Texture Image Classification Using Complex Texton
Texture Image Classification Using Complex Texton Zhenhua Guo1, Qin Li2, Lin Zhang2, Jane You2, Wenhuang Liu1, and Jinghua Wang2 1
Graduate School at Shenzhen, Tsinghua University, Shenzhen, China Department of Computing, the Hong Kong Polytechnic University, Hong Kong {zhenhua.guo,liuwh}@sz.tsinghua.edu.cn, {csqinli,cslinzhang,csyjia,csjihuwang}@comp.polyu.edu.hk 2
Abstract. Statistical textons has shown its potential ability in texture image classification. The maximal response 8 (MR8) method extracts an 8dimensional feature set from 38 filters. It is one of state-of-the-art rotation invariant texture classification methods. This method assumes that each local patch has a dominant orientation, thus it keeps the maximal response from six responses of different orientations in the same scale. To validate whether local dominant orientation is necessary for texture classification, in this paper, a complex texton, complex response 8 (CR8), is proposed. The average and standard deviation of filter responses for different orientations is computed, and then an 8-dimensional complex texton is extracted. After using k-means clustering algorithm to learn a texton dictionary, a histogram of texton distribution could be built for a given image. Experimental results on one large public database show that CR8 could get comparable results with MR8. Keywords: Texture classification, texton, maximal response 8, clustering.
1
Introduction
Texture analysis is a hot research topic in the fields of computer vision and image processing. It includes four fundamental problems: classifying images based on texture content; segmenting an image into regions of homogeneous texture; synthesizing textures for graphics applications; and establishing shape information from texture cue [1]. It has been applied widely in different areas, such as medical image analysis [2], remote sensing [3], and biometrics [4]. At the beginning, extracting statistical feature to classify texture images, such as the co-occurrence matrix method [5] and the filtering based methods [6], is the main stream. Rotation invariance is a critical issue in many applications. In order to address it, many algorithms were proposed. Kashyap and Khotanzad [7] were among the first researchers to study rotation-invariant texture classification by using a circular autoregressive model. Later, many other models were explored, including the multiresolution autoregressive model [8], hidden Markov model [9], and Gaussian Markov random field [10]. Generally speaking, there are three main methods for rotation invariant texture classification: computing global rotation invariant feature [11], extracting local rotation invariant feature [12-13], and global matching scheme with local rotation variant feature [14]. Local rotation invariant feature is intuitive and simple, and it D.-S. Huang et al. (Eds.): ICIC 2011, LNAI 6839, pp. 98–104, 2012. © Springer-Verlag Berlin Heidelberg 2012
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could get good results, especially for small size images [11]. In [12], Ojala et al. proposed to use the local binary pattern (LBP) histogram for rotation invariant texture classification. LBP is a simple but efficient operator to describe local image patterns. Using a group of filter banks, Varma and Zisserman [13] proposed a statistical learning based algorithm, namely maximal response 8 (MR8), with which a rotation invariant texton library is first built from a training set and then an unknown texture image is classified according to its texton distribution. LBP and MR8 are two typical local rotation invariant features, while their underlying local invariance is different: the former extracts an isotropic feature, as it does not consider any local dominant orientation; the latter selects an anisotropic feature, as it defines a dominant orientation from six orientations and keeps the response at that orientation only. To investigate whether local dominant orientation is important for local rotation invariant, a complex response 8 (CR8) is proposed. Instead of getting the maximal response among six orientations, average and standard deviation of responses are computed and an 8-dimensional feature is extracted. After that, similar to MR8, a complex texton library is built from a training set by k-means clustering algorithm and then an texton distribution is computed for a given texture image. Since CR8 and MR8 use the same filters and feature extraction scheme, it is relatively fair to evaluate the role of local dominant orientation in texture classification. The rest of the paper is organized as follows: Section 2 introduces the proposed CR8. Section 3 reports the experimental results on one representative texture database. Section 4 gives the conclusion and future work.
2
Complex Response 8
The MR8 filter bank consists of 38 filters, which are shown in Fig.1. To achieve rotation invariance, the filters are implemented at multiple orientations and multiple scales. At each scale only the maximal response among the different orientations is kept. The final response at each position is an 8-dimension feature vector.
Fig. 1. The MR8 filter bank consists of a series of anisotropic filters (an edge and a bar filter at 6 orientations and 3 scales), and 2 rotationally symmetric ones (a Gaussian and a Laplacian of Gaussian) [13]
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Fig. 2. The top row shows 3 texture images. The central image patch (highlighted by red rectangle) is matched with an edge filter at all orientations. The magnitude of the filter response versus the orientation is plotted in the bottom row [13].
As shown in Fig. 2, some local regions may have multiple dominant orientations or no dominant orientations. One dominant orientation may not be able to fully represent the local characteristics. Average and standard deviation of filter responses for the same scale could convey more information and they are rotation invariant. They were also proven to contain discriminant and robust features for classification [15]. Thus, a complex response is defined:
⎧⎪u k (x, y )+ii σ k (x, y ), k =1,2,...6 CR8 k (x, y ) = ⎨ k ⎪⎩ii F (x, y ), k =7,8 5
∑ Fθ
5
k
u k (x, y )=
j =0
(x,y) j
6
∑ (Fθ
k
, σ k (x, y )=
j =0
Fθkj (x,y) = fθkj * I (x, y ), k =1,2,...,6, θ j = F (x,y) = f * I (x, y ), k =7,8 k
k
(1)
j
(x,y)-u k (x, y )) 2
(2)
5 jπ (j = 0,1,...,5) 6
(3)
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where i is the imaginary unit, * is the convolution operation, • is the multiply operation, and I is the input image. Fig.3 shows an example to illustrate MR8 and CR8. It is empirically found that representing F 7 (x,y) and F 8 (x,y) as imaginary part could get better result. Similar to MR8, after getting an 8-dimensional feature for each pixel, a texton dictionary is learnt through clustering method from a training set [12]. Before clustering, different weights could be assigned for real and imaginary part of CR8, as it is found that average and standard deviation of filter response could represent different properties of image and these values have different discriminant ability on different databases.
CR8(x, y )=wr i real(CR8 (x, y )) + wi i ii imagery(CR8(x, y ))
(4)
where wr and wi are two weights for real and imaginary part. These two weights are set empirically. k-means clustering [16] is used to learn the CR8 dictionary. For a given image, the 8-dimensinal feature of each pixel is labeled by the closest texton in the dictionary; finally a histogram representing the frequency of each texton is built as the feature for classification.
Fig. 3. An illustration of MR8 and CR8
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Experimental Results
In this section, we will compare the proposed feature extraction scheme with MR8 and one isotropic local feature, LBP [13]. To evaluate the effectiveness of the proposed methods, experiments on one large public texture database were done and their results were shown in the following. In MR8 and CR8, 40 textons were clustered from each texture classes using the training samples, and then a histogram based on learnt dictionary was computed for each model and sample image. For LBP, each texture sample was normalized to have an average intensity 128 and a standard deviation 20 [13]. For MR8 and CR8 methods, the image sample was normalized to have an average intensity of 0 and a standard deviation of 1 [12]. This is to remove global intensity and contrast [12-13]. The chi-square dissimilarity [13] and the nearest neighborhood classifier were used for all methods here. The Outex database includes two test suites: Outex_TC_00010 (TC10) and Outex_TC_00012 (TC12) [17]. The two test suites contain the same 24 classes of textures, which were collected under 3 different illuminants (“horizon”, “inca”, and “t184”) and 9 different rotation angles (00, 50, 100, 150, 300, 450, 600, 750 and 900). There are 20 non-overlapping 128•128 texture samples for each class under each situation. The experiment setups are as follows: 1.
2.
For TC10, samples of illuminant “inca” and angle 00 in each class were used for classifier training and the other 8 rotation angles with the same illuminant were used for testing. Hence, there are 480 (24•20) training samples and 3,840 (24•8•20) validation samples. For TC12, the classifier was trained with the same training samples as TC10, and it was tested with all samples captured under illuminant “t184” or “horizon”. Hence, there are 480 (24•20) models and 4,320 (24•20•9) validation samples for each illuminant.
Table 1 lists the experimental results by different schemes. Under TC12, “t” represents the test setup of illuminant “t184” and “h” represents “horizon”. wr and wi were set to 0 and 1 empirically. Table 1. Classification rate (%) for Outex database Method riu 2 8,1
LBP
+ LBP
riu 2 16,2
MR8 CR8
+ LBP
riu 2 24,3
Feature Size
TC10
TC12 “t”
TC12 “h”
54
97.21
89.21
84.32
960 960
93.59 94.06
92.55 92.31
92.82 92.80
Two findings could be found from Table 1. First, CR8 and MR8 get better results than LBP for TC12 test set, but they are worse than LBP in TC10. It is probably because of the fact that LBP has finer orientation resolution (150 when P=24) than CR8 and MR8 (300), so it could get better performance when there is only rotation variance. However, when the illumination changes, like TC12, LBP is too short to contain enough discriminant information. Second, CR8 could get comparable results with MR8. It validates that local dominant orientation may not be necessary for rotation invariant texture classification.
Texture Image Classification Using Complex Texton
4
103
Conclusion
To achieve rotation invariance, extracting local isotropic and anisotropic features are two popular methods. To the best of our knowledge, no work has compared different ways to see which way is more suitable for texture classification. As a counterpart of MR8, a local isotropic operator, CR8 is proposed. By one large public database, it is empirically shown that local dominant orientation may not be necessary for texture classification. In the future we will investigate other statistical texton based operators, such as local patch [18]. Another direction is to explore the correlation between CR8 and MR8 to further improve recognition accuracy by their fusion. Acknowledgments. The work is partially supported China Postdoctoral Science Foundation under Grant No. 20100480301.
References 1. Tuceryan, M., Jain, A.K.: In: Chen, C.H., Pau, L.F., Wang, P.S.P. (eds.) Handbook of Pattern Recognition and Computer Vision, pp. 235–276. World Scientific Publishing Co., Singapore (1993) 2. Anys, H., He, D.C.: Evaluation of Textural and Multipolarization Radar Features for Crop Classification. IEEE Transactions on Geoscience and Remote Sensing 33(5), 1170–1181 (1995) 3. Ji, Q., Engel, J., Craine, E.: Texture Analysis for Classification of Cervix Lesions. IEEE Transactions on Medical Imaging 19(11), 1144–1149 (2000) 4. Jia, W., Huang, D.S., Zhang, D.: Palmprint Verification Based on Robust Line Orientation Code. Pattern Recognition 41(5), 1504–1513 (2008) 5. Haralik, R.M., Shanmugam, K., Dinstein, I.: Texture Features for Image Classification. IEEE Trans. on Systems, Man, and Cybertics 3(6), 610–621 (1973) 6. Randen, T., Husy, J.H.: Filtering for Texture Classification: a Comparative Study. IEEE Transactions on Pattern Analysis and Machine Intelligence 21(4), 291–310 (1999) 7. Kashyap, R.L., Khotanzed, A.: A Model-based Method for Rotation Invariant Texture Classification. IEEE Transactions on Pattern Analysis and Machine Intelligence 8(4), 472–481 (1986) 8. Mao, J., Jain, A.K.: Texture Classification and Segmentation Using Multiresolution Simultaneous Autoregressive Models. Pattern Recognition 25(2), 173–188 (1992) 9. Wu, W.R., Wei, S.C.: Rotation and Gray-scale Transform-invariant Texture Classification Using Spiral Resampling, Subband Decomposition, and Hidden Markov Model. IEEE Transactions on Image Processing 5(10), 1423–1434 (1996) 10. Deng, H., Clausi, D.A.: Gaussian MRF Rotation-invariant Features for Image Classification. IEEE Transactions on Pattern Analysis and Machine Intelligence 26(7), 951–955 (2004) 11. Xu, Y., Ji, H., Fermuller, C.: Viewpoint Invariant Texture Description Using Fractal Analysis. International Journal of Computer Vision 83(1), 85–100 (2009) 12. Varma, M., Zisserman, A.: A statistical Approach to Texture Classification from Single Images. International Journal of Computer Vision 62(1-2), 61–81 (2005)
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13. Ojala, T., Pietikäinen, M., Mäenpää, T.T.: Multiresolution Gray-scale and Rotation Invariant Texture Classification with Local Binary Pattern. IEEE Transactions on Pattern Analysis and Machine Intelligence 24(7), 971–987 (2002) 14. Ahonen, T., Matas, J., He, C., Pietikäinen, M.: Rotation Invariant Image Description with Local Binary Pattern Histogram Fourier Features. In: Salberg, A.-B., Hardeberg, J.Y., Jenssen, R. (eds.) SCIA 2009. LNCS, vol. 5575, pp. 61–70. Springer, Heidelberg (2009) 15. Manjunath, B.S., Ma, W.Y.: Texture Features for Browsing and Retrieval of Image Data. IEEE Transactions on Pattern Analysis and Machine Intelligence 18(8), 837–842 (1996) 16. Duda, R.O., Hart, P.E., Stork, D.G.: Pattern classification, 2nd edn. Wiley, Chichester (2000) 17. Ojala, T., Mäenpää, T., Pietikäinen, M., Viertola, J., Kyllönen, J., Huovinen, S.: Outex – New Framework for Empirical Evaluation of Texture Analysis Algorithm. In: International Conference on Pattern Recognition, pp. 701–706 (2002) 18. Varma, M., Zisserman, A.: A statistical Approach to Material Classification Uusing Image Patch Exemplars. IEEE Transactions on Pattern Analysis and Machine Intelligence 31(11), 2032–2047 (2009)
Graduate School at Shenzhen, Tsinghua University, Shenzhen, China Department of Computing, the Hong Kong Polytechnic University, Hong Kong {zhenhua.guo,liuwh}@sz.tsinghua.edu.cn, {csqinli,cslinzhang,csyjia,csjihuwang}@comp.polyu.edu.hk 2
Abstract. Statistical textons has shown its potential ability in texture image classification. The maximal response 8 (MR8) method extracts an 8dimensional feature set from 38 filters. It is one of state-of-the-art rotation invariant texture classification methods. This method assumes that each local patch has a dominant orientation, thus it keeps the maximal response from six responses of different orientations in the same scale. To validate whether local dominant orientation is necessary for texture classification, in this paper, a complex texton, complex response 8 (CR8), is proposed. The average and standard deviation of filter responses for different orientations is computed, and then an 8-dimensional complex texton is extracted. After using k-means clustering algorithm to learn a texton dictionary, a histogram of texton distribution could be built for a given image. Experimental results on one large public database show that CR8 could get comparable results with MR8. Keywords: Texture classification, texton, maximal response 8, clustering.
1
Introduction
Texture analysis is a hot research topic in the fields of computer vision and image processing. It includes four fundamental problems: classifying images based on texture content; segmenting an image into regions of homogeneous texture; synthesizing textures for graphics applications; and establishing shape information from texture cue [1]. It has been applied widely in different areas, such as medical image analysis [2], remote sensing [3], and biometrics [4]. At the beginning, extracting statistical feature to classify texture images, such as the co-occurrence matrix method [5] and the filtering based methods [6], is the main stream. Rotation invariance is a critical issue in many applications. In order to address it, many algorithms were proposed. Kashyap and Khotanzad [7] were among the first researchers to study rotation-invariant texture classification by using a circular autoregressive model. Later, many other models were explored, including the multiresolution autoregressive model [8], hidden Markov model [9], and Gaussian Markov random field [10]. Generally speaking, there are three main methods for rotation invariant texture classification: computing global rotation invariant feature [11], extracting local rotation invariant feature [12-13], and global matching scheme with local rotation variant feature [14]. Local rotation invariant feature is intuitive and simple, and it D.-S. Huang et al. (Eds.): ICIC 2011, LNAI 6839, pp. 98–104, 2012. © Springer-Verlag Berlin Heidelberg 2012
Texture Image Classification Using Complex Texton
99
could get good results, especially for small size images [11]. In [12], Ojala et al. proposed to use the local binary pattern (LBP) histogram for rotation invariant texture classification. LBP is a simple but efficient operator to describe local image patterns. Using a group of filter banks, Varma and Zisserman [13] proposed a statistical learning based algorithm, namely maximal response 8 (MR8), with which a rotation invariant texton library is first built from a training set and then an unknown texture image is classified according to its texton distribution. LBP and MR8 are two typical local rotation invariant features, while their underlying local invariance is different: the former extracts an isotropic feature, as it does not consider any local dominant orientation; the latter selects an anisotropic feature, as it defines a dominant orientation from six orientations and keeps the response at that orientation only. To investigate whether local dominant orientation is important for local rotation invariant, a complex response 8 (CR8) is proposed. Instead of getting the maximal response among six orientations, average and standard deviation of responses are computed and an 8-dimensional feature is extracted. After that, similar to MR8, a complex texton library is built from a training set by k-means clustering algorithm and then an texton distribution is computed for a given texture image. Since CR8 and MR8 use the same filters and feature extraction scheme, it is relatively fair to evaluate the role of local dominant orientation in texture classification. The rest of the paper is organized as follows: Section 2 introduces the proposed CR8. Section 3 reports the experimental results on one representative texture database. Section 4 gives the conclusion and future work.
2
Complex Response 8
The MR8 filter bank consists of 38 filters, which are shown in Fig.1. To achieve rotation invariance, the filters are implemented at multiple orientations and multiple scales. At each scale only the maximal response among the different orientations is kept. The final response at each position is an 8-dimension feature vector.
Fig. 1. The MR8 filter bank consists of a series of anisotropic filters (an edge and a bar filter at 6 orientations and 3 scales), and 2 rotationally symmetric ones (a Gaussian and a Laplacian of Gaussian) [13]
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Z. Guo et al.
Fig. 2. The top row shows 3 texture images. The central image patch (highlighted by red rectangle) is matched with an edge filter at all orientations. The magnitude of the filter response versus the orientation is plotted in the bottom row [13].
As shown in Fig. 2, some local regions may have multiple dominant orientations or no dominant orientations. One dominant orientation may not be able to fully represent the local characteristics. Average and standard deviation of filter responses for the same scale could convey more information and they are rotation invariant. They were also proven to contain discriminant and robust features for classification [15]. Thus, a complex response is defined:
⎧⎪u k (x, y )+ii σ k (x, y ), k =1,2,...6 CR8 k (x, y ) = ⎨ k ⎪⎩ii F (x, y ), k =7,8 5
∑ Fθ
5
k
u k (x, y )=
j =0
(x,y) j
6
∑ (Fθ
k
, σ k (x, y )=
j =0
Fθkj (x,y) = fθkj * I (x, y ), k =1,2,...,6, θ j = F (x,y) = f * I (x, y ), k =7,8 k
k
(1)
j
(x,y)-u k (x, y )) 2
(2)
5 jπ (j = 0,1,...,5) 6
(3)
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where i is the imaginary unit, * is the convolution operation, • is the multiply operation, and I is the input image. Fig.3 shows an example to illustrate MR8 and CR8. It is empirically found that representing F 7 (x,y) and F 8 (x,y) as imaginary part could get better result. Similar to MR8, after getting an 8-dimensional feature for each pixel, a texton dictionary is learnt through clustering method from a training set [12]. Before clustering, different weights could be assigned for real and imaginary part of CR8, as it is found that average and standard deviation of filter response could represent different properties of image and these values have different discriminant ability on different databases.
CR8(x, y )=wr i real(CR8 (x, y )) + wi i ii imagery(CR8(x, y ))
(4)
where wr and wi are two weights for real and imaginary part. These two weights are set empirically. k-means clustering [16] is used to learn the CR8 dictionary. For a given image, the 8-dimensinal feature of each pixel is labeled by the closest texton in the dictionary; finally a histogram representing the frequency of each texton is built as the feature for classification.
Fig. 3. An illustration of MR8 and CR8
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Experimental Results
In this section, we will compare the proposed feature extraction scheme with MR8 and one isotropic local feature, LBP [13]. To evaluate the effectiveness of the proposed methods, experiments on one large public texture database were done and their results were shown in the following. In MR8 and CR8, 40 textons were clustered from each texture classes using the training samples, and then a histogram based on learnt dictionary was computed for each model and sample image. For LBP, each texture sample was normalized to have an average intensity 128 and a standard deviation 20 [13]. For MR8 and CR8 methods, the image sample was normalized to have an average intensity of 0 and a standard deviation of 1 [12]. This is to remove global intensity and contrast [12-13]. The chi-square dissimilarity [13] and the nearest neighborhood classifier were used for all methods here. The Outex database includes two test suites: Outex_TC_00010 (TC10) and Outex_TC_00012 (TC12) [17]. The two test suites contain the same 24 classes of textures, which were collected under 3 different illuminants (“horizon”, “inca”, and “t184”) and 9 different rotation angles (00, 50, 100, 150, 300, 450, 600, 750 and 900). There are 20 non-overlapping 128•128 texture samples for each class under each situation. The experiment setups are as follows: 1.
2.
For TC10, samples of illuminant “inca” and angle 00 in each class were used for classifier training and the other 8 rotation angles with the same illuminant were used for testing. Hence, there are 480 (24•20) training samples and 3,840 (24•8•20) validation samples. For TC12, the classifier was trained with the same training samples as TC10, and it was tested with all samples captured under illuminant “t184” or “horizon”. Hence, there are 480 (24•20) models and 4,320 (24•20•9) validation samples for each illuminant.
Table 1 lists the experimental results by different schemes. Under TC12, “t” represents the test setup of illuminant “t184” and “h” represents “horizon”. wr and wi were set to 0 and 1 empirically. Table 1. Classification rate (%) for Outex database Method riu 2 8,1
LBP
+ LBP
riu 2 16,2
MR8 CR8
+ LBP
riu 2 24,3
Feature Size
TC10
TC12 “t”
TC12 “h”
54
97.21
89.21
84.32
960 960
93.59 94.06
92.55 92.31
92.82 92.80
Two findings could be found from Table 1. First, CR8 and MR8 get better results than LBP for TC12 test set, but they are worse than LBP in TC10. It is probably because of the fact that LBP has finer orientation resolution (150 when P=24) than CR8 and MR8 (300), so it could get better performance when there is only rotation variance. However, when the illumination changes, like TC12, LBP is too short to contain enough discriminant information. Second, CR8 could get comparable results with MR8. It validates that local dominant orientation may not be necessary for rotation invariant texture classification.
Texture Image Classification Using Complex Texton
4
103
Conclusion
To achieve rotation invariance, extracting local isotropic and anisotropic features are two popular methods. To the best of our knowledge, no work has compared different ways to see which way is more suitable for texture classification. As a counterpart of MR8, a local isotropic operator, CR8 is proposed. By one large public database, it is empirically shown that local dominant orientation may not be necessary for texture classification. In the future we will investigate other statistical texton based operators, such as local patch [18]. Another direction is to explore the correlation between CR8 and MR8 to further improve recognition accuracy by their fusion. Acknowledgments. The work is partially supported China Postdoctoral Science Foundation under Grant No. 20100480301.
References 1. Tuceryan, M., Jain, A.K.: In: Chen, C.H., Pau, L.F., Wang, P.S.P. (eds.) Handbook of Pattern Recognition and Computer Vision, pp. 235–276. World Scientific Publishing Co., Singapore (1993) 2. Anys, H., He, D.C.: Evaluation of Textural and Multipolarization Radar Features for Crop Classification. IEEE Transactions on Geoscience and Remote Sensing 33(5), 1170–1181 (1995) 3. Ji, Q., Engel, J., Craine, E.: Texture Analysis for Classification of Cervix Lesions. IEEE Transactions on Medical Imaging 19(11), 1144–1149 (2000) 4. Jia, W., Huang, D.S., Zhang, D.: Palmprint Verification Based on Robust Line Orientation Code. Pattern Recognition 41(5), 1504–1513 (2008) 5. Haralik, R.M., Shanmugam, K., Dinstein, I.: Texture Features for Image Classification. IEEE Trans. on Systems, Man, and Cybertics 3(6), 610–621 (1973) 6. Randen, T., Husy, J.H.: Filtering for Texture Classification: a Comparative Study. IEEE Transactions on Pattern Analysis and Machine Intelligence 21(4), 291–310 (1999) 7. Kashyap, R.L., Khotanzed, A.: A Model-based Method for Rotation Invariant Texture Classification. IEEE Transactions on Pattern Analysis and Machine Intelligence 8(4), 472–481 (1986) 8. Mao, J., Jain, A.K.: Texture Classification and Segmentation Using Multiresolution Simultaneous Autoregressive Models. Pattern Recognition 25(2), 173–188 (1992) 9. Wu, W.R., Wei, S.C.: Rotation and Gray-scale Transform-invariant Texture Classification Using Spiral Resampling, Subband Decomposition, and Hidden Markov Model. IEEE Transactions on Image Processing 5(10), 1423–1434 (1996) 10. Deng, H., Clausi, D.A.: Gaussian MRF Rotation-invariant Features for Image Classification. IEEE Transactions on Pattern Analysis and Machine Intelligence 26(7), 951–955 (2004) 11. Xu, Y., Ji, H., Fermuller, C.: Viewpoint Invariant Texture Description Using Fractal Analysis. International Journal of Computer Vision 83(1), 85–100 (2009) 12. Varma, M., Zisserman, A.: A statistical Approach to Texture Classification from Single Images. International Journal of Computer Vision 62(1-2), 61–81 (2005)
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13. Ojala, T., Pietikäinen, M., Mäenpää, T.T.: Multiresolution Gray-scale and Rotation Invariant Texture Classification with Local Binary Pattern. IEEE Transactions on Pattern Analysis and Machine Intelligence 24(7), 971–987 (2002) 14. Ahonen, T., Matas, J., He, C., Pietikäinen, M.: Rotation Invariant Image Description with Local Binary Pattern Histogram Fourier Features. In: Salberg, A.-B., Hardeberg, J.Y., Jenssen, R. (eds.) SCIA 2009. LNCS, vol. 5575, pp. 61–70. Springer, Heidelberg (2009) 15. Manjunath, B.S., Ma, W.Y.: Texture Features for Browsing and Retrieval of Image Data. IEEE Transactions on Pattern Analysis and Machine Intelligence 18(8), 837–842 (1996) 16. Duda, R.O., Hart, P.E., Stork, D.G.: Pattern classification, 2nd edn. Wiley, Chichester (2000) 17. Ojala, T., Mäenpää, T., Pietikäinen, M., Viertola, J., Kyllönen, J., Huovinen, S.: Outex – New Framework for Empirical Evaluation of Texture Analysis Algorithm. In: International Conference on Pattern Recognition, pp. 701–706 (2002) 18. Varma, M., Zisserman, A.: A statistical Approach to Material Classification Uusing Image Patch Exemplars. IEEE Transactions on Pattern Analysis and Machine Intelligence 31(11), 2032–2047 (2009)
