基于广义Ricci曲率及深度信息的图像采样方法
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摘要
随着采样技术的提高、数据量的剧增,给数据的存储及传输造成了一定困难,因此对数据进行重采样,以压缩数据量是解决该问题的一个有效手段.针对灰度图像采样问题,利用密度流形的广义Ricci曲率提出一种采样点之间相关性的衡量方法.首先,将图像看做是对二维流形的着色,通过处理目标物的深度或构造其深度,保留需要着重采样区域的深度信息;其次,结合深度与灰度信息计算密度流形的Ricci曲率;最后,根据相关性原则筛选采样点并重建图像.此外,针对采样过程提出了全局采样及加速的局部采样2种方式,用于权衡速度与精度.采用大量的标准测试图进行实验结果表明,该方法可以有效地应用于灰度图像的压缩;与已有方法相比,该方法在灰度变化剧烈、复杂的边缘采样点分布更为密集,同时对灰度变化平缓的区域采样点也相对更少.
The improvement of sampling technology and the dramatic increasement of data have affected the storage and transmission of data, thus resampling is an important issue to compress the big amount of data.In this paper, we peer into the sampling techniques of gray scale images. Ricci curvature in density manifolds is introduced to obtain the measurement of sampling points. First of all, images are regarded as the color-patch map of two-dimensional manifolds. The auxiliary or constructed depth information is filtered to make the object areas kept for resampling. Then, both depth and gray information are leveraged to get the Ricci curvature in density manifolds. Finally, the candidate sampling points are selected and the image is reconstructed based on the measurement relationship. In addition, in order to balance the speed and precision of the reconstruction, both global sampling and local sampling are proposed. A large number of standard test images are used in the experiments, and the results show that the proposed method can be used to compress gray image effectively. Compared with the state-of-the-arts, the proposed method has more sampling points distributed on the edge of the object area where the gray value changes dramatically, while the sampling points are relatively less in the smooth area.
The improvement of sampling technology and the dramatic increasement of data have affected the storage and transmission of data, thus resampling is an important issue to compress the big amount of data.In this paper, we peer into the sampling techniques of gray scale images. Ricci curvature in density manifolds is introduced to obtain the measurement of sampling points. First of all, images are regarded as the color-patch map of two-dimensional manifolds. The auxiliary or constructed depth information is filtered to make the object areas kept for resampling. Then, both depth and gray information are leveraged to get the Ricci curvature in density manifolds. Finally, the candidate sampling points are selected and the image is reconstructed based on the measurement relationship. In addition, in order to balance the speed and precision of the reconstruction, both global sampling and local sampling are proposed. A large number of standard test images are used in the experiments, and the results show that the proposed method can be used to compress gray image effectively. Compared with the state-of-the-arts, the proposed method has more sampling points distributed on the edge of the object area where the gray value changes dramatically, while the sampling points are relatively less in the smooth area.
引文
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[3]Unser M.Sampling-50 years after Shannon[J].Proceedings of the IEEE,2000,88(4):569-587
[4]Eldar Y,Lindenbaum M,Porat M,et al.The farthest point strategy for progressive image sampling[J].IEEE Transactions on Image Processing,1997,6(9):1305-1315
[5]Ramponi G,Carrato S.An adaptive irregular sampling algorithm and its application to image coding[J].Image and Vision Computing,2001,19(7):451-460
[6]Sochen N,Kimmel R,Malladi R.A general framework for low level vision[J].IEEE Transactions on Image Processing,1998,7(3):310-318
[7]Leibon G,Letscher D.Delaunay triangulations and Voronoi diagrams for Riemannian manifolds[C]//Proceedings of the 16th Annual Symposium on Computational Geometry.New York:ACM Press,2000:341-349
[8]Cheng S W,Dey T K,Ramos E A.Manifold reconstruction from point samples[C]//Proceedings of the 16th Annual ACM-SIAM Symposium on Discrete Algorithms.Philadelphia:Society for Industrial and Applied Mathematics Press,2005:1018-102
[9]Saucan E,Appleboim E,Zeevi Y Y.Sampling and reconstruction of surfaces and higher dimensional manifolds[J].Journal of Mathematical Imaging and Vision,2008,30(1):105-123
[10]Saucan E,Appleboim E,Zeevi Y Y.Geometric approach to sampling and communication[J].Sampling Theory in Signal&Image Processing,2012,11(1):1-24
[11]Lin S,Luo Z X,Zhang J L,et al.Generalized Ricci curvature based sampling and reconstruction of images[C]//Proceedings of the 23rd European Signal Processing Conference.Los Alamitos:IEEE Computer Society Press,2015:604-608
[12]Morgan F.Manifolds with density[J].Notices of the American Mathematical Society,2005,52(8):853-858
[13]Bakry D,émery M.Diffusions hypercontractives[C]//Proceedings Soféminaire de Probabilités XIX 1983/84.Heidelberg:Springer,1985,1123:177-206
[14]Bakry D,Ledoux M.Lévy-Gromov’s isoperimetric inequality for an infinite dimensional diffusion generator[J].Inventiones Mathematicae,1996,123(1):259-281
[15]Lai K,Bo L F,Fox D.Unsupervised feature learning for 3Dscene labeling[C]//Proceedings of the IEEE International Conference on Robotics and Automation.Los Alamitos:IEEEComputer Society Press,2014:3050-3057