臺灣博碩士論文加值系統

紋理在圖像以及視訊中佔有一個相當大的地位，如何指出不同紋理之間的異處也逐漸成為了一個重要的議題。本論文藉由賈伯濾波器的參數探索了賈伯濾波器在紋理分析的能力。而賈伯濾波器所包含的能力有：一、適應不同物件大小的多大小(multi-scale)特性；二、大小不變性、位移不變性、旋轉不變性等特徵不變性；三、多重方向性特徵之萃取；四、頻率成分的坐落資訊。上述的特徵可以透過調整賈伯濾波器不同的參數來達成。因此，本論文便針對每個不同的參數來加以探索，了解每個參數所帶來的影響，以及應用賈伯濾波器來分割在Brodatz中的紋理圖像。選擇Brodatz的原因是因為在紋理分析的這個領域之中，它是一個相當廣為應用的一個紋理圖像資料庫，其中的圖像都有其較為明顯的特徵，以及在紋理之間也有著明顯的差異性，可以幫助判別紋理。
除此之外，在此論文中提出也應用小波轉換、Radon轉換、共發生矩陣等特徵萃取的方式來達成紋理分割等方法來跟所提出的演算法做相比較。從實驗結果中，發現因為賈伯濾波器有著其他特徵萃取的方式沒有的重要特性，所以分割結果可以達到一個較好的境界。另一方面，此論文也探索了賈伯濾波器應用於影像分割的可能性。最後可以發現賈伯濾波器確實能夠有效地分析紋理。

Texture plays a critical role in images and videos and different representation of one texture to another texture is a critical issue. This thesis explored the capability of Gabor filter banks in analyzing texture via the parameters of the bases of the Gabor filter. The versatile properties of Gabor filter bank includes (a) the multi-scale property in being adaptive to objects having different scales, (b) invariant features, including scale, shifting, and rotational invariance, (c) the ability to characterize natural textures with multiple directions, and (d) the capability in providing locality information for different frequency components. This thesis discussed the utilization of these Gabor properties in the analysis of natural textures contained within the Brodatz album, a popular database in the texture analysis field. Other algorithms such as wavelet transform, Radon transform, and co-occurrence matrix are also applied to texture segmentation for comparison to the proposed Gabor transform. Experimental results show the superiority of the Gabor filters over the above mentioned algorithms in terms of feature extraction and texture segmentation. Furthermore, the thesis also explored the potentials of Gabor filter banks in the segmentation of natural images.

Abstract ii
Table of Contents iii
List of Tables v
List of Figures vi
Chapter 1 Introduction 1
1.1 Background 1
1.2 Motivation 2
1.3 Organization of this Thesis 2
Chapter 2 The State-of-the-art Survey of Texture Segmentation 3
2.1 Gabor Filter 3
2.1.1 One-Dimensional Gabor Filter 4
2.1.2 Two-Dimensional Gabor Filter 5
2.1.3 Properties of Gabor Filter’s Parameters 9
2.1.4 Properties of Gabor Filter Based Feature 10
2.1.5 Design Methodology of Gabor Filter Bank 11
2.2 Co-occurrence Matrix 14
2.3 Radon Transform with Multi-scale Analysis 17
2.4 Wavelet Packet Transform 19
2.5 Log-Polar Transform 20
Chapter 3 Evaluation of Gabor Filter Parameters 23
3.1 One-Dimensional Gabor Filter 23
3.1.1 Standard Deviation of Gaussian Function (?) 24
3.1.2 Frequency of Fourier Basis Carrier (?) 30
3.2 Two-Dimensional Gabor Filter 37
3.2.1 Standard Deviation of Gaussian Function (?x) 37
3.2.2 Standard Deviation of Gaussian Function (?y) 41
3.2.3 Frequency of Fourier Basis Carrier (?) 44
3.2.4 Orientation of Gabor Filter (?) 47
3.3 Conclusion 50
Chapter 4 Proposed Algorithm 52
4.1 Design Parameters of Gabor Filter 53
4.2 Feature Extraction 60
4.3 Nonparametric Density Estimation 60
4.4 Clustering 64
4.4.1 k-means Clustering 64
Chapter 5 Experimental Result 69
5.1 Texture Segmentation 71
Chapter 6 Conclusion and Future Work 79
6.1 Conclusion 79
6.2 Future Work 80
Chapter 7 Reference 85

[1]L. Lucchese and S. K. Mitra, “Color image segmentation: A state-of-art survey, in Proc. Indian Nat. Sci. Acad. (INSA-A), vol. 67-A, New Delhi, India, Mar. 2001, pp. 207–221.
[2]Y. Tao, V. Muthukkumarasamy, B. Verma, M. Blumenstein, “A texture feature extraction technique using 2D–DFT and hamming distance, Proceedings of the International Conference on Computational Intelligence and Multimedia Applications (ICCIMA ‘03), Xian, China, pp. 120-125, 2003.
[3]M.M.Hadhoud, ElKilani, W.S., Samaan, M.I., “An adaptive algorithm for fingerprints image enhancement using Gabor filters, In: IEEE International Conference on Computer Engineering and Systems, pp. 227–236 (2007)
[4]D. Gabor. “Theory of communications, Journal of International Electrical Engineers, vol. 93, part III, No. 26, pp. 427-457, 1946.
[5]A. K. Jain and F. Farrokhnia, “Unsupervised texture segmentation using Gabor filters, Pattern Recognition, Vol. 24, No. 12, pp. 1167-1186, 1991
[6]A.K. Jain and N.K. Ratha, “Object detection using Gabor filters, Pattern Recognition, vol. 30, no. 2, pp. 295–309, February, 1997.
[7]V. Kyrki, J.-K. Kamarainen, and H. K?alvi?ainen, “Content based image matching using Gabor filtering, In ACIVS’2001 3rd International Conference on Advanced Concepts for Intelligent Vision Systems Theory and Applications, pages 45–49, Baden-Baden, Germany, July 2001.
[8]V. Kyrki, J.-K. Kamarainen, and H. K?alvi?ainen, “Invariant shape recognition using global Gabor features, In 12th Scandinavian Conference on Image Analysis, pages 671–678, Bergen, Norway, June 2001.
[9]R. Mehrotra, K. Namuduri, and N. Ranganathan, “Gabor filter–based edge detection, Pattern Recognition, vol. 25 no. 12, pp. 1479-1494, 1992.
[10]W.M. Pan, C. Y. Suen, and T. D. Bui, “Scripts identification using Steerable Gabor Filters, in 8th International Conference on Document Analysis and Recognition, 2005, Seoul, Korea, Republic of, August 31, 2005 - September 1, pp. 883-887
[11]D. A. Clausi and H. Deng, “Design-based texture feature fusion using Gabor filters and co-occurrence probabilities, IEEE Trans. Image Process., vol. 14, no. 7, pp. 925–936, Jul. 2005.
[12]V. Kyrki, J-K. Kamarainen, H. Kalviainen, “Simple Gabor feature space for invariant object recognition, Pattern Recognit. Lett., Vol. 25, no. 3, pp. 311-318, February, 2004.
[13]V. Kruger, G. Sommer, “Gabor wavelet networks for efficient head pose estimation, Image and Vision Computing, Vol. 20 no.9-10, pp. 665-672, August, 2002
[14]Y. Hamamoto, S. Uchimura, M. Watanabe, T. Yasuda, Y. Mitani, and S. Tomita, “A Gabor filter-based method for recognizing handwritten numerals, Pattern Recognition, Vol. 31, no. 4, pp. 395-400, April, 1998
[15]CJ Lee, SD Wang, “Fingerprint feature extraction using Gabor filters, Electronics Letters. Vol. 35, no. 4, pp. 288-290, February, 1999
[16]C. Liu, H. Wechsler, “Gabor feature based classification using the enhanced Fisher linear discriminant model for face recognition, IEEE Trans Image Process, Vol. 11, no. 4, pp.467-476, April, 2002
[17]O. Ayinde, YH Yang, “Face recognition approach based on rank correlation of Gabor-filtered images, Pattern Recognition, Vol. 35, no. 6, pp. 1275–1289, June, 2002
[18]Fasel IR, Barlett MS, Movellan JR (2002) “A comparison of Gabor filter methods for automatic detection of facial landmarks, In: Proceedings of the 5th IEEE international conference on automatic face and gesture recognition, pp 231–235
[19]Lyons MJ et al (2000) “Classifying facial attributes using a 2-D Gabor wavelet representation and discriminant analysis, In: Proceedings of IEEE conference on automatic face and gesture recognition, pp 202–207
[20]Shen L, Bai L (2004) “Face recognition based on Gabor features using kernel methods, In: Proceedings of the 6th IEEE conference on face and gesture recognition, Korea, pp 170–175
[21]HY. Wu, Y. Yoshida, T. Shioyama, “Optimal Gabor filters for high speed face identification, Proceedings of international conference on pattern recognition, Vol. 16, no. 1, pp. 107-110, 2002
[22]CJ Liu, H. Wechsler, “Independent component analysis of Gabor feature’s for face recognition, IEEE Transactions on Neural Networks, Vol. 14, no. 4, pp. 919-928, July, 2003
[23]L. Shen and L. Bai, “A review on Gabor wavelets for face recognition, Pattern Analysis and Applications, Vol.9, no. 2, pp. 273–292, 2006.
[24]X. Xie, J. Gong, Q. Dai, and F. Xu, “Rotation and Scaling Invariant Texture Classification Based on Gabor Wavelets, in IET Conference Publications, 2008,p. 393-396.
[25]B.S. Manjunath and W.Y. Ma, ?Texture Features for Browsing and Retrieval of Image Data, IEEE Trans. Pattern Analysis and Machine Intelligence, Vol. 18, no. 8, pp. 837-842, August, 1996
[26]C. Yang, W. Runsheng, “Texture segmentation using independent component analysis of Gabor features, in: 18th International Conference on Pattern Recognition, Vol. 2, August 2006, pp. 20-24.
[27]R. Jenssen, T. Eltoft, “ICA filter bank for segmentation of textured images, in: Proceedings of the International Workshop on Independent Component Analysis and Blind Signal Separation (ICA2003), 2003, pp. 827–832
[28]J. Han and K.-K. Ma, “Rotation-invariant and scale-invariant Gabor features for texture image retrieval, Image Vision Comput. Vol. 25, no. 9, pp. 1474-1481, September, 2007.
[29]D. F. Dunn, W.E. Higgins, and J. Wakeley, “Texture Segmentation Using 2-D Gabor Elementary Functions, IEEE Trans. Pattern Analysis and Machine Intelligence, Vol. 22, no. 2, pp. 130-149, February, 1994.
[30]J. Daugman, “Uncertainty Relation for Resolution in Space, Spatial Frequency, and Orientation Optimized by Two-Dimensional Visual Cortical Filters, J. Opticl Soc. of Am. A, Vol. 2, no. 7, pp. 1160-1169, 1985.
[31]D.J. Field, “Relations between the statistics of natural images and the response properties of cortical cells, Journal of the Optical Society of America 4 (1987), pp. 2379–2394.
[32]J.-K. Kamarainen, and V. Kyrki, “Invariance Properties of Gabor Filter-Based Features – Overview and Applicaions, IEEE Trans. Omage Processing, Vol. 15, No. 5, pp. 1088-1099, May 2006. 1996.
[33]J. Zhang and T. Tan, “Brief Review of Invariant Texture Analysis Methods, Pattern Recognition, Vol. 35, no. 3, pp. 735-747, March, 2002.
[34]D. F. Dunn, W. E. Higgins, and J. Wakeley, “Determining Gabor-filter parameters for texture segmentation, in Intelligent robots and computer vision XI, vol. 1826, 1992, pp. 51-63,
[35]S. Bi, D. Liang, “Texture segmentation using adaptive Gabor filters based on HVS, in: SPIE, vol. 6057, 2006.
[36]D.-M. Tsai, S.-K. Wu and M.-C. Chen, “Optimal Gabor filter design for texture segmentation using stochastic optimization, Image and Vision Computing, Vol. 19, no. 5, pp. 299-316, April, 2001.
[37]D.F. Dunn and W.E. Higgins, “Optimal Gabor Filters for Texture Segmentation, IEEE Trans. Image Processing, Vol. 4, no. 7, pp. 947-964, July 1995.
[38]T.P. Weldon and W.E. Higgins, “Design of Multiple Gabor Filters for Texture Segmentation, Proc. Int’l Conf. Acoustic Speech, Signal Proc., Atlanta, Ga., pp. 2,243–2,246, May 1996
[39]T. P. Weldon and W. E. Higgins, ‘‘An algorithm for designing multiple Gabor filters for segmenting multi-textured images,’’ in Proc. IEEE Int. Conf. on Image Processing, Chicago ~1998.
[40]Michael Lindenbaum, Roman Sandler: “Gabor Filter Analysis for Texture Segmentation, Technical Report CIS-2005-05 - 2005, Technion - Computer Science Department.
[41]J. F. Khan, R. R. Adhani and S. M.A. Bhuiyan, “A customized Gabor filter for unsupervised color image segmentation Image and Vision Computing, Vol. 27, no. 4, pp.489-501, March, 2009.
[42]A. K. Jain , F. Farrokhnia, “Unsupervised texture segmentation using Gabor filters, Pattern Recognition, Vol. 24 no. 12, pp. 1167-1186, December, 1991.
[43]D. A. Clausi and M. Jernigan, “Designing Gabor Filters for Optimal Texture Separability, Pattern Recognition, Vol. 33, no. 11, pp. 1835-1849, November, 2000.
[44]Javier R. Movellan: “Tutorial on Gabor Filters, Tutorial paper [Online] http://mplab.ucsd.edu/tutorials/pdfs/gabor.pdf.
[45]Mryka Hall-Beyer, The GLCM Tutorial Home Page, [Online] http://www.fp.ucalgary.ca/mhallbey/tutorial.htm
[46]Jobanputra, R. and D. Clausi (2004). “Texture analysis using Gaussian weighted grey level cooccurrence probabilities. In Proceedings of the Canadian Conference on Computer and Robot Vision - CRV, pp. 51–57.
[47]P. Cui, J. Li, Q. Pan and H. Zhang, “Rotation and scaling invariant texture classification based on Radon transform and multiscale analysis, Pattern Recognition Letters, Vol. 27, no. 5, pp. 408-413, April, 2006.
[48]Xiong H, Zhang T. “A translation- and scale-invariant adaptive wavelet transform, IEEE Trans. Image Processing, Vol. 9, no. 9, pp. 2100-2108, December, 2000.
[49]R. Manthalkar, P.K. Biswas and B.N. Chatterji, “Rotation and scale invariant texture features using discrete wavelet packet transform, Pattern Recognition Lett. Vol. 24 no. 14, pp. 2455-2462, October, 2003.
[50]C.-M. Pun and M.-C. Lee, “Log-polar wavelet energy signatures for rotation and scale invariant texture classification, IEEE Transactions on Pattern Analysis and Machine Intelligence, Vol. 25, no. 5, pp. 590-603, May 2003.
[51]F.Bianconi and A. Fern?ndez. “Evaluation of the effects of Gabor filter parameters on texture classification. Pattern Recognition, Vol. 40, no. 12, pp.3325-3335, December, 2007.
[52]Kardi Teknomo. Kardi Teknomo’s page “Tutorials on similarity and distance, [Online] http://people.revoledu.com/kardi/tutorial/Similarity/index.html