面向线目标提取的多源信息融合技术研究
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摘要
典型线目标(道路和海岸线)的提取,在军事和民用领域的各方面已获得广泛的应用,并发挥着巨大的作用。而随着遥感技术的发展,仅依靠单个光谱信息的传统分类方法难以满足实际需求,为了进一步提高信息的利用率,我们将融合思想引入到线目标的提取。利用不同数据源的信息协同处理来提高线目标识别的精准度。本论文针对多源遥感图像的特点及优势,以可见光全色图像、多光谱图像和SAR图像为数据源,以线目标(道路和海岸线)为研究对象,主要利用了新型小波(双树复小波和非下采样的Contourlet变换)融合的手段,对多源遥感图像中的线目标提取问题做了研究和分析。
论文首先研究了小波和新型小波的基本理论及融合算法,深入研究了双树复小波和非下采样的Contourlet变换的性质及特点,通过实验对新型小波的性质进行了验证,并从多方向性、平移不变性和各向异性三方面进行了分析。在此基础上,提出了将双树复小波和非下采样的Contourlet变换相结合的改进融合算法,通过优势互补,提高了融合后图像对边缘和细节的保持能力。该方法可以使融合后的图像的线特征更加明显,便于后续线目标的提取。
然后,研究了基于融合的道路和海岸线目标提取方法。针对不同数据源特点,采用不同的道路预处理方法,并提出了一种基于数学形态学和局部Hough变换的道路融合提取算法。采用“提取—融合—后处理”流程完成了对道路目标提取的整个过程。通过实验证明,该算法对于不同分辨率和不同信源的图像,都能以较高的精确度提取出道路并有效保持其原始形状。针对海岸线,采用基于融合的分类算法进行海岸线提取,克服了分类算法对边缘保持较差的缺点,经过融合分类后,去除了大部分的干扰信息,有利于后续对海岸线的边缘检测。
The extraction of typical line objects (road and coastline) is widely used not only in military reconnaissance but also in civilian use. With the development of remote sensing technology, the information from a single sensor can not fully reflect the characteristics of the target. In order to gain more information, the idea of fusion is be introduced into the extraction of line objects. Therefore, the collaborative use of the information of spatial and spectral characteristics can improve the accuracy of recognition. In this dissertation, panchromatic images, multi-spectral images and SAR images for the data source, the issue of line objects extraction in multi-source remote sensing images is researched and analyzed mainly by the use of new-type wavelet fusion(dual-tree complex wavelets(DT-CWT) and nonsubsampled contourlet transform(NSCT).
Firstly, on the basis of research on wavelet, the new-typical wavelets theories is deeply studied, especially in the nature of DT-CWT and NSCT. The nature are analyzed from the multi-direction, shift invariant and anisotropy. A image fusion method based on the combination of DT-CWT and NSCT is presented. This method can make line features more obvious in the fused image, which is in favor of the following process of target extraction.
Secondly, this dissertation researches the method of extracting road and coastline object which are based on fusion. In response to the features of different sources, the different pretreatment for the extraction is used. A road extraction method based on the Hough transform and mathematical morphology is presented. This method extracts roads through the " Extraction - Fusion- Aftertreatment " three steps with the primitive roads. This method can increase the precision for the extraction of road. For the coastline, an improved method for classification is used to extract coastline from the fused image. This method can get over shortcomings of classification, make line features more obvious in the image.
论文首先研究了小波和新型小波的基本理论及融合算法,深入研究了双树复小波和非下采样的Contourlet变换的性质及特点,通过实验对新型小波的性质进行了验证,并从多方向性、平移不变性和各向异性三方面进行了分析。在此基础上,提出了将双树复小波和非下采样的Contourlet变换相结合的改进融合算法,通过优势互补,提高了融合后图像对边缘和细节的保持能力。该方法可以使融合后的图像的线特征更加明显,便于后续线目标的提取。
然后,研究了基于融合的道路和海岸线目标提取方法。针对不同数据源特点,采用不同的道路预处理方法,并提出了一种基于数学形态学和局部Hough变换的道路融合提取算法。采用“提取—融合—后处理”流程完成了对道路目标提取的整个过程。通过实验证明,该算法对于不同分辨率和不同信源的图像,都能以较高的精确度提取出道路并有效保持其原始形状。针对海岸线,采用基于融合的分类算法进行海岸线提取,克服了分类算法对边缘保持较差的缺点,经过融合分类后,去除了大部分的干扰信息,有利于后续对海岸线的边缘检测。
The extraction of typical line objects (road and coastline) is widely used not only in military reconnaissance but also in civilian use. With the development of remote sensing technology, the information from a single sensor can not fully reflect the characteristics of the target. In order to gain more information, the idea of fusion is be introduced into the extraction of line objects. Therefore, the collaborative use of the information of spatial and spectral characteristics can improve the accuracy of recognition. In this dissertation, panchromatic images, multi-spectral images and SAR images for the data source, the issue of line objects extraction in multi-source remote sensing images is researched and analyzed mainly by the use of new-type wavelet fusion(dual-tree complex wavelets(DT-CWT) and nonsubsampled contourlet transform(NSCT).
Firstly, on the basis of research on wavelet, the new-typical wavelets theories is deeply studied, especially in the nature of DT-CWT and NSCT. The nature are analyzed from the multi-direction, shift invariant and anisotropy. A image fusion method based on the combination of DT-CWT and NSCT is presented. This method can make line features more obvious in the fused image, which is in favor of the following process of target extraction.
Secondly, this dissertation researches the method of extracting road and coastline object which are based on fusion. In response to the features of different sources, the different pretreatment for the extraction is used. A road extraction method based on the Hough transform and mathematical morphology is presented. This method extracts roads through the " Extraction - Fusion- Aftertreatment " three steps with the primitive roads. This method can increase the precision for the extraction of road. For the coastline, an improved method for classification is used to extract coastline from the fused image. This method can get over shortcomings of classification, make line features more obvious in the image.
引文
1 Yi Yang, Chongzhao Han, Xin Kang. An Overview on Pixel-Level Image Fusion in Remote Sensing . IEEE International Conference on Automation and Logistics , 2007: 2339 ~ 2344
2 J. H. Jang, Kim. Y. S, Ra. J.B. Image enhancement in multi-resolution multi-sensor fusion. IEEE Conference on advanced video and signal based surveillance, 2007: 289~294
3周前祥,敬忠良,姜世忠.多源遥感影像信息融合研究现状与展望.宇航学报, 2002, 23(5):89~94
4 Jin Wu Yang, Liu Jian, Liu Jinwen. Wavelet Based Remote Sensing Image Fusion with Color Compensation Rule and IHS Transform. IEEE International Conference on Mechatronics and Automation, 2006 :2079~2083
5 Gonzalez-Audicana, M. Saleta, J. L. Catalan, R. G. Garcia. Fusion of multi-spectral and panchromatic images using improved IHS and PCA mergers based on wavelet decomposition. IEEE Transactions on Geoscience and Remote Sensing, 2004: 1291~1299
6 Zhiwei Ye, Huili Gong, Wenji Zhao. Subpixel urban area thermal pattern analysis using ASTER and SPOT-5. IEEE. Urban Remote Sensing Event, 2009:1~6
7 P. J. Brut, E. H. Adelson. The Laplacian pyramid as a compact image code.IEEE Transactions on Communications, 1983, 31(4):532~540
8 A Toet. Multiscale contrast enhancement with applications to image fusion. Optical Engineering, 1992, 31(5):1026~1031
9 Burt. P. J, Kolczynski. P. J. Enhanced image capture througe fusion. Proceeding Fourth Internat Conference on Computer Vision, Berlin, Germany, 1993: 173~182
10 Chui. C. K, Lian. J. A. A study of orthonomal multi-wavekets. Apple Numer Math, 1996, 20(3):273~298
11 Chibano. Y, Houacine. A. On the use of the redundant wavelet transform for multisensor image fusion. The 7th IEEE International Conference on Electronics, Circuits and Systems, 2000:442~445
12刘斌,彭嘉雄.基于小波包变换的区域图像融合方法.计算机工程与应用,2004, 21(5):36~40.
13 Jiwonkim. Fast texture transfer through the use of wavelet-based image fusion. IEEE. International Conference on Wavelet Analysis and Pattern Recognition, 2007, (1): 270 ~275
14 J. Nunez, X. Otazu, O. Fors,et al. Multiresolution based image fusion with additive wavelet decomposition. IEEE Trans. Geoscience and Remote Sensing, 1999, 37(3): 1024 ~ 1211
15李伟,朱学峰.基于第二代小波变换的图像融合方法及性能评价.自动化学报, 2007,33(8):817~822
16 Wong. A, Clausi. D, Fieguth. P.Phase-adaptive image sigal fusion using complex-valued wavelets. IEEE, The 19th International Conference on Pattern Recognition, 2008:1~4
17 Lewis. J, Callaghan. R, Nikolov. S. Region-Based Image Fusion Using Complex Wavelets. Proc of the 7th Conf on Information Fusion, 2004:1965~1969
18 Selesnick. I. W, Baraniuk. R. G, Kingsbury. N. C. The Dual-Tree Complex Wavelet Transform . IEEE Signal Processing Magazine , 2004 :568~573
19 Styliani. I, Vassilia. K. Investigation of the Dual-Tree Complex and Shift Invar-iant Discrete Wavelet Transforms on Quickbird Image Fusion. IEEE, Geoscience and Remote Sensing Letters, 2007, (4):166~170
20 Wange Yajie, Xu Xinhe. Shift Invariance Based Image Fusion Algorithm. IEEE. Control and Decision Conference, 2008:5185~5188
21 Celik. T, Tjahjadi. T. Image Resolution Enhancement Using Dual-Tree Complex Wavelet Transform . Geoscience and Remote Sensing Letters, IEEE, 2010:554~557
22 Minh. N. Do, Martin Vetterli. The Nonsubsampled Contourlet Transform: Theory, Design, and Applications. IEEE Transactions on Image Processing Transactions , 2006, (15):3089~3101
23何同弟,汪西莉.基于小波-Contourlet变换的遥感图像融合.计算机工程与设计, 2008:235~240
24阳方林,郭红阳,杨风暴.像素级图像融合效果的评价方法研究.测试技术学报, 2002,16(4):276~279
25 Heipke C. Semiautomatic Extraction of Road from Aerial Images. IAPRS Comm. III Workshop, Munich, 1994:365~372
26 Shukla.V, Chandrakanth.R, Ramachandran. R.Semi-Automatic Road Extrac-tion Algorithm for High Resolution Images Using Path Following Approach. ICVGIP Space Applications Centre Ahmedabad, 2002:369~375
27 Vosselman. G, Knecht de j. Road Tracing by Profile Matching and Kalman Filtering.Automatic Extraction of manmade Objects from Aerial and Space images. Birkhauser Verlag Basel,1995:265~274
28胡翔云,张祖勋,张剑清.航空图像上线状地物的半自动提取.中国图像图形学报, 2004, 7(2):137~140
29 Gruen. A, Li. H. Semiautomatic Linear Feature Extraction by Dynamic Programming and LSB-Snakes. Photogrammetric.Engineering and Remote Sensing, 1997:874~880
30 Trinder. C, Wang. D, Sowmya. A. Artificial Intelligence in 3D Feature Extraction. Automatic Extraction of Man-made Objects from Aerial and Space Images. Basel:Birkhaeuser Verlag, 1997:257~265
31 Ton. J, Jain. A. K, Enslin. W. R, et al. Automatic Road Identification and Labeling in Landsat 4 TM Images.Photogrammetric, 1989, 43(2):257~276
32 Mayer. H, Laptev. I, Baumgartner. A, Steger C.Automatic Road Extraction Based on Multi-Scale Modeling, Context and Snakes. IAPRS, 1997, 30(3): 106~113
33 Baumgartner. A, Eckstein. W, Heipke. C, Hinz. S, Mayer. H, Rading. B, Steger.C. Research on Road Extraction.Festschrift for Prof.Dr.-Ing.Heinrich Ebner zum60, Gevertstag, 1999:43~64
34 Rellier. G, Descombes. X. Zerubia. J. Deformation of a cartographic road network on a SPOT satellite image. IEEE. International Conference on Image Processing, 2000, (2):736~739.
35 Katartzis. A, Sahli. H, Pizurica, V. Cornelis.J. A model-based approach to the automatic extraction of linear features from airborne images. IEEE Transactions on Geoscience and Remote Sensing.2001,(39):2073~2079
36 Zhang. C. S, Murai.S, Baltsavias E. Road Network Detection by Mathematical Morphology. ISPRS Workshop"3D Feospatial Data Production:Meeting Application Requirements", Paris, France, 1999:185~200
37 Monga. O, Armande. N, Montesinor P. Thin Nets and Crest Lines: Application to Satellite Data and Medical Images.Computer Vision and ImageUnderstanding, 1997, 67(3):285~295
38 Price K.Road Grid Extraction and Verification.International Archives of Photo-grammerty and Remote Sensing,1999,32(3~5):101~106
39 Baumgartner.A, Steger. C, et al. Automatic Road Extraction in Rural Areas. International Archives of Photogrammetry and Remote Sensing, 1999, 36(3~5):107~112
40 Mayer. H, Steger. C, A New Approach for Line Extraction and its Integration in multi-Scale, Multi-Abstraction-level Road Extraction System.IAPR TC-7 Workshop:Mapping Buildings, Roads and other Man-made Structures from Images, Oldenbourg Verlag, Wien, Austria, 2008:331~348
41 Mayer. H, Laptev. I, Baumgartner.A, Steger C.Automatic Road Extraction Based on Multi-Scale Modeling,Context,and Snakes.IAPRS,1997, 30(2~3): 106~113
42 Baumgartner. A, Eckstein. W, Heipke. C, Hinz.S, Mayer. H, Rading. B, Steger. C, Wiedemann. C. T_REX:TUM_Research on Road Extraction.Festschrift for Prof.Dr.-Ing. Heinrich Ebner zum60, Gevertstag, 1999:43~64
43 Donoho, D. L. Denoising by soft-thresholding.IEEE Transactions on IT,1992:41~46
44 Y. CHIBANI, A. HOUSCINE. The joint use of IHS transform and redundant wavelet decomposition for fusing multispectral and panchromatic images.INT. REMOTE SENSING, 2002, 23(18):3821~3833
45后斌,乔伟峰,孙在宏.基于IHS变换与àtrous小波分解的遥感影像融合.南京师大学报(自然科学版), 2006, 29(1):116~120
46 E. J. Candes. Ridgelets: Theory and Applications.Ph. D.Thesis, Department of Statistcs, Stanforf University, 1998:568~581
47 E. J. Candes. Harmonic analysis of neural networks. Applied and Computational Harmonic Analysis ,1999,65(3):197~218
48 E. J. Candes. Monoscale Ridgelets for the Representation of Image with Edges. Tech.Report, Department of Statistics, Stanford University, 1999:876~882
49 E. J. Candes. On the Representation of Mutilated Sobolev Functions. SIAM J.Math.Analysis, 1999,6(2):197~218
50 E. J. Candes, D. L. Donoho.Curvelets.Tech.Report,Department of Statics, Stan-ford University, 1999: 536~540
51 F. G. Meyer, R. R. Coifman. Brushlets: a tool for directional image analysis andimage compression. Applied and Computational Harmonic Analysis , 1997, 55(2):147~187
52 Easley. G. R, Labate. D. Wang-Q Lim; Optimally Sparse Image Representations using Shearlets. IEEE. Signals, Systems and Computers, conference on Forieth Asilomar, 2006:974~978
53 Feng Chen, Yun-Feng Li. A multiresolution segmentation method for tree crown image using wavelets .IEEE. International Conference on Wavelet Analysis and Pattern Recognition, 2007, (4):1556~1559
54 M.N.Do. Contourlet: A directional multi-resolution image represention. Rochewter. Proc. of IEEE International Conference on Image Prcossing. 2002 : 357~360
55 V. Chappelier, C. Guillemot, S. Marinkovic.Image coding with iterated contour-let And wavelet transforms. IEEE.International Conference on Image Processing, 2003: 3157~3160
56 Arthur. L, da Cunha, Jianping Zhou, The nonsubsampled contourlet transform theory, design, dan applications .IEEE Transactions on Image Processing, 2006:356~342
57 Taxt T, Solberg AHS. Information Fusion in Remote Sensing.Vistas in Astrono-my, 1997,41(3):337~342
58霍宏涛.数字图像处理.北京:北京理工大学出版社, 2002:69~74
59余慧.多聚焦图像融合算法研究.河海大学. 2006:201~214
60 Wang Haihui, Wang Yanli, Zhao Tongzhou. Automated Detection in SAR Images by Using Wavelet Filtering and Hough Transform .IEEE。Second International Workshop on Education Technology and Computer Science, 2010, (3):202~206
2 J. H. Jang, Kim. Y. S, Ra. J.B. Image enhancement in multi-resolution multi-sensor fusion. IEEE Conference on advanced video and signal based surveillance, 2007: 289~294
3周前祥,敬忠良,姜世忠.多源遥感影像信息融合研究现状与展望.宇航学报, 2002, 23(5):89~94
4 Jin Wu Yang, Liu Jian, Liu Jinwen. Wavelet Based Remote Sensing Image Fusion with Color Compensation Rule and IHS Transform. IEEE International Conference on Mechatronics and Automation, 2006 :2079~2083
5 Gonzalez-Audicana, M. Saleta, J. L. Catalan, R. G. Garcia. Fusion of multi-spectral and panchromatic images using improved IHS and PCA mergers based on wavelet decomposition. IEEE Transactions on Geoscience and Remote Sensing, 2004: 1291~1299
6 Zhiwei Ye, Huili Gong, Wenji Zhao. Subpixel urban area thermal pattern analysis using ASTER and SPOT-5. IEEE. Urban Remote Sensing Event, 2009:1~6
7 P. J. Brut, E. H. Adelson. The Laplacian pyramid as a compact image code.IEEE Transactions on Communications, 1983, 31(4):532~540
8 A Toet. Multiscale contrast enhancement with applications to image fusion. Optical Engineering, 1992, 31(5):1026~1031
9 Burt. P. J, Kolczynski. P. J. Enhanced image capture througe fusion. Proceeding Fourth Internat Conference on Computer Vision, Berlin, Germany, 1993: 173~182
10 Chui. C. K, Lian. J. A. A study of orthonomal multi-wavekets. Apple Numer Math, 1996, 20(3):273~298
11 Chibano. Y, Houacine. A. On the use of the redundant wavelet transform for multisensor image fusion. The 7th IEEE International Conference on Electronics, Circuits and Systems, 2000:442~445
12刘斌,彭嘉雄.基于小波包变换的区域图像融合方法.计算机工程与应用,2004, 21(5):36~40.
13 Jiwonkim. Fast texture transfer through the use of wavelet-based image fusion. IEEE. International Conference on Wavelet Analysis and Pattern Recognition, 2007, (1): 270 ~275
14 J. Nunez, X. Otazu, O. Fors,et al. Multiresolution based image fusion with additive wavelet decomposition. IEEE Trans. Geoscience and Remote Sensing, 1999, 37(3): 1024 ~ 1211
15李伟,朱学峰.基于第二代小波变换的图像融合方法及性能评价.自动化学报, 2007,33(8):817~822
16 Wong. A, Clausi. D, Fieguth. P.Phase-adaptive image sigal fusion using complex-valued wavelets. IEEE, The 19th International Conference on Pattern Recognition, 2008:1~4
17 Lewis. J, Callaghan. R, Nikolov. S. Region-Based Image Fusion Using Complex Wavelets. Proc of the 7th Conf on Information Fusion, 2004:1965~1969
18 Selesnick. I. W, Baraniuk. R. G, Kingsbury. N. C. The Dual-Tree Complex Wavelet Transform . IEEE Signal Processing Magazine , 2004 :568~573
19 Styliani. I, Vassilia. K. Investigation of the Dual-Tree Complex and Shift Invar-iant Discrete Wavelet Transforms on Quickbird Image Fusion. IEEE, Geoscience and Remote Sensing Letters, 2007, (4):166~170
20 Wange Yajie, Xu Xinhe. Shift Invariance Based Image Fusion Algorithm. IEEE. Control and Decision Conference, 2008:5185~5188
21 Celik. T, Tjahjadi. T. Image Resolution Enhancement Using Dual-Tree Complex Wavelet Transform . Geoscience and Remote Sensing Letters, IEEE, 2010:554~557
22 Minh. N. Do, Martin Vetterli. The Nonsubsampled Contourlet Transform: Theory, Design, and Applications. IEEE Transactions on Image Processing Transactions , 2006, (15):3089~3101
23何同弟,汪西莉.基于小波-Contourlet变换的遥感图像融合.计算机工程与设计, 2008:235~240
24阳方林,郭红阳,杨风暴.像素级图像融合效果的评价方法研究.测试技术学报, 2002,16(4):276~279
25 Heipke C. Semiautomatic Extraction of Road from Aerial Images. IAPRS Comm. III Workshop, Munich, 1994:365~372
26 Shukla.V, Chandrakanth.R, Ramachandran. R.Semi-Automatic Road Extrac-tion Algorithm for High Resolution Images Using Path Following Approach. ICVGIP Space Applications Centre Ahmedabad, 2002:369~375
27 Vosselman. G, Knecht de j. Road Tracing by Profile Matching and Kalman Filtering.Automatic Extraction of manmade Objects from Aerial and Space images. Birkhauser Verlag Basel,1995:265~274
28胡翔云,张祖勋,张剑清.航空图像上线状地物的半自动提取.中国图像图形学报, 2004, 7(2):137~140
29 Gruen. A, Li. H. Semiautomatic Linear Feature Extraction by Dynamic Programming and LSB-Snakes. Photogrammetric.Engineering and Remote Sensing, 1997:874~880
30 Trinder. C, Wang. D, Sowmya. A. Artificial Intelligence in 3D Feature Extraction. Automatic Extraction of Man-made Objects from Aerial and Space Images. Basel:Birkhaeuser Verlag, 1997:257~265
31 Ton. J, Jain. A. K, Enslin. W. R, et al. Automatic Road Identification and Labeling in Landsat 4 TM Images.Photogrammetric, 1989, 43(2):257~276
32 Mayer. H, Laptev. I, Baumgartner. A, Steger C.Automatic Road Extraction Based on Multi-Scale Modeling, Context and Snakes. IAPRS, 1997, 30(3): 106~113
33 Baumgartner. A, Eckstein. W, Heipke. C, Hinz. S, Mayer. H, Rading. B, Steger.C. Research on Road Extraction.Festschrift for Prof.Dr.-Ing.Heinrich Ebner zum60, Gevertstag, 1999:43~64
34 Rellier. G, Descombes. X. Zerubia. J. Deformation of a cartographic road network on a SPOT satellite image. IEEE. International Conference on Image Processing, 2000, (2):736~739.
35 Katartzis. A, Sahli. H, Pizurica, V. Cornelis.J. A model-based approach to the automatic extraction of linear features from airborne images. IEEE Transactions on Geoscience and Remote Sensing.2001,(39):2073~2079
36 Zhang. C. S, Murai.S, Baltsavias E. Road Network Detection by Mathematical Morphology. ISPRS Workshop"3D Feospatial Data Production:Meeting Application Requirements", Paris, France, 1999:185~200
37 Monga. O, Armande. N, Montesinor P. Thin Nets and Crest Lines: Application to Satellite Data and Medical Images.Computer Vision and ImageUnderstanding, 1997, 67(3):285~295
38 Price K.Road Grid Extraction and Verification.International Archives of Photo-grammerty and Remote Sensing,1999,32(3~5):101~106
39 Baumgartner.A, Steger. C, et al. Automatic Road Extraction in Rural Areas. International Archives of Photogrammetry and Remote Sensing, 1999, 36(3~5):107~112
40 Mayer. H, Steger. C, A New Approach for Line Extraction and its Integration in multi-Scale, Multi-Abstraction-level Road Extraction System.IAPR TC-7 Workshop:Mapping Buildings, Roads and other Man-made Structures from Images, Oldenbourg Verlag, Wien, Austria, 2008:331~348
41 Mayer. H, Laptev. I, Baumgartner.A, Steger C.Automatic Road Extraction Based on Multi-Scale Modeling,Context,and Snakes.IAPRS,1997, 30(2~3): 106~113
42 Baumgartner. A, Eckstein. W, Heipke. C, Hinz.S, Mayer. H, Rading. B, Steger. C, Wiedemann. C. T_REX:TUM_Research on Road Extraction.Festschrift for Prof.Dr.-Ing. Heinrich Ebner zum60, Gevertstag, 1999:43~64
43 Donoho, D. L. Denoising by soft-thresholding.IEEE Transactions on IT,1992:41~46
44 Y. CHIBANI, A. HOUSCINE. The joint use of IHS transform and redundant wavelet decomposition for fusing multispectral and panchromatic images.INT. REMOTE SENSING, 2002, 23(18):3821~3833
45后斌,乔伟峰,孙在宏.基于IHS变换与àtrous小波分解的遥感影像融合.南京师大学报(自然科学版), 2006, 29(1):116~120
46 E. J. Candes. Ridgelets: Theory and Applications.Ph. D.Thesis, Department of Statistcs, Stanforf University, 1998:568~581
47 E. J. Candes. Harmonic analysis of neural networks. Applied and Computational Harmonic Analysis ,1999,65(3):197~218
48 E. J. Candes. Monoscale Ridgelets for the Representation of Image with Edges. Tech.Report, Department of Statistics, Stanford University, 1999:876~882
49 E. J. Candes. On the Representation of Mutilated Sobolev Functions. SIAM J.Math.Analysis, 1999,6(2):197~218
50 E. J. Candes, D. L. Donoho.Curvelets.Tech.Report,Department of Statics, Stan-ford University, 1999: 536~540
51 F. G. Meyer, R. R. Coifman. Brushlets: a tool for directional image analysis andimage compression. Applied and Computational Harmonic Analysis , 1997, 55(2):147~187
52 Easley. G. R, Labate. D. Wang-Q Lim; Optimally Sparse Image Representations using Shearlets. IEEE. Signals, Systems and Computers, conference on Forieth Asilomar, 2006:974~978
53 Feng Chen, Yun-Feng Li. A multiresolution segmentation method for tree crown image using wavelets .IEEE. International Conference on Wavelet Analysis and Pattern Recognition, 2007, (4):1556~1559
54 M.N.Do. Contourlet: A directional multi-resolution image represention. Rochewter. Proc. of IEEE International Conference on Image Prcossing. 2002 : 357~360
55 V. Chappelier, C. Guillemot, S. Marinkovic.Image coding with iterated contour-let And wavelet transforms. IEEE.International Conference on Image Processing, 2003: 3157~3160
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