多尺度Bandelets图像压缩与融合
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摘要
Bandelets变换是一种基于边缘的图像表示方法,它能够自适应的跟踪图像的几何正则方向,从而有效地表示图像。第二代Bandelets变换采用多尺度Bandelets,它充分利用了图像在多个尺度上的几何正则性,能获得较单尺度Bandelets变换更加稀疏的数据表示。本文在对Bandelets变换理论和第二代Bandelets变换研究的基础上,对多尺度Bandelets在图像压缩与多聚焦图像融合方面的应用进行了研究。主要工作概括如下：
(1)第二代Bandelets变换中,在四叉树剖分后的每个子块中,最佳几何流采用拉格朗日函数优化得到。然而,该方法得到的几何流方向是有限精度的。针对该问题,本文提出一种改进的几何流优化方法,先利用图像分割得到均匀区域,根据均匀区域内几何流方向的相似性,对每四个二进剖分子块上的几何流进行修正,以找到更加精确地几何流方向。将该算法应用于光学和SAR图像压缩,能够在较高比特率下获得较第二代Bandelets高的峰值信噪比。
(2)对于NxN大小的图像,第二代Bandelets变换几何流优化的复杂度是O(N2(log2N)2)。随着N的增大,复杂度迅速增加。针对这一问题,本文提出了一种低复杂度的Bandelets变换。采用提升小波做多尺度变换,并将小波多尺度分解系数重新排列,对矩阵的每一列做弯曲小波变换,快速计算得出子块内的最佳几何流方向,最后采用优化截断嵌入式编码(EBCOT)方法对Bandelets系数进行编码,使Bandelets的实现复杂度降到了O(N2)。将该算法应用于SAR图像压缩,在较高比特率时取得了优于JPEG2000的压缩效果。
(3)非下采样Bandelets具有平移不变性,变换得到的各个高频子带里具有丰富的方向信息,可以用于多聚焦图像融合。本文给出了非下采样Bandelets的构造方法,提出了结合非下采样Bandelets和形态学处理的图像融合规则,采用形态学方法处理融合决策图,用相似的方法处理邻近的像素,可以得到更为精确的融合结果。研究结果表明：本文融合方法能够得到优于非下采样小波的融合效果,获得了高质量的融合图像。
本文的工作得到了国家自然科学基金(No.60201029、No.60971112)的资助。
Bandelets transformation is a method based on the edge of the image representation, which can be adaptive to track the direction of the image geometry, and then express the image effectively. The second generation Bandelets transform is multi-scale Bandelets, which make full use of the geometric regularity of the image in multiple scales, and can get more sparse data representation than single-scale Bandelets transform. In this paper, based on an investigation into the theory of Bandelets transform and the construction of the second generation Bandelets, exploring researches on multi-scale Bandelets were done in image compression and multi-focus image fusion. Main tasks can be summarized as follows:
(1) In the second generation Bandelets transformation, in each subblock by quadtree subdividing, the best geometry flow can obtain by optimizing Lagrange function. For the size of L×L subblock, you can get uniform discrete angle amount of L2-1. The geometry flow direction that can make the Lagrange function smallest is the optimal geometry flow direction. However, the geometry flow obtained by the methods is limited precision. To solve the problem, we present an improved geometry flow optimization method:getting the homogeneous region by image segmenting firstly; then correct the geometry in each four subblocks according to the geometric similarity of flow direction within the homogeneous region, in order to find a more precise geometry flow direction. The algorithm is applied to optical and SAR image compression, in the 1.0-2.0 bit rate, can obtain about 0.1-0.2dB higher than the second generation Bandelets in PSNR. And the keeping of detail information of the reconstructed image is quite to the second generation Bandelets.
(2) The geometric flow is optimized in the second Bandelets, which requires O(N2(log2N)2) operations for an image of NxN pixels. With the increasing of N, the complexity increases fast. Based on this problem, an improved algorithm for its fast computation is developed. Perform a lifting wavelet transform for the multi-scale transform. Then we used a fixed size of image partition in each high frequency subband, and rearrange the wavelet coefficients in the high frequency subbands for computing the geometry quickly. At last EBCOT coding is used for coding the obtained coefficients. It is worth noting that our method provides a (log2N)2 times reduction in the running time. And our methods are outperforming JPEG2000 and comparable with 2G-Bandelets for SAR image compression at high bit.
(3) In the tasks of image fusion based on the multi-scale analysis, multi-scale analysis tools often need to have redundancy and translational invariance. The use of nonsubsampled wavelet transform, can obtain the corresponding nonsubsampled Bandelets transformation. By the nonsubsampled Bandelets which have translation invariance, the various high-frequency subbands have the rich direction information; so can be used for multi-focus image fusion. A method for multi-focus image fusion which combined with nonsubsampled Bandelets and morphological processing was proposed. As the fusion decision map was treated using the morphological method and the similar approach to the adjacent pixels, more accurate fusion results were obtained. The results show that the fusion method in this paper is much better than the nonsubsampled wavelet fusion method, and clear image of all objects in the scene could be obtained.
The research is supported by the National Nature Science Foundation of China (No. 60201029、No.60971112).
(1)第二代Bandelets变换中,在四叉树剖分后的每个子块中,最佳几何流采用拉格朗日函数优化得到。然而,该方法得到的几何流方向是有限精度的。针对该问题,本文提出一种改进的几何流优化方法,先利用图像分割得到均匀区域,根据均匀区域内几何流方向的相似性,对每四个二进剖分子块上的几何流进行修正,以找到更加精确地几何流方向。将该算法应用于光学和SAR图像压缩,能够在较高比特率下获得较第二代Bandelets高的峰值信噪比。
(2)对于NxN大小的图像,第二代Bandelets变换几何流优化的复杂度是O(N2(log2N)2)。随着N的增大,复杂度迅速增加。针对这一问题,本文提出了一种低复杂度的Bandelets变换。采用提升小波做多尺度变换,并将小波多尺度分解系数重新排列,对矩阵的每一列做弯曲小波变换,快速计算得出子块内的最佳几何流方向,最后采用优化截断嵌入式编码(EBCOT)方法对Bandelets系数进行编码,使Bandelets的实现复杂度降到了O(N2)。将该算法应用于SAR图像压缩,在较高比特率时取得了优于JPEG2000的压缩效果。
(3)非下采样Bandelets具有平移不变性,变换得到的各个高频子带里具有丰富的方向信息,可以用于多聚焦图像融合。本文给出了非下采样Bandelets的构造方法,提出了结合非下采样Bandelets和形态学处理的图像融合规则,采用形态学方法处理融合决策图,用相似的方法处理邻近的像素,可以得到更为精确的融合结果。研究结果表明：本文融合方法能够得到优于非下采样小波的融合效果,获得了高质量的融合图像。
本文的工作得到了国家自然科学基金(No.60201029、No.60971112)的资助。
Bandelets transformation is a method based on the edge of the image representation, which can be adaptive to track the direction of the image geometry, and then express the image effectively. The second generation Bandelets transform is multi-scale Bandelets, which make full use of the geometric regularity of the image in multiple scales, and can get more sparse data representation than single-scale Bandelets transform. In this paper, based on an investigation into the theory of Bandelets transform and the construction of the second generation Bandelets, exploring researches on multi-scale Bandelets were done in image compression and multi-focus image fusion. Main tasks can be summarized as follows:
(1) In the second generation Bandelets transformation, in each subblock by quadtree subdividing, the best geometry flow can obtain by optimizing Lagrange function. For the size of L×L subblock, you can get uniform discrete angle amount of L2-1. The geometry flow direction that can make the Lagrange function smallest is the optimal geometry flow direction. However, the geometry flow obtained by the methods is limited precision. To solve the problem, we present an improved geometry flow optimization method:getting the homogeneous region by image segmenting firstly; then correct the geometry in each four subblocks according to the geometric similarity of flow direction within the homogeneous region, in order to find a more precise geometry flow direction. The algorithm is applied to optical and SAR image compression, in the 1.0-2.0 bit rate, can obtain about 0.1-0.2dB higher than the second generation Bandelets in PSNR. And the keeping of detail information of the reconstructed image is quite to the second generation Bandelets.
(2) The geometric flow is optimized in the second Bandelets, which requires O(N2(log2N)2) operations for an image of NxN pixels. With the increasing of N, the complexity increases fast. Based on this problem, an improved algorithm for its fast computation is developed. Perform a lifting wavelet transform for the multi-scale transform. Then we used a fixed size of image partition in each high frequency subband, and rearrange the wavelet coefficients in the high frequency subbands for computing the geometry quickly. At last EBCOT coding is used for coding the obtained coefficients. It is worth noting that our method provides a (log2N)2 times reduction in the running time. And our methods are outperforming JPEG2000 and comparable with 2G-Bandelets for SAR image compression at high bit.
(3) In the tasks of image fusion based on the multi-scale analysis, multi-scale analysis tools often need to have redundancy and translational invariance. The use of nonsubsampled wavelet transform, can obtain the corresponding nonsubsampled Bandelets transformation. By the nonsubsampled Bandelets which have translation invariance, the various high-frequency subbands have the rich direction information; so can be used for multi-focus image fusion. A method for multi-focus image fusion which combined with nonsubsampled Bandelets and morphological processing was proposed. As the fusion decision map was treated using the morphological method and the similar approach to the adjacent pixels, more accurate fusion results were obtained. The results show that the fusion method in this paper is much better than the nonsubsampled wavelet fusion method, and clear image of all objects in the scene could be obtained.
The research is supported by the National Nature Science Foundation of China (No. 60201029、No.60971112).
引文
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[3]Choi H. and Baraniuk R.. Multiscale image segmentation using wavelet-domain hidden Markov models. IEEE Trans. Image Processing,2001,10(9):1309-1321.
[4]Candes E J. Ridgelets:Theory and Applications. USA:Department of Statistics, Stanford University.1998.
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[6]Penne E Le, Mallat S. Image compression with geometrical wavelets. In Proceedings of IEEE Conference on Image Processing (ICIP'00). Vancouver, Canada, September.2000,1(1):661-664.
[7]Do M N, Vetterli M. The contourlet transform:An efficient directional multi-resolution image representation. IEEE Trans. Image Processing.2005, 14(12):2091-2106.
[8]Donoho D L. Wedgelets:nearly-minimax estimation of edges. Annals of Statistics. 1999,27(3):859-897.
[9]Donoho D L, Huo X M. Beamlet pyramids:a new form of multi-resolution analysis, suited for extracting lines, curves, and objects from very noise image data. Proceedings of SPIE, Wavelet Applications in Signal and Image Processing VIII, Aldroubi A, Laine A F, Unser M A (Eds),2000,4119:434-444.
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[11]Meyer F G, Coifman R R. Directional image compression with brushlets. Proceedings of the IEEE-SP International Symposium on Time-Frequency and Time-Scale Analysis, Paris, France,1996,189-192.
[12]Meyer F G, Coifman R R. Brushlets:A Tool for Directional Image Analysis and Image Compression. Applied and Computational Harmonic Analysis.1997, 6(4):147-187.
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[19]Tan S, Zhang X R, Jiao L C. Monoscale dual ridgelet frame.in:Proceedings of International Conference on Image Analysis and Recognition. Toronto, Canada, 2005,3449:263-269.
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[21]张旭东、卢国栋、冯健.图像编码基础和小波压缩技术——原理、算法和标准.第1版.北京：清华大学出版社.2004.
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[23]Huffman D.A, A method for the construction of minimum redundancy codes, Proc.IRE,1952, (40):1098-1111.
[24]Rafael C.Gonzalez, Richard E.Woods,阮秋琦等译.Digital Image Processing, (Second Edition),数字图像处理(第二版),电子工业出版社.
[25]R.J.Clark. Transform Coding of Images. Academic Press, New York.1985.
[26]王志武,丁国清,颜国正等.多传感器数据融合在切割机器人系统中的应用.上海交通大学学报.2002(7),36(7)：995-998.
[27]Yu Song, Mantian Li. A New Wavelet Based Multi-focus Image Fusion Scheme and Its Application on Optical Microscopy. Robotics and Biomimetics. IEEE International Conference.2006:401-405.
[28]A.Toet. Multiscale contrast enhancement with application to image fusion. Optical Engineering.1992,31(5):1026-1031.
[29]M.Pavel, J.Larimer, A.Ahumada. Sensor fusion for synthetic vision. Society for InformationDisplay Digest of Technical Papers.1992:475-478.
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[42]Lucas. B, Kanade. T. An iterative image registration technique with an application to stereo vision, in Proc.7th Int. Joint Conf. Artificial Intelligence, Vancouver, BC, Canada.1981:674-679.
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[2]Krista A., Zhang Yun, Dare Peter. Wavelet based image fusion techniques-An introduction, review and comparison. ISPRS Journal of Photogrammetry & Remote Sensing.2007, (62):249-263.
[3]Choi H. and Baraniuk R.. Multiscale image segmentation using wavelet-domain hidden Markov models. IEEE Trans. Image Processing,2001,10(9):1309-1321.
[4]Candes E J. Ridgelets:Theory and Applications. USA:Department of Statistics, Stanford University.1998.
[5]Candes E J, Donoho D L. Curvelets-a surprisingly effective nonadaptive representation for objects with edges. In Curve and Surface Fitting, Cohen A, Rabut C, Schumaker L L (Eds), Saint-Malo:Vanderbilt University Press.1999.
[6]Penne E Le, Mallat S. Image compression with geometrical wavelets. In Proceedings of IEEE Conference on Image Processing (ICIP'00). Vancouver, Canada, September.2000,1(1):661-664.
[7]Do M N, Vetterli M. The contourlet transform:An efficient directional multi-resolution image representation. IEEE Trans. Image Processing.2005, 14(12):2091-2106.
[8]Donoho D L. Wedgelets:nearly-minimax estimation of edges. Annals of Statistics. 1999,27(3):859-897.
[9]Donoho D L, Huo X M. Beamlet pyramids:a new form of multi-resolution analysis, suited for extracting lines, curves, and objects from very noise image data. Proceedings of SPIE, Wavelet Applications in Signal and Image Processing VIII, Aldroubi A, Laine A F, Unser M A (Eds),2000,4119:434-444.
[10]Donoho D L, Huo X M. Beamlets and Multiscale Image Analysis. Standford University, Report,2001.
[11]Meyer F G, Coifman R R. Directional image compression with brushlets. Proceedings of the IEEE-SP International Symposium on Time-Frequency and Time-Scale Analysis, Paris, France,1996,189-192.
[12]Meyer F G, Coifman R R. Brushlets:A Tool for Directional Image Analysis and Image Compression. Applied and Computational Harmonic Analysis.1997, 6(4):147-187.
[13]Easley G R, Labate D, Lim W Q. Optimally sparse multidimensional representations using shearlets. Fortieth Asilomar Conference on Signals, Systems and Computers (ACSSC'06).2006:974-978.
[14]Velisavljevic V, Beferull-Lozano B, Vetterli M. Approximation power of directionlets. Proceedings of IEEE International Conference on Image Processing (ICIP'05).2005,1(1):741-744.
[15]Velisavljevic V, Beferull-Lozano B, Vetterli M, et al. Directionlets:anisotropic multi-directional representation with separable filtering. IEEE Trans. on Image Processing.2006,15(7):1916-1933.
[16]Velisavljevic V, Beferull-Lozano B, Vetterli M. Space-frequency quantization for image compression with directionlets. IEEE Trans. Image Processing.2007,16(7): 1761-1773.
[17]侯彪,刘芳,焦李成.基于脊波变换的直线特征检测.中国科学.2003,33(1)：65-73.
[18]Tan S, Zhang X R, Jiao L C. Dual ridgelet frame constructed using biorthonormal wavelet basis. Proceedings of IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASS'05).2005:997-1000.
[19]Tan S, Zhang X R, Jiao L C. Monoscale dual ridgelet frame.in:Proceedings of International Conference on Image Analysis and Recognition. Toronto, Canada, 2005,3449:263-269.
[20]李伟,杨晓慧,石光明等.基于几何多尺度方向窗的小波图像去噪.西安电子科技大学学报(自然科学版).2006,33(5).682-686.
[21]张旭东、卢国栋、冯健.图像编码基础和小波压缩技术——原理、算法和标准.第1版.北京：清华大学出版社.2004.
[22]吴乐南.数据压缩.北京：电子工业出版社,2000.
[23]Huffman D.A, A method for the construction of minimum redundancy codes, Proc.IRE,1952, (40):1098-1111.
[24]Rafael C.Gonzalez, Richard E.Woods,阮秋琦等译.Digital Image Processing, (Second Edition),数字图像处理(第二版),电子工业出版社.
[25]R.J.Clark. Transform Coding of Images. Academic Press, New York.1985.
[26]王志武,丁国清,颜国正等.多传感器数据融合在切割机器人系统中的应用.上海交通大学学报.2002(7),36(7)：995-998.
[27]Yu Song, Mantian Li. A New Wavelet Based Multi-focus Image Fusion Scheme and Its Application on Optical Microscopy. Robotics and Biomimetics. IEEE International Conference.2006:401-405.
[28]A.Toet. Multiscale contrast enhancement with application to image fusion. Optical Engineering.1992,31(5):1026-1031.
[29]M.Pavel, J.Larimer, A.Ahumada. Sensor fusion for synthetic vision. Society for InformationDisplay Digest of Technical Papers.1992:475-478.
[30]P.J.Burt, R.J.Lolczynski. Enhanced image capture through fusion. In:Proceedings of the 4th International Conference on Computer Vision. Berlin, Germany.1993. 173-182.
[31]S.Richard, F.Sims, M.A Phillips. Target signature consistency of image data fusion alternatives. Optical Engineering,1997,36(3):743-754.
[32]G.K.Matsopoulos, S.Marshall, J.Brunt. Multiresolution morphological fusion of MR and CT images of the human brain. In:Proceedings of IEE, Vision, Image and Signal Processing.1994,141(3):137-142.
[33]Pennec. E.L, Mallat. S. Image compression with geometrical wavelets [A]. In Proc. Of ICIP'2000[C].Vancouver, Canada.2000,9:661-664.
[34]Fukanaga. K, Hostetler. L. D. The Estimation of the Gradient of a Density Function, with Application in Pattern Recognition. IEEE Trans. Information Theory.1975,21:32-40.
[35]Comaniciu. D, Meer. P. Mean shift:a robust approach toward feature space analysis. IEEE trans. Pattern Analysis and Machine Intelligence.2002,24(5): 603-619.
[36]Fukunaga. K. Introduction to statistical pattern recognition, Second Ed.. Boston: Academic Press,1990.
[37]Yi Z CH. Mean Shift, Mode Seeking, and Clustering. IEEE Transactions on Pattern Analysis and Machine Intelligence.1995,17(8):790-799.
[38]Comaniciu. D, Meer. P. Mean Shift:A Robust Approach towards Feature Space Analysis, IEEE Trans. Pattern Analysis and Machine Intelligence.2002,24(5): 603-619.
[39]Bradski. G. R. Real Time Face and Object Tracking as a Component of a Perceptual User Interface, Proc. IEEE Workshop on Applications of Computer Vision, Princeton.1998:214-219.
[40]Comaniciu. D, Ramesh. V, Meer. P. Real-Time Tracking of Non-Rigid Objects Using Mean Shift, Proc. IEEE Conference on Computer Vision and Pattern Recognition.2000:142-149.
[41]Comaniciu.D, Ramesh. V, Meer. P. Kernel-Based Object Tracking, IEEE Trans. Pattern Analysis and Machine Intelligence.2003,25(5):564-577.
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