP operator is a statistical texture descriptor of the characteristics of the local structure. LBP provides a unified description including both statistical and structural characteristics of a texture patch, so that it is more powerful for texture analysis. The concept of LBP is also extend in applications such as face recognition and age classification \hyperref[b15]{[15,}\hyperref[b16]{16,}\hyperref[b17]{17]}, industrial visual inspection \hyperref[b18]{[18,}\hyperref[b19]{19]}, segmentation of remote-sensing images \hyperref[b20]{[20]}, and classification of real outdoor images \hyperref[b21]{[21]}.\par
An efficient nonparametric methodology for texture analysis based on magnitude LBP (MLBP) \hyperref[b22]{[22,}\hyperref[b23]{23,}\hyperref[b24]{24,}\hyperref[b25]{25,}\hyperref[b26]{26]} is recently proposed and it has been made into a powerful measure of image texture, in terms of accuracy and computational complexity in many empirical studies. To address the connectivity limitations of LBP and MLBP, we propose a matrix called Triangular Neighborhood Matrix (TNM), which generates 2×2 texton patterns. A fuzzy member ship is introduced on TNM to extract local texture information efficiently. The present paper derived run length matrix on the proposed scheme and evaluated runlength features for efficient, precise and accurate classification of textures.A ( D D D D ) F 2012 
\section[{Year}]{Year}\par
The rest of the paper is organised as follows. Section 2 describes the proposed method. Section 3 describes the results and discussions and conclusions are given in section 4. pattern (FTGP), triangular neighbor pixels local greylevel matrix (LGM). 
\section[{II.}]{II.} 
\section[{Methodology}]{Methodology} 
\section[{Derivation of TNM (Triangular Neighborhood Matrix)}]{Derivation of TNM (Triangular Neighborhood Matrix)}\par
The present paper derived FTGP to overcome the disadvantages of LBP and other local binary approaches. Runlength features are evaluated on FGTP for a precise classification in 5 steps.\par
Step 1: Formation of Local Grey level Matrix (LGM):\par
A neighborhood of 3×3 pixels is denoted by a set containing nine elements: P= \{P1, P1 ...P9\}, here P5 represents the intensity value of the central pixel and remaining value are the intensity of neighboring pixels as shown in Fig. \hyperref[fig_0]{1(a)}. The Local Grey level Matrix (LGM) values of the neighboring pixels (LGMPi) are obtained by evaluating the absolute difference between the neighboring pixel and the gray value of the central pixel, as described by the Equation (1) as shown in Fig. \hyperref[fig_0]{1}.P 1 P 2 P 3\par
LGMP 1\par
LGMP 2\par
LGMP 3 P 4 P 5 P 6\par
LGMP 4\par
LGMP 5\par
LGMP 6 P 7 P 8 P 9\par
LGMP 7\par
LGMP 8\par
LGMP 9 \par
Where LGMP i is the obtained grey value of the pixel P i of the LGM. The equation 1 demonstrates that always LGMP 5 value (central pixel value) will be always zero.\par
Step 2: Generation of Triangular Neighborhood Matrix (TNM) from LGM of step 1:\par
The 2 x 2 TNM is generated from LGM by taking the average value of the Triangular Neighbor Pixels (TNP) of the 3 x 3 LGM as shown in figure \hyperref[fig_1]{3} and as given in equation 2,3, 4 and 5 . The triangular neighbors are considered because the central pixel of LGM is always zero. That is one need not necessary to consider this.?????? 1 = (LGMP 1 + LGMP 1 + LGMP 1 )\textbf{3}?????? 2 = ?LGMP 2 + LGMP 3 + LGMP 6 ?\textbf{3}?????? 3 = (LGMP 4 + LGMP 7 + LGMP 8 )\textbf{3}?????? 4 = (LGMP 6 + LGMP 8 + LGMP 9 )\textbf{3}\par
LGMP 1\par
LGMP 2\par
LGMP 3\par
LGMP 4\par
LGMP 5\par
LGMP 6 TNP 1 TNP 2\par
LGMP 7\par
LGMP 8\par
LGMP 9 Fuzzy logic has certain major advantages over traditional Boolean logic when it comes to real world applications such as texture representation of real images. LBP patterns are formed and counted from 0's and 1's. However, the dangerous situation of LBP is that even if the difference is minimum let us say 1 or maximum i.e. 255, it converts it into 1. That is LBP treats even the difference of 1 and 255 as homogeneous. This clearly indicates the patterns of LBP will never gives totally useful and significant information. The above property misuses the power of LBP method. To address this in the proposed method fuzzy member ship is introduced. The aim of fuzzy approach in forming FTGP is to extract local texture information from TNM pixels for representing the texture information accurately. To deal accurately with the regions of natural images even in the presence of noise and the different processes of caption and digitization FTGP is introduced on TNM. For example, even if the human eye perceives two neighboring pixels as equal, they rarely have exactly the same intensity values. The fuzzy patterns are chosen in the present paper because, recently, fuzzy based methods have been used in texture analysis and in image segmentation \hyperref[b28]{[28,}\hyperref[b29]{29]}. The FTGP consists of fuzzy patterns with 5 values \{0, 1, 2, 3 and 4\} instead of two patterns of LBP. Though the present paper considers five possible fuzzy grey level values, but at any time only a maximum of four fuzzy patterns will appear because the FTGP is a 2 x 2 matrix. In LBP binary patterns are evaluated by comparing the neighboring pixels with central pixel. The FTGP are derived by comparing the each pixel of the 2 x 2 TNM with the average pixel values of the TNM. The FTGP representation is shown in Fig. \hyperref[fig_2]{4}. The following Eqn. (  {\ref 6}) is used to determine the elements, FTGP i of the TNM. For example, the process of evaluating FTGP from a sub TNM image of 2 x 2 is shown in Fig. \hyperref[fig_3]{5}. In this example x and y are chosen as v 0 /2 and 3v o /2 respectively. The membership values of FTGP neighboring pixels are useful for characterization of textures. To address this difficulty the present approach derived Run length matrix (RLM) on the FTGP of the image. 
\section[{Definition of the Run-Length Matrices: Galloway}]{Definition of the Run-Length Matrices: Galloway}\par
proposed the use of a run-length matrix for texture feature extraction \hyperref[b12]{[12]}. For a given texture image, a runlength matrix P(i; j) is defined as the number of runs with fuzzy value i and run length j. Various texture features can then be derived from this run-length matrix.\par
For a given image, the proposed method defines a RLM (i,j) on FTGP as number of runs starting from location (i,j) of the FTGP image. The proposed method derived five different RLM-FTGP. The RLM-FTGP 0 , RLM-FTGP 1 , RLM-FTGP 2 RLM-FTGP 3 and RLM-FTGP 4 contain the run length values for zero, one, two, three and four.\par
Step 5: Extraction of Texture Features on RLM -FTGP:\par
Many researchers used three sets of texture features from RLM for texture classification. The first set of RLM Features (RF) is Traditional Run-Length Features. The five original features of run-length statistics derived by Galloway \hyperref[b27]{[27]} are Short Run Emphasis (SRE), Long Run Emphasis (LRE), Gray-Level Non uniformity (GLN), Run Length Non uniformity (RLN), and Run Percentage (RP) are described by the Equation (8) to Equation \hyperref[b12]{(12)}. Chu et al. \hyperref[b30]{[30]} proposed another set of two new features, such as Low Gray-Level Run Emphasis (LGRE), and High Gray-Level Run Emphasis (HGRE) are described in Equation (  {\ref 13}) to Equation \hyperref[b14]{(14)}.\par
In a recent study, Dasarathy and Holder \hyperref[b31]{[31]} described another set of four feature extraction functions following the idea of joint statistical measure of gray level and run length, as follows: Short Run Low Gray-Level Emphasis (SRLGE), Short Run High Gray-Level Emphasis (SRHGE), Long Run Low Gray-Level Emphasis (LRLGE), and Long Run High Gray-Level Emphasis (LRHGE) are described in Equation \hyperref[b15]{(15)} to Equation \hyperref[b18]{(18)}.\par
The novelty of the present study is it evaluated the first five RFs as described in equations from 8 to 12 for efficient classification purpose on FTGP. For a comparative analysis the present paper also evaluated all the features for classification purpose.?????? = 1 ?? ?? ? ? ??(??,?? ) ?? 2 ?? ?? =1 ?? ??=1 (8) ?????? = 1 ?? ?? ? ? ??(??, ??) * ?? 2 ?? ?? =1 ?? ??=1 ?????? = 1 ?? ?? ? ? ??(??,?? ) ?? 2 ?? ?? =1 ?? ??=1 (10) ?????? = 1 ?? ?? ? ?? ??(??, ??) ?? ?? =1 ? 2 ?? ??=1 (11) ???? = n r n p\textbf{(12)}\par
In the above equations, n r is the total number of runs and n p is the number of pixels in the image.???????? = 1 ?? ?? ? ? ??(??,?? ) ?? 2 ?? ?? =1 ?? ??=1 (13) ???????? = 1 ?? ?? ? ? ??(??, ??) * ?? 2 ?? ?? =1 ?? ??=1 (14) ?????????? = 1 ?? ?? ? ? ??(??,?? ) ?? 2 * ?? 2 ?? ?? =1 ?? ??=1 (15) ?????????? = 1 ?? ?? ? ? ??(??,?? ) * ?? 2 ?? 2 ?? ?? =1 ?? ??=1 (16) ?????????? = 1 ?? ?? ? ? ??(??,?? ) * ?? 2 ?? 2 ?? ?? =1 ?? ??=1 (17) ?????????? = 1 ?? ?? ? ? ??(??, ??) * ?? 2 ?? ?? =1 ?? ??=1 * ?? 2\textbf{(18)}\par
III. 
\section[{RESULTS and DISCUSSIONS}]{RESULTS and DISCUSSIONS}\par
Experiments are carried out to demonstrate the effectiveness of the proposed FTGP -with RF for stone   {\ref I}, Table  {\ref II}.  Table \hyperref[tab_4]{3} shows the classification rate for various group of textures by the proposed FTGP-RF with other existing methods like compound local binary pattern (CLBP) of Faisal Ahmed et.al \hyperref[b32]{[32]} and run-length features for image classification by Yung-Kuan Chan et.al \hyperref[b33]{[33]}. From Table \hyperref[tab_4]{3}, it is clearly evident that, the proposed FTGP-RF exhibits a high classification rate than the existing methods. The graphical representation of the percentage mean classification rate for the proposed RLM-FTGP and other existing methods are shown in Fig. \hyperref[fig_6]{8}.   
\section[{Conclusion}]{Conclusion}\par
The proposed FTGP scheme reduces the overall dimension of the image while preserving the significant attributes, primitives, and properties of the local texture. The proposed RLM-FTGP overcomes the disadvantages of the previous Run length matrices for texture classification.\par
LGM is an efficient tool that overcomes the traditional neighborhood problems. By directly using the entire run-length matrix for feature extraction, much of the texture information is preserved. The novelty of the proposed scheme is, it is proved that one need not necessary to evaluate all the RF on the FTGP for classification purpose. For a precise, significant and accurate classification, the present paper evaluated only 5 RLMF on FTGP, which reduced overall complexity. Comparisons of this new approach with the compound local binary pattern (CLBP) by Faisal Ahmed et.al \hyperref[b32]{[32]} and run-length features for image classification by Yung-Kuan Chan et.al \hyperref[b33]{[33]} demonstrated the supremacy of the proposed FTGP method. \begin{figure}[htbp]
\noindent\textbf{1}\includegraphics[]{image-2.png}
\caption{\label{fig_0}Fig. 1 :}\end{figure}
 \begin{figure}[htbp]
\noindent\textbf{3}\includegraphics[]{image-3.png}
\caption{\label{fig_1}Figure 3 :}\end{figure}
 \begin{figure}[htbp]
\noindent\textbf{4}\includegraphics[]{image-4.png}
\caption{\label{fig_2}Fig. 4 :}\end{figure}
 \begin{figure}[htbp]
\noindent\textbf{5}\includegraphics[]{image-5.png}
\caption{\label{fig_3}Fig. 5 :}\end{figure}
 \begin{figure}[htbp]
\noindent\textbf{}\includegraphics[]{image-6.png}
\caption{\label{fig_4}}\end{figure}
 \begin{figure}[htbp]
\noindent\textbf{617}\includegraphics[]{image-7.png}
\caption{\label{fig_5}Fig. 6 : 1 Fig. 7 :}\end{figure}
 \begin{figure}[htbp]
\noindent\textbf{8}\includegraphics[]{image-8.png}
\caption{\label{fig_6}Fig. 8 :}\end{figure}
 \begin{figure}[htbp]
\noindent\textbf{Ia} \par 
\begin{longtable}{P{0.36347668079951545\textwidth}P{0.2610236220472441\textwidth}P{0.06075105996365839\textwidth}P{0.10399757722592368\textwidth}P{0.06075105996365839\textwidth}}
2012\tabcellsep \tabcellsep \tabcellsep \tabcellsep \\
Year\tabcellsep \tabcellsep \tabcellsep \tabcellsep \\
20\tabcellsep \tabcellsep \tabcellsep \tabcellsep \\
D D D D ) F\tabcellsep \tabcellsep \tabcellsep \tabcellsep \\
(\tabcellsep \tabcellsep \tabcellsep \tabcellsep \\
Sno\tabcellsep Tex ture Name\tabcellsep Classifica\tabcellsep Tex ture\tabcellsep Classifica\\
\tabcellsep \tabcellsep tion Rate\tabcellsep Name\tabcellsep tion Rate\\
1\tabcellsep concrete\textunderscore bricks\textunderscore 170756\tabcellsep 94.22\tabcellsep Brick.0001\tabcellsep 95.06\\
2\tabcellsep concrete\textunderscore bricks\textunderscore 170757\tabcellsep 94.58\tabcellsep Brick.0002\tabcellsep 91.49\\
3\tabcellsep concrete\textunderscore bricks\textunderscore 170776\tabcellsep 89.64\tabcellsep Brick.0003\tabcellsep 97.28\\
4\tabcellsep crazy\textunderscore paving\textunderscore 5091370\tabcellsep 95.2\tabcellsep Brick.0004\tabcellsep 95.9\\
5\tabcellsep crazy\textunderscore paving\textunderscore 5091376\tabcellsep 96.56\tabcellsep Brick.0005\tabcellsep 93.39\\
6\tabcellsep crazy\textunderscore tiles\textunderscore 130356\tabcellsep 93.54\tabcellsep Brick.0006\tabcellsep 96.65\\
7\tabcellsep crazy\textunderscore tiles\textunderscore 5091369\tabcellsep 95.88\tabcellsep \tabcellsep 94.51\\
8\tabcellsep dirty\textunderscore floor\textunderscore tiles\textunderscore footprints\textunderscore 2564\tabcellsep 93.17\tabcellsep Brick.0008\tabcellsep 93.25\\
9\tabcellsep dirty\textunderscore tiles\textunderscore 200137\tabcellsep 93.99\tabcellsep Brick.0009\tabcellsep 93.37\\
\multicolumn{2}{l}{10 floor\textunderscore tiles\textunderscore 030849}\tabcellsep 96.55\tabcellsep Brick.0010\tabcellsep 95.96\\
\multicolumn{2}{l}{11 grubby\textunderscore tiles\textunderscore 2565}\tabcellsep 94.68\tabcellsep Brick.0011\tabcellsep 92.46\\
\multicolumn{2}{l}{12 kitchen\textunderscore tiles\textunderscore 4270064}\tabcellsep 95.48\tabcellsep Brick.0012\tabcellsep 94.52\\
\multicolumn{2}{l}{13 moroccan\textunderscore tiles\textunderscore 030826}\tabcellsep 96.35\tabcellsep Brick.0013\tabcellsep 93.62\\
\multicolumn{2}{l}{14 moroccan\textunderscore tiles\textunderscore 030857}\tabcellsep 95.77\tabcellsep Brick.0014\tabcellsep 91.48\\
\multicolumn{2}{l}{15 mosaic\textunderscore tiles\textunderscore 8071010}\tabcellsep 96.16\tabcellsep Brick.0015\tabcellsep 93.61\\
\multicolumn{2}{l}{16 mosaic\textunderscore tiles\textunderscore leaf\textunderscore pattern\textunderscore 201005060}\tabcellsep 94.97\tabcellsep Brick.0016\tabcellsep 92.01\\
\multicolumn{2}{l}{17 mosaic\textunderscore tiles\textunderscore roman\textunderscore pattern\textunderscore 201005034}\tabcellsep 90.91\tabcellsep Brick.0017\tabcellsep 94.58\\
\multicolumn{2}{l}{18 motif\textunderscore tiles\textunderscore 6110065}\tabcellsep 95.34\tabcellsep Brick.0018\tabcellsep 92.47\\
\multicolumn{2}{l}{19 ornate\textunderscore tiles\textunderscore 030845}\tabcellsep 96.44\tabcellsep Brick.0019\tabcellsep 96.13\\
\multicolumn{2}{l}{20 repeating\textunderscore tiles\textunderscore 130359}\tabcellsep 90.84\tabcellsep Brick.0020\tabcellsep 95.37\end{longtable} \par
  {\small\itshape [Note: Results of texture classification by proposed RF on FTGP of mosaic and brick textures in Dataset-1 © 2012 Global Journals Inc. (US) Global Journal of Computer Science and Technology Volume XII Issue XV Version I]} 
\caption{\label{tab_0}Table Ia :}\end{figure}
 \begin{figure}[htbp]
\noindent\textbf{Ib} \par 
\begin{longtable}{}
\end{longtable} \par
 
\caption{\label{tab_1}Table Ib :}\end{figure}
 \begin{figure}[htbp]
\noindent\textbf{2a} \par 
\begin{longtable}{}
\end{longtable} \par
 
\caption{\label{tab_2}Table 2a :}\end{figure}
 \begin{figure}[htbp]
\noindent\textbf{2b} \par 
\begin{longtable}{}
\end{longtable} \par
 
\caption{\label{tab_3}Table 2b :}\end{figure}
 \begin{figure}[htbp]
\noindent\textbf{3} \par 
\begin{longtable}{P{0.18992673992673992\textwidth}P{0.3051282051282051\textwidth}P{0.16813186813186812\textwidth}P{0.18681318681318682\textwidth}}
\tabcellsep \multicolumn{2}{l}{with other existing methods}\tabcellsep \\
Image Dataset\tabcellsep Compound Local Binary Pattern (CLBP)\tabcellsep Run-length Features\tabcellsep Proposed Method (FTGP-RF)\\
Brodatz\tabcellsep 90.29\tabcellsep 93.79\tabcellsep 96.31\\
VisTex\tabcellsep 91.53\tabcellsep 93.56\tabcellsep 95.85\\
Mayang\tabcellsep 92.34\tabcellsep 94.43\tabcellsep 97.32\\
Outtex,\tabcellsep 91.59\tabcellsep 93.63\tabcellsep 96.96\\
CUReT\tabcellsep 91.76\tabcellsep 93.46\tabcellsep 97.54\\
Paulbourke\tabcellsep 90.98\tabcellsep 94.56\tabcellsep 96.77\\
Average\tabcellsep 91.41\tabcellsep 93.91\tabcellsep 96.79\end{longtable} \par
 
\caption{\label{tab_4}Table 3 :}\end{figure}
 			\footnote{© 2012 Global Journals Inc. (US)} 		 		\backmatter   			 
\subsection[{Acknowledgment}]{Acknowledgment}\par
The authors would like to express their gratitude to Sri K.V.V. Satya Narayana Raju, Chairman, and K. Sashi Kiran Varma, Managing Director, Chaitanya group of Institutions for providing necessary infrastructure. Authors would like to thank anonymous reviewers for their valuable comments and Dr. G.V.S. Ananta Lakshmi for her invaluable suggestions which led to improvise the presentation quality of this paper. 			  			  				\begin{bibitemlist}{1}
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\end{document}
