一种三维图像欧拉数快速计算方法
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摘要
欧拉数是二值图像的重要拓扑属性之一.针对现有三维图像欧拉数计算方法中存在的像素存取次数过多的问题,提出了一种新的基于三维立方体模式计数的三维图像欧拉数算法.首先改变处理立方体模式时像素的检查顺序,对于部分立方体模式只需检查一个像素即可完成处理;然后通过合并部分立方体模式,尽量减少处理一个立方体模式所需检查的像素个数,提高算法效率.在较为复杂的不同密度三维噪声图像上的实验结果表明,该算法在绝大多数情况下都要优于现有三维图像欧拉数算法.
The Euler number is one of the most important topological properties in a binary image.A new Euler number computing algorithm for 3 D images is proposed to reduce the redundant pixel accesses existed in the conventional algorithm based on cube pattern counting.Firstly,the pixel checking order is changed in processing cube patterns,and only one pixel will be checked for processing a cube pattern in some cases.Then,the number of pixels needs to be checked for processing a cube pattern is reduced by merging some cube patterns,and the efficiency of the algorithm is improved.The experimental results on complex 3 D noise images with different densities demonstrated that the proposed algorithm is better than the conventional Euler number algorithm in most cases.
The Euler number is one of the most important topological properties in a binary image.A new Euler number computing algorithm for 3 D images is proposed to reduce the redundant pixel accesses existed in the conventional algorithm based on cube pattern counting.Firstly,the pixel checking order is changed in processing cube patterns,and only one pixel will be checked for processing a cube pattern in some cases.Then,the number of pixels needs to be checked for processing a cube pattern is reduced by merging some cube patterns,and the efficiency of the algorithm is improved.The experimental results on complex 3 D noise images with different densities demonstrated that the proposed algorithm is better than the conventional Euler number algorithm in most cases.
引文
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[15] 杨敬安,张奠成.三维数字图象Euler数新的有效计算法[J].应用科学学报,1992,10(4):339-346.
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[17] 林小竹,籍俊伟,黄寿萱,等.关于三维图像Euler数的新公式的证明[J].模式识别与人工智能,2010,23(1):52-58.
[18] H.Sánchez Cruz,H.Sossa Azuela,U.D.Braumann.The Euler-Poincaré formula through contact surfaces of voxelized objects[J].Journal of Applied Research and Technology,2013,11(2):65-78.
[2] A.Hashizume,R.Suzuki,H.Yokouchi,et al.An algorithm of automated RBC classification and its evaluation[J].Bio Medical Engineering,1990,28(1):25-32.
[3] 原玉磊,蒋理兴,钦桂勤.基于字符特征的数字字符识别算法[J].海洋测绘,2009,29(1):56-58.
[4] 王华军,冯露菲,王雪丽,等.非饱和土壤内部水-气界面特性的微CT分析[J].太阳能学报,2016,37(12):3 104-3 108.
[5] K.Ramani,K.Lou,S.Jayanti,et al.Three-dimensional shape searching:State-of-the-art review and future trends[J].Computer-Aided Design,2005,37(5):509-530.
[6] H.J.Vogel,K.Roth.Quantitative morphology and network representation of soil pore structure[J].Advances in Water Resources,2001,24:233-242.
[7] A.Pierret,Y.Capowiez,L.Belzunces,et al.3D reconstruction and quantification of macropores using X-ray computed tomography and image analysis[J].Geoderma,2002,106:247-271.
[8] P.Lehmann,M.Berchtold,B.Ahrenholz,et al.Impact of geometrical properties on permeability and fluid phase distribution in porous media[J].Advances in Water Resources,2008,31(9):1 188-1 204.
[9] A.Velichko,C.Holzapfel,A.Siefers,et al.Unambiguous classification of complex microstructures by their three-dimensional parameters applied to graphite in cast iron[J].Acta Materialia,2008,56(9):1 981-1 990.
[10] L.Kubínová,X.Mao,J.Janácek.Blood capillary length estimation from three-dimensional microscopic data by image analysis and stereology[J].Microscopy and Microanalysis,2013,19:898-906.
[11] C.M.Park,A.Rosenfeld.Connectivity and genus in three dimension[D].Washington:University of Maryland,College Park,1971.
[12] C.N.Lee,A.Rosenfeld.Computing the euler number of a 3D image[C]// First IEEE International Conference on Computer Vision.London:IEEE,1987:567-571.
[13] D.G.Morgenthaler.Three dimension digital topology:the Genus[D].Washington:University of Maryland,College Park,1980.
[14] A.Nakamura,K.Aizawa.On the recognition of properties of three-dimensional pictures[J].IEEE Transactions on Pattern Analysis and Machine Intelligence,1985,PAMI-7(6):708-713.
[15] 杨敬安,张奠成.三维数字图象Euler数新的有效计算法[J].应用科学学报,1992,10(4):339-346.
[16] P.K.Saha,B.B.Chaudhuri.3D digital topology under binary transformation with applications[J].Computer Vision and Image Understanding,1996,63(3):418-429.
[17] 林小竹,籍俊伟,黄寿萱,等.关于三维图像Euler数的新公式的证明[J].模式识别与人工智能,2010,23(1):52-58.
[18] H.Sánchez Cruz,H.Sossa Azuela,U.D.Braumann.The Euler-Poincaré formula through contact surfaces of voxelized objects[J].Journal of Applied Research and Technology,2013,11(2):65-78.