International Journal of Signal and Image Processing (Vol.1-2010/Iss.1) Reddy et al. / Texture Classification Method using Wavelet Transforms ... / pp. 35-39
Texture Classification Method using Wavelet Transforms Based on Gaussian Markov Random Field B.V. Ramana Reddy*, M. Radhika Mani**, K.V. Subbaiah*** * Assoc. Prof., Dept. of CSE, KSRM COE, Kadapa, A.P., India. e-mail:
[email protected]
** Asst. Prof., Dept. of CSE, GIET, Rajahmundry, A.P., India e-mail:
[email protected]
*** Assoc. Prof., Dept. of CSE, PBRVIT, Kavail, A.P., India e-mail:
[email protected] Submitted: 03/01/2010 Accepted: 12/01/2010 Appeared: 16/01/2010 HyperSciences.Publisher
Abstract— The problem of texture classification arises in several disciplines such as remote sensing, computer vision, and image analysis. The present paper presents a feature extraction method for the classification of textures using GMRF model on linear wavelets. The Seven features are extracted using least square error estimation method on third order markov neighborhood. The experimental results on various textures using different one level wavelet transform clearly indicate the efficiency of the proposed method.
Keywords: Model based, Classification, One level Wavelet, Feature Extraction.
1. INTRODUCTION
fractional Brownian motion (fBm) (Mandelbrot, B.B. (1982), Chen, C.C. et al. (1989)), where the former sets the conditional probability of the intensity of a certain pixel depending on the values of the neighbouring pixels while the latter exploits the self-similarity of texture at varying scales. For statistical-based methods, first and second order statistics are derived after analyzing the spatial distributions of pixel grey level values. Gray level co-occurrence (Haralick, R.M. et al. (1973)), run-length (Galloway, M.M. (1975)) and autocovariance function methods were selected for feature extraction.
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The important task in texture classification is to extract texture features which is most completely embody the information of texture in the original image. Historically, statistical and structural approaches have been adopted for texture feature extraction. The statistical approach focuses on the statistical properties of textures. This method gives good results for homogeneous purely random micro texture fields, but is problematic in handling more structured macro textures. The structural methods represent a texture pattern by its textural primitives and their spatial placement rules. The main deficiency of the structural methods is that they are incapable of capturing or generating the randomness that natural textures often possess (Yong, Huang. et al. (1980)).
Recently various pattern based texture classification methods are proposed using wavelets (Vijaya Kumar, V. et al. (2009), Raju, U.S.N. et al. (2008), Vijaya Kumar, V. et al. (2008)). These wavelet based methods classified the textures precisely. Good texture classification results are obtained using simple patterns and long linear patterns (Vijaya Kumar, V. et al. (2008), Eswar Reddy, B. et al. (2007), Vijaya Kumar, V. et al. (2007)). The paper is organized as follows. Section 2 deals the introduction to wavelets, Section 3 deals with methodology and Section 4 describes results and discussions followed by conclusions at Section 5.
Various texture analysis approaches tend to represent views of the examined textures from different perspectives, and due to multi-dimensionality of perceived texture, there is not an individual method that can be sufficient for all textures (Tuceryan, M. et al. (1998)). In the model-based approach, a set of parameters which are driven from the variation of pixel elements of texture are used to define an image model. The two models methods used in this work are the Gaussian Markov random field (GMRF) (Petrou, M. et al. (2006)) and
2. INTRODUCTION TO WAVELETS The wavelet transform is a multi-resolution technique, which can be implemented as a pyramid or tree structure and is similar to sub-band decomposition (Antonini, M. et al. (1992), Daubechies, I. (1992)). There are various wavelet transforms like Haar, Daubechies, Coiflet, Symlet and etc. They differ with each other in the formation and reconstruction. The wavelet transform divides the original
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The authors would like to express their cordial thanks to K. Sivananda Reddy, Secretary& Correspondent and K.S.N. Reddy, Director KSRCE, Kadapa for providing research facilities. Authors would like to thank Dr. G.V.S. Anantha Lakshmi, for their invaluable suggestions and constant encouragement that led to improvise the presentation quality of the paper. Authors also thankful to members of Srinivasa Ramanujan Research Forum (SRRF)-GIET.
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International Journal of Signal and Image Processing (Vol.1-2010/Iss.1) Reddy et al. / Texture Classification Method using Wavelet Transforms ... / pp. 35-39
image into four subbands and they are denoted by LL(lowlow), LH(low-high), HL(high-low) and HH(high-high) frequency subbands. The HH subimage represents diagonal details (high frequencies in both directions – the corners), HL gives horizontal high frequencies (vertical edges), LH gives vertical high frequencies (horizontal edges), and the image LL corresponds to the lowest frequencies. At the subsequent scale of analysis, the image LL undergoes the decomposition using the same filters, having always the lowest frequency component located in the upper left corner of the image. Each stage of the analysis produces next 4 subimages whose size is reduced twice when compared to the previous scale. i.e. for level ‘n’ we get a total of ‘4+(n-1)*3’ subbands. The size of the wavelet representation is the same as the size of the original. The Haar wavelet is the first known wavelet and was proposed in 1909 by Alfred Haar. Haar used these functions to give an example of a countable orthonormal system for the space of square-integrable functions on the real line. The Haar wavelet's scaling function coefficients are h{k}={0.5, 0.5}and wavelet function coefficients are g{k}={0.5, -0.5}. The Daubechies wavelets (Daubechies, I. (1992)) are a family of orthogonal wavelets defining a discrete wavelet transform and characterized by a maximal number of vanishing moments for some given support. With each wavelet type of this class, there is a scaling function which generates an orthogonal multiresolution analysis. Coiflet is a discrete wavelet designed by Ingrid Daubechies to be more symmetrical than the Daubechies wavelet. Whereas Daubechies wavelets have N/2−1 vanishing moments, Coiflet scaling functions have N/3−1 zero moments and their wavelet functions have N/3. The solution for the wavelets which was given by Daubechies is not always unique. She gave solutions with minimal phase (maximum smoothness). Other choices can lead to more symmetric solutions. They are never completely symmetric. Symlets have the following properties: Orthonormal, Compact Support, Filter length N=2p, It has p vanishing moments, It has nearly linear phase. Therefore, this work is mainly concerned with texture classification accuracy improvement using texture features derived from model based GMRF method using different wavelet transforms.
2 n I ij − ∑ α l × S kl ;l 1 l =1 exp 2σ 2 2πσ 2
p ( I ij | I kl , ( k , l ) ∈ N ij ) =
(1)
Ii+2,j
Ii-1,j+1
Ii+1,j
Ii+1,j+1
Ii,j-1
Iij
Ii,j+1
Ii-1,j-1
Ii-1,j
Ii+1,j-1
Ii,j-2
Ii,j+2
Ii-2,j
Fig.1. Third order Markov neighborhood for each sample image pixel (Iij) The right hand side of Equation (1) represents the probability of a pixel (i,j) having a specific grey value Iij given the values of its neighbours, n is the total number of pixels in the neighborhood Nij of pixel Iij which influence its value, αl is the parameter with which a neighbor influences the value of (i,j), and Skl;l is the value of the pixel at the corresponding position as shown in Fig. 1 as given in Equations from (2) to (7).
S ij ;1 = I i −1, j + I i +1, j
(2)
S ij ; 2 = I i , j −1 + I i , j +1
(3)
S ij ;3 = I i − 2, j + I i + 2, j
(4)
S ij ; 4 = I i , j − 2 + I i , j + 2
(5)
S ij ;5 = I i −1, j −1 + I i +1, j +1
(6)
S ij ;6 = I i −1, j +1 + I i +1, j −1
(7)
For an image segment of size M×N the GMRF parameters α and σ are estimated using least square error estimation method, as shown in Equations (8) and (9). α 1 S ij ;1 S ij ;1 . . = ∑ . ij . α n S ij ;1 S ij ;1
3. METHODOLOGY In the current work, a Gaussian Markov Random Field (GMRF) model is employed (Mauricio, Gomez. et al. (2006), Omar S. Al-Kadi (2008), Erika Dana´e L´opez-Espinoza et al. (2008) and William Robson Schwartz et al. (2004)). The Gaussian distribution is often adopted as a description for natural phenomena since it can represent behavior which arises from the superposition of a number of random effects, no one of which dominates. Based upon the Markovian property, which is simply the dependence of each pixel in the image on its neighbours only, a GMRF for third order Markov neighborhood as shown in Fig. 1 was used (Petrou, M. et al. (2006)).
−1
. . S ij ;1 S ij ;1 S ij ;1 . . . . × ∑ I ij . . . . ij S . . S ij ;1 S ij ;1 ij ;n
n α l S ij ;l I − ∑ij ij ∑ l =1 σ2 = ( M − 2)( N − 2)
(8)
(9)
The present paper applied the above seven GMRF features on original and on Haar, Daubechies 6 (Db6), Coiflet 6 (Cf6) and Symlet 8(Sym8) wavelet transformed images based on Algorithm 1.
The GMRF model is defined by the Equation (1).
Algorithm 1: Calculating the GMRF parameters on one level LL subband by selecting sequential window of size 64×64.
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International Journal of Signal and Image Processing (Vol.1-2010/Iss.1) Reddy et al. / Texture Classification Method using Wavelet Transforms ... / pp. 35-39
Begin 1.
Let A be the input image
2.
Apply one level wavelet transformation on A and store the LL subband in array res.
3.
get the size of I(row1,col1) and set the sequential window size as 64×64 (row, col)
4.
for x=1:row:row1-(row-1)
5.
for y=1:col:col1-(col-1)
6.
p=x;
7.
q=y;
8.
for k=1:row
9.
for l=1:col
10.
I(k,l)=res(p,q);
11.
q=q+1;
12.
end
13.
p=p+1;
14.
q=y;
15.
end
16. Calculate the six Sij values, six α values and σ2 value. 17.
end
18. end End 4. RESULTS AND DISCUSSIONS The experiments are conducted with 23 textures of each size 256×256, collected from Brodatz album (Brodatz, P. (1996)) as shown in Fig. 2. On the one level LL subband of wavelet transformed image, seven GMRF parameters are calculated by considering the sequential window of size 64×64. The average of these features of 4 parts is computed and taken as training set and are stored in texture feature library. The texture classification is implemented by considering the extracted texture feature from the sample X with the corresponding feature values of all the texture classes v stored in the feature library using the distance vector formula given by the Equation (10) N
D (v) =
∑ abs( f
j
( x) − f j (k ))
(10)
j =0
where N is the number of features in f, fj(x) represents the jth texture feature of the test sample x, while fj(v) represents the jth feature of the v th texture class in the library. Then the test texture is classified as v th texture, if the distance D(v) is minimum among all the texture classes available in the library. Based on the distance function the percentage of correct classification rate is calculated and are represented in Table1.
Fig.2. Input Textures from Brodatz Album (a) D1 (b) D4 (c) D10 (d) D11 (e) D16 (f) D17 (g) D18 (h) D21 (i) D33 (j) D37 (k) D47 (l) D49 (m) D51 (n) D53 (o) D55 (p) D57 (q) D64 (r) D68 (s) D77 (t) D78 (u) D79 (v) D82 (w) D96.
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International Journal of Signal and Image Processing (Vol.1-2010/Iss.1) Reddy et al. / Texture Classification Method using Wavelet Transforms ... / pp. 35-39
IEEE Transactions on Medical Imaging, vol. 8, pp. 133142. Daubechies, I. (1992). Ten Lectures on Wavelets. Rutgers University and AT&T Laboratories. Erika Dana´e L´opez-Espinoza., Leopoldo AltamiranoRobles. (2008). Method Based on Tree-Structured Markov Random Field and a Texture Energy Function for Classification of Remote Sensing Images. 5th International Conference on Electrical Engineering, Computing Science and Automatic Control (CCE 2008), pp. 540-544. Eswar Reddy, B., Vijaya Kumar, V. et al. (2007). Texture Classification by Simple Edge Direction Movements. International Journal of Computer Science and Network Security, vol. 7, no.11, pp. 221-225. Galloway, M.M. (1975). Texture analysis using gray level run lengths. Computer Graphics Image Processing, vol. 4, pp. 172-179. Haralick, R. M., Shanmuga, K. and Dinstein, I. (1973). Textural Features for Image Classification. IEEE Transactions on Systems, Man and Cybernetics, vol. SMC3, pp. 610-621. Mandelbrot, B.B. (1982). Fractal Geometry of Nature. San Francisco, CA: Freeman. Mauricio, Gomez., Renato, A. and Salinas. (2006). A New Technique for Texture Classification Using Markov Random Fields. International Journal of Computers, Communications & Control, Vol. I, No. 2, pp. 41-51. Omar S. Al-Kadi, (2008). Combined Statistical and Model Based Texture Features for Improved Image Classification, IET 4th International conference on Advances in Medical, Signal and Information processing, pp. 1-4 . Petrou, M. and Gacia Sevilla, P. (2006). Image processing: Dealing with texture, Wiley. Raju, U.S.N., Vijaya Kumar, V. et al. (2008). Texture Classification based on Extraction of Skeleton Primitives using Wavelets. Information Technology Journal, vol. 7, no. 6, pp. 883-889. Tuceryan, M. and Jain, A. (1998). The Handbook of pattern Recognition and Computer Vision, 2 ed. World Scientific Publishing Co. Vijaya Kumar, V., Eswar Reddy, B. et al. (2007). An Innovative Technique of Texture Classification and Comparision based on Long Linear Patterns. Journal of Computer Science, Science Publications, vol. 3(8), pp.633-638. Vijaya Kumar, V., Raju, U.S.N. et al. (2008). A New Method of Texture Classification using Wavelet Transforms based on Primitive Patterns. International Journal of Graphics Vision and Image Processing, vol. 8, no. 2, pp. 21-27. Vijaya Kumar, V., Eswar Reddy, B., et al. (2008). Classification of Textures by Avoiding Complex Patterns. Journal of Computer Science, vol. 4(2), pp.133138. Vijaya Kumar, V., Raju, U.S.N. et al. (2009). Employing Long Linear Patterns for Texture Classification relying on Wavelets. International Journal of Graphics Vision and Image Processing, vol. 8, no. 5, pp. 13-21.
Table 1. Percentage of Correct Classification Rate for Input Textures. Percentage of Correct Classification Rate Texture
Original
Haar Wavelet
Db6 Wavelet
Cf6 Wavelet
Sym8 Wavelet
D1
100.00
100.00
100.00
75.00
75.00
D4
100.00
100.00
100.00
100.00
100.00
D10
100.00
100.00
100.00
100.00
100.00
D11
100.00
100.00
100.00
100.00
100.00
D16
100.00
100.00
100.00
75.00
75.00
D17
100.00
100.00
100.00
100.00
100.00
D18
100.00
100.00
100.00
100.00
100.00
D21
100.00
100.00
100.00
100.00
75.00
D33
100.00
100.00
100.00
100.00
100.00
D37
100.00
100.00
100.00
100.00
100.00
D47
100.00
100.00
100.00
100.00
100.00
D49
100.00
100.00
100.00
75.00
75.00
D51
100.00
100.00
100.00
100.00
100.00
D53
100.00
100.00
100.00
100.00
100.00
D55
100.00
100.00
75.00
75.00
75.00
D57
100.00
100.00
100.00
100.00
100.00
D64
93.75
100.00
100.00
100.00
100.00
D68
100.00
100.00
100.00
100.00
100.00
D77
100.00
100.00
100.00
100.00
100.00
D78
93.75
100.00
75.00
75.00
50.00
D79
100.00
100.00
50.00
50.00
50.00
D82
100.00
100.00
100.00
100.00
100.00
D96
100.00
100.00
100.00
50.00
50.00
99.46
100.00
95.65
90.22
88.04
5. CONCLUSION The present paper developed model based texture classification method by using GMRF on wavelets by selecting sequential window of size 64×64. The results of Table 1 clearly indicates a high classification rate of present method using one-level linear wavelet transforms. The results also exhibit that Haar wavelet gives a greater classification over other wavelet transforms and original image. From this the present paper concludes that GMRF model is a useful technique on wavelets for precise classification of any textures. REFERENCES Antonini, M., Barlaud, M., Mathieu, P., Daubechies, I. (1992). Image coding using wavelet transform. IEEE Trans. Image Processing, Vol.1 (2), pp. 205–220. Brodatz, P. (1996). A Photographic Album for Artists and Designers, New York: Dover. Chen, C.C., Daponte, J. S., and Fox, M.D. (1989). Fractal Feature Analysis and Classification in Medical Imaging.
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International Journal of Signal and Image Processing (Vol.1-2010/Iss.1) Reddy et al. / Texture Classification Method using Wavelet Transforms ... / pp. 35-39
William Robson Schwartz., and Hili Pedrini. (2004). Texture Classification based on Spatial Dependence Features using Co-Occurrence Matrices and Markov Random Fields, IEEE International Conference on Image Processing (UP), pp. 239-242. Yong Huang, Kap Luk Chan, and Zhongyang Huang. (1980). An Adaptive Model for Texture Classification. IEEE, pp .893-896. AUTHORS PROFILE B.V.Ramana Reddy received the B.Tech degree from S.V.University, Tirupati, A.P., India in 1991. He completed M.Tech in Computer Science from JNT University, Masab Tank, Hyderabad, India in 2002. He is having nearly 15 years of teaching and industrial experience. He is currently working as Associate Professor, Dept of C.S.E, KSRM College of Engineering, Kadapa, Andhrapradesh, India. He is a member of Srinivasa Ramanujan Research Forum (SRRF), Godavari Institute of Science and Technology (GIET), Rajahmundry. He is pursuing his PhD from JNT University Anantapur in computer Science. He is a life member of Indian Science Congress Association. He published 5 papers in various conferences. M. Radhika Mani received the B.Tech (CSE) degree from Sir C.R. Reddy College of Engineering, Andhra University, A.P., India in 2005 and received her M. Tech. (Software Engineering) from Godavari Institute of Engineering and Technology (GIET), JNT University in 2008. Presently she is working as an Assistant Professor in GIET, Rajahmundary. She is pursuing her Ph.D. from JNT University Kakinada in Computer Science. She is a member of SRRF-GIET, Rajahmundry. She has published more than 10 research publications in various National, Inter National conferences, proceedings and Journals. K.V. Subbaiah completed MCA from University Of Madras in April, 1997 and received M.E (Master of Engineering) in Computer Science & Engineering in April 2006, from Satyabhama University, Chennai. He is pursuing Ph.D in Computer Science in Rayalaseema University, Kunrool, A.P., under the Guidence of Dr. V.Vijay Kumar. Currently working as Assoc. Prof. in Dept. of CSE, PBR Visvodaya Institute of Technology & Science, Kavali, A.P., India.
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