不变量理论在模式识别中的应用
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摘要
在对3D空间的目标进行识别时，通常目标相对摄像系统会发生方位和姿态的变化，具体表现为目标的平移、旋转、伸缩等，这将给正确的识别带来困难。为解决此类问题，本文将不变量理论应用于目标识别中，以解决因目标移动造成的失真问题。本文主要围绕各种矩的不变特性进行了研究，并设计了基于不变量的图像识别系统，用于解决目标的平移、旋转、伸缩和倾斜问题，取得了很好的效果。
本文第一部分回顾了矩技术及其相关特性，并提出了一种对图像矩的规格化方法。该方法首先计算给定模式的协方差矩阵，然后根据协方差矩阵的特征向量来旋转和伸缩给定模式，使结果模式对平移和伸缩失真是不变的，而将倾斜问题转化为旋转问题，然后根据“图像椭圆倾角”以及旋转后的图像的三阶矩的符号来旋转图像，以使其对旋转变换也保持不变。这样，结果模式对平移、伸缩、旋转和倾斜变换都是不变的。第二部分实现了一种基于Zernike矩的图像识别系统，该系统首先通过第一部分提出的图像规格化方法解决平移和伸缩失真，并将倾斜问题转化为旋转问题；然后使用正交Zernike矩的幅值作为旋转不变特征解决旋转失真问题。在提取特征时，目前大多数已有技术都使用确定数目的特征，本文提出了基于重建过程来确定所需Zernike矩的最高阶次的系统方法，并用加权规格化互相关方法和26类字符数据对该方法进行了测试，得到的分类精度远远高于用规则矩和矩不变量作为特征的方法。最后，将该识别系统嵌入到实际的监控系统中进行测试，得到了很好的识别结果，证明了改进后的识别算法能够很好的解决失真问题。
In object recognition system the objects always make movements relative to the camera, which represent as translation, scaling, rotation and skew of the objects. In this article Invariant Theory is used in the image recognition to resolve the image distortions problems. This paper studied the invariable character of the moment techniques and used the character to resolve the image distortions. The work of this paper mainly includes two parts.
The first part looked back the moment techniques and some characters of it. Then a new method for image normalization is provided, which can correctly normalize the images distorted by translation, scaling, rotation, and skew transformations, while extant normalization methods can normalize three distortions at most. This new method first process the input image using compact algorithm, then rotate the compact image according to image eclipse tilt angle.
In the second part a new set of rotation invariant features for image recognition is introduced. The features are the magnitudes of a set of orthogonal complex moments of the image called Zernike moments. Taking advantage of the orthogonal property, a systematic feature selection method for choosing an appropriate number of the Zernike features is developed. It is based on computing a measure of the information content differences of features of different classes. The performance of the method is experimentally tested on a 26-class data set involving differently oriented binary images. At last the system is added to a watching system. The recognition result proved that the method introduced in this part is more effective for the image recognition.
本文第一部分回顾了矩技术及其相关特性，并提出了一种对图像矩的规格化方法。该方法首先计算给定模式的协方差矩阵，然后根据协方差矩阵的特征向量来旋转和伸缩给定模式，使结果模式对平移和伸缩失真是不变的，而将倾斜问题转化为旋转问题，然后根据“图像椭圆倾角”以及旋转后的图像的三阶矩的符号来旋转图像，以使其对旋转变换也保持不变。这样，结果模式对平移、伸缩、旋转和倾斜变换都是不变的。第二部分实现了一种基于Zernike矩的图像识别系统，该系统首先通过第一部分提出的图像规格化方法解决平移和伸缩失真，并将倾斜问题转化为旋转问题；然后使用正交Zernike矩的幅值作为旋转不变特征解决旋转失真问题。在提取特征时，目前大多数已有技术都使用确定数目的特征，本文提出了基于重建过程来确定所需Zernike矩的最高阶次的系统方法，并用加权规格化互相关方法和26类字符数据对该方法进行了测试，得到的分类精度远远高于用规则矩和矩不变量作为特征的方法。最后，将该识别系统嵌入到实际的监控系统中进行测试，得到了很好的识别结果，证明了改进后的识别算法能够很好的解决失真问题。
In object recognition system the objects always make movements relative to the camera, which represent as translation, scaling, rotation and skew of the objects. In this article Invariant Theory is used in the image recognition to resolve the image distortions problems. This paper studied the invariable character of the moment techniques and used the character to resolve the image distortions. The work of this paper mainly includes two parts.
The first part looked back the moment techniques and some characters of it. Then a new method for image normalization is provided, which can correctly normalize the images distorted by translation, scaling, rotation, and skew transformations, while extant normalization methods can normalize three distortions at most. This new method first process the input image using compact algorithm, then rotate the compact image according to image eclipse tilt angle.
In the second part a new set of rotation invariant features for image recognition is introduced. The features are the magnitudes of a set of orthogonal complex moments of the image called Zernike moments. Taking advantage of the orthogonal property, a systematic feature selection method for choosing an appropriate number of the Zernike features is developed. It is based on computing a measure of the information content differences of features of different classes. The performance of the method is experimentally tested on a 26-class data set involving differently oriented binary images. At last the system is added to a watching system. The recognition result proved that the method introduced in this part is more effective for the image recognition.
引文
1 孙即祥.模式识别中的特征提取与计算机视觉不变量.北京:国防工业出版社,2001:223
2 I. Weiss. Projective Invariants of Shapes. Proceedings of DARPA Image Under-standing Workshop,2001(2):1125-1134
3 H. Ballard. Dana, M.Brown. Christorphen. Principles of Animate Vision. ImageUnderstanding,2000,56(1):3-21
4 B. Ruzean, C. Mario. Active and Explorary Perception. Image Understanding,2002,56(1):31-40
5 J. L. Mundy, A. Zisserman. Geometric Invariant in Computer Vision. Compu-ter Science,1990(7):186-187
6 K. Kanatani. Group Theoretical Methods in Image Understanding. New York:S-pringer Verlag,1990,2(3):554-557
7 D. Forsyth, J. L. Mundy. Invariant Descriptors for 3D Object Recognition a-nd Pose. IEEE Transaction on Pattern Analysis and Machine Intelligence,1991,13(10):971-991
8 T. H. Reiss. Object Recognition Using Algebraic and Differential Invariants. S-ignal Processing,2003,15(1):264-265
9 I. Weiss. Improved Moment Invariant for Shape Discrimination. Pattern Recog-nition,2001,10(2):683-686
10 E. Rivlin, I. Weiss. Local Invariance for Recognition. IEEE Trans Pattern A-nal Mach Intel,2002,17(3):226-238
11 宋克欧,黄凤岗.视觉不变量与机器视觉研究.中国图像图形学报,1997,2(7):221-223
12 边肇祺,张学工.模式识别.北京:清华大学出版社,2000:1-3
13 阮秋琦.数字图像处理.北京:电子工业出版社,2001:481-483
14 程民德.图像识别导论.上海:上海科学技术出版社,1983:1-2
15 李金宗.模式识别导论.北京:高等教育出版社,1994:1-5
16 福永圭之介著.统计图形识别导论.陶笃纯译.北京:科学出版社,1978:3
17 颜孙震,孙即祥.矩不变量在目标形状识别中的应用研究.国防科技大学学报,1998,20(5):75-80
18 Y. Cheng. Analysis of Affine Invariants as Approximate Perspective Invariants.Computer Vision and Image Understanding,2001,63(2):197-207
19 H. Reiss. Thomas. Recognizing Planar Objects Using Invariant Image Features.New York:Springer Verlag,2000:259-312
20 M. K. Hu. Pattern Recognition by Moment Invariants. Proc.IRE,1961,(49):1428
21 M. Hueckel. A Operator which Locates Edges in Digital Pictures. J.ACM,1978,18(1):113-125
22 R. J. Prokop, A. P. Reeves. A Survey of Moment-Based Techniques for Unoc-cludedObject. Representation and Recognition,2001,54(5):438-460
23 M. K. Hu. Visual Pattern Recognition by Moment Invariants. Proc.IRE Trans.I-nform.Theory,1962,(8):179-187
24 M. R. Teague. Image Analysis via the General Theory of Moments. J.Opt.Soc.Amer,1980,70:920-930
25 R. W. Taylor, A. P. Reeves. Three-Dimensional Image Transforms in MomentSpace.Proceedings of the IEEE Computer Society Workshop on Computer Vi-sion,2002,(3):366-368
26 J. F. Boyce, W. J. Hossack. Moment Invariants for Pattern Recognition. PatternRecognition Lett.I,1983,10(1):451-456
27 S. O. Belkasim, M. Shridhar and M. Ahmadi. Shape-Contour Recognition Usi-ng Moment Invariants. Pattern Recognition,2000,(10):649-651
28 C. H. Teh, R. T. Chin. On Image Analysis by the Method of Moments. IEEE Trans.Pattern Anal.Mach.Intelligence PAMI,1988,(10):496-513
29 H. Zenkouar, A. Nachit. Images Compression Using Moments Method of Orth-ogonal Polynomials. Materials Science and Engineering,2001,(4):211
30 B. H. Yin, H. Mack. Target Classification Algorithms for Video and FLIR Imag-ery.Proc.SPIE,1981,3(2):134-140
31 Y. S. Abu, D. Psaltis. Recognitive Aspects of Moments Invariants. IEEE Trans.Pattern Anal.Machine Intell,1984,5(1):698-706
32 Li Yajun. Reforming the Theory of Invariants Moments for Pattern Recognition.Pattern Recognition,2001,25(7):723-730
33 J. Flusser, T. Suk. Pattern Recognition by Affine Moment Invariants. Pattern Recognition,2001,26(1):167-174
34 Shen Dinggang, H.S.Ip. Horace.Discriminative Wavelet Shape Descriptors for Recognition of 2-D Patterns. Pattern Recognition,2002,32(1):151-165
35 J. Flusser, T. Suk and S. Saic. Image Features Invariant with Respect to Blur.Pattern Recognition,2000,28(11):1723-1732
36 T. Chohuak, C. Roland. On Image Analysis by the Methods of Moments. IEEE Transactions on Pattern Analysis and Machine Intelligence,1988,10(4):496-513
37 C. T. Zahn, R. S. Roskies. Fourier Descriptors for Plate Closed Curves. IEEE Trans.Comput,1972,21:269-281
38 E. Persoon, K. S. Fu. Shape Discrimination Using Fourier Descriptors. IEEE Trans.Syst.Man.Cybern,1977,7:170-179
39 D. H. Ballard. Generalizing the Hough Transform to Detect Arbitrary Shape. Patt.Recog,1981,13(2):111-122
40 A. Taza, C. Y.Suen. Discrimination of Planar Shapes Using Shape Matrices. IEEE Trans.Syst.Man.Cybern,1989,19(5):1281-1289
41 A. Rosenfeld, A. C. Kak. Digital Picture Processing. Academic Press. NewYork:Springer Verlag,1982:322-327
42 J. G. Leu. Shape Normalization Through Compacting. Patt.Recogn.Lett,1989,10:243-250
43 M. R. Teague. Image Analysis via the General Theory of Moments. J.Opt.Soc.Am,1980,70(8):920-930
44 Pei SooChang, Lin ChaoNan. Image Normalization for Pattern Recognition. Im-age and Vision Computing,2000,13(10):711-723
45 Y. S. Abu, D. Psaltis. Image Normalization by Complex Moments. IEEE Trans.PAMI,1985,7(1):46-55
46 D. H. Ballard, C. M. Brown. Computer Vision. New York:Springer Verlag,2000:115-120
47 A. Rosenfeld, A. C. Kak. Digital Picture Processing. Academic Press. Florida:Springer Verlag,1992:254-260
48 E. Persoon, K. S. Fu. Shape Discrimination Using Fourier Descriptors. IEEE Trans.Syst.Man.Cybern.SMC,1977(7):388-397
49 Y. N. Hsu, H. H. Arsenault and G. April. Rotational Invariant Digital Pattern Recognition Using Circular Harmonic Expansion. Appl.Opt,1982,4:4012-4015
50 易英辉,宋克欧.一个基于代数不变量的目标识别算法.中国图形图像学报,1996,4(3):207-211
51 陈燕新,戚飞虎.一组用于识别平面多边形的射影不变量.红外与毫米波学报,1998,17(2):99-106
52 刘沿双,官弼根,杨国等.交比不变量在平面目标识别中的应用.应用科技,2000,(3):55-62
53 王延平,袁洁,苏祥芳.几种拐点不变量及其在目标识别中的应用.中国图形图像学报,1999,4A(10):854-859
54 朱仲涛,张钹,张再兴.曲线在拓扑形变下的准不变量.计算机学报,1999,22(9):897-901
55 朱仲涛,张钹.图像关于边缘提取算子的微分不变性.计算机学报,1999,22(9):903-910
56 张铃,张钹,吴福朝.对图形识别具有平移、旋转、伸缩不变性的神经网络.计算机学报,1998,21(2):127-136
57 廖原,袁捷,赵恒卓等.基于几种不变量融合信息的缺损目标识别.武汉大学学报,1998,44(1):81-84
2 I. Weiss. Projective Invariants of Shapes. Proceedings of DARPA Image Under-standing Workshop,2001(2):1125-1134
3 H. Ballard. Dana, M.Brown. Christorphen. Principles of Animate Vision. ImageUnderstanding,2000,56(1):3-21
4 B. Ruzean, C. Mario. Active and Explorary Perception. Image Understanding,2002,56(1):31-40
5 J. L. Mundy, A. Zisserman. Geometric Invariant in Computer Vision. Compu-ter Science,1990(7):186-187
6 K. Kanatani. Group Theoretical Methods in Image Understanding. New York:S-pringer Verlag,1990,2(3):554-557
7 D. Forsyth, J. L. Mundy. Invariant Descriptors for 3D Object Recognition a-nd Pose. IEEE Transaction on Pattern Analysis and Machine Intelligence,1991,13(10):971-991
8 T. H. Reiss. Object Recognition Using Algebraic and Differential Invariants. S-ignal Processing,2003,15(1):264-265
9 I. Weiss. Improved Moment Invariant for Shape Discrimination. Pattern Recog-nition,2001,10(2):683-686
10 E. Rivlin, I. Weiss. Local Invariance for Recognition. IEEE Trans Pattern A-nal Mach Intel,2002,17(3):226-238
11 宋克欧,黄凤岗.视觉不变量与机器视觉研究.中国图像图形学报,1997,2(7):221-223
12 边肇祺,张学工.模式识别.北京:清华大学出版社,2000:1-3
13 阮秋琦.数字图像处理.北京:电子工业出版社,2001:481-483
14 程民德.图像识别导论.上海:上海科学技术出版社,1983:1-2
15 李金宗.模式识别导论.北京:高等教育出版社,1994:1-5
16 福永圭之介著.统计图形识别导论.陶笃纯译.北京:科学出版社,1978:3
17 颜孙震,孙即祥.矩不变量在目标形状识别中的应用研究.国防科技大学学报,1998,20(5):75-80
18 Y. Cheng. Analysis of Affine Invariants as Approximate Perspective Invariants.Computer Vision and Image Understanding,2001,63(2):197-207
19 H. Reiss. Thomas. Recognizing Planar Objects Using Invariant Image Features.New York:Springer Verlag,2000:259-312
20 M. K. Hu. Pattern Recognition by Moment Invariants. Proc.IRE,1961,(49):1428
21 M. Hueckel. A Operator which Locates Edges in Digital Pictures. J.ACM,1978,18(1):113-125
22 R. J. Prokop, A. P. Reeves. A Survey of Moment-Based Techniques for Unoc-cludedObject. Representation and Recognition,2001,54(5):438-460
23 M. K. Hu. Visual Pattern Recognition by Moment Invariants. Proc.IRE Trans.I-nform.Theory,1962,(8):179-187
24 M. R. Teague. Image Analysis via the General Theory of Moments. J.Opt.Soc.Amer,1980,70:920-930
25 R. W. Taylor, A. P. Reeves. Three-Dimensional Image Transforms in MomentSpace.Proceedings of the IEEE Computer Society Workshop on Computer Vi-sion,2002,(3):366-368
26 J. F. Boyce, W. J. Hossack. Moment Invariants for Pattern Recognition. PatternRecognition Lett.I,1983,10(1):451-456
27 S. O. Belkasim, M. Shridhar and M. Ahmadi. Shape-Contour Recognition Usi-ng Moment Invariants. Pattern Recognition,2000,(10):649-651
28 C. H. Teh, R. T. Chin. On Image Analysis by the Method of Moments. IEEE Trans.Pattern Anal.Mach.Intelligence PAMI,1988,(10):496-513
29 H. Zenkouar, A. Nachit. Images Compression Using Moments Method of Orth-ogonal Polynomials. Materials Science and Engineering,2001,(4):211
30 B. H. Yin, H. Mack. Target Classification Algorithms for Video and FLIR Imag-ery.Proc.SPIE,1981,3(2):134-140
31 Y. S. Abu, D. Psaltis. Recognitive Aspects of Moments Invariants. IEEE Trans.Pattern Anal.Machine Intell,1984,5(1):698-706
32 Li Yajun. Reforming the Theory of Invariants Moments for Pattern Recognition.Pattern Recognition,2001,25(7):723-730
33 J. Flusser, T. Suk. Pattern Recognition by Affine Moment Invariants. Pattern Recognition,2001,26(1):167-174
34 Shen Dinggang, H.S.Ip. Horace.Discriminative Wavelet Shape Descriptors for Recognition of 2-D Patterns. Pattern Recognition,2002,32(1):151-165
35 J. Flusser, T. Suk and S. Saic. Image Features Invariant with Respect to Blur.Pattern Recognition,2000,28(11):1723-1732
36 T. Chohuak, C. Roland. On Image Analysis by the Methods of Moments. IEEE Transactions on Pattern Analysis and Machine Intelligence,1988,10(4):496-513
37 C. T. Zahn, R. S. Roskies. Fourier Descriptors for Plate Closed Curves. IEEE Trans.Comput,1972,21:269-281
38 E. Persoon, K. S. Fu. Shape Discrimination Using Fourier Descriptors. IEEE Trans.Syst.Man.Cybern,1977,7:170-179
39 D. H. Ballard. Generalizing the Hough Transform to Detect Arbitrary Shape. Patt.Recog,1981,13(2):111-122
40 A. Taza, C. Y.Suen. Discrimination of Planar Shapes Using Shape Matrices. IEEE Trans.Syst.Man.Cybern,1989,19(5):1281-1289
41 A. Rosenfeld, A. C. Kak. Digital Picture Processing. Academic Press. NewYork:Springer Verlag,1982:322-327
42 J. G. Leu. Shape Normalization Through Compacting. Patt.Recogn.Lett,1989,10:243-250
43 M. R. Teague. Image Analysis via the General Theory of Moments. J.Opt.Soc.Am,1980,70(8):920-930
44 Pei SooChang, Lin ChaoNan. Image Normalization for Pattern Recognition. Im-age and Vision Computing,2000,13(10):711-723
45 Y. S. Abu, D. Psaltis. Image Normalization by Complex Moments. IEEE Trans.PAMI,1985,7(1):46-55
46 D. H. Ballard, C. M. Brown. Computer Vision. New York:Springer Verlag,2000:115-120
47 A. Rosenfeld, A. C. Kak. Digital Picture Processing. Academic Press. Florida:Springer Verlag,1992:254-260
48 E. Persoon, K. S. Fu. Shape Discrimination Using Fourier Descriptors. IEEE Trans.Syst.Man.Cybern.SMC,1977(7):388-397
49 Y. N. Hsu, H. H. Arsenault and G. April. Rotational Invariant Digital Pattern Recognition Using Circular Harmonic Expansion. Appl.Opt,1982,4:4012-4015
50 易英辉,宋克欧.一个基于代数不变量的目标识别算法.中国图形图像学报,1996,4(3):207-211
51 陈燕新,戚飞虎.一组用于识别平面多边形的射影不变量.红外与毫米波学报,1998,17(2):99-106
52 刘沿双,官弼根,杨国等.交比不变量在平面目标识别中的应用.应用科技,2000,(3):55-62
53 王延平,袁洁,苏祥芳.几种拐点不变量及其在目标识别中的应用.中国图形图像学报,1999,4A(10):854-859
54 朱仲涛,张钹,张再兴.曲线在拓扑形变下的准不变量.计算机学报,1999,22(9):897-901
55 朱仲涛,张钹.图像关于边缘提取算子的微分不变性.计算机学报,1999,22(9):903-910
56 张铃,张钹,吴福朝.对图形识别具有平移、旋转、伸缩不变性的神经网络.计算机学报,1998,21(2):127-136
57 廖原,袁捷,赵恒卓等.基于几种不变量融合信息的缺损目标识别.武汉大学学报,1998,44(1):81-84