A fast terrain matching algorithm based on 3D Zernike moment
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摘要: 针对当前基于3D Zernike矩的地形匹配算法存在计算量大、实时性差的问题，通过分析3D Zernike矩的计算过程和构成地形特征向量的奇偶阶描述子的性能，提出了适用于地形匹配的3D Zernike矩快速计算方法和只使用奇数阶描述子构成特征向量的匹配方式. 仿真实验表明：本文所提快速算法不仅能大幅降低计算量，还提高了匹配精度.
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关键词:
- 3D Zernike矩 /
- 地形匹配 /
- 快速算法 /
- 奇数阶描述子 /
- 偶数阶描述子
Abstract: In view of the current terrain matching algorithm based on 3D Zernike moment, which is computationally heavy and has poor real-time performance, this paper proposes a fast calculation method of 3D Zernike moment for terrain matching and a matching method that only uses odd-order descriptors to form feature vectors. The forming of method is based on the analysis of the computational process of 3D Zernike moments and the performance of odd-order descriptors. The simulation results show that the fast algorithm proposed in this paper can not only significantly reduce the amount of computation, but also improve the matching accuracy.-
Key words:
- 3D Zernike moment /
- terrain matching /
- fast algorithm /
- odd-order descriptor /
- even-order descriptor
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表 3
${ \varOmega _{n,l}^m} $ 与${r,s,t}$ 组合的对应关系${ \varOmega _{n,l}^m} $ r s t ${ \varOmega _{n,l}^m} $ r s t $ \varOmega _{2,0}^0 $ 0 0 0 $ \varOmega _{3,1}^1 $ 0 1 0 0 0 2 1 0 2 0 2 0 0 3 0 2 0 0 1 0 0 $ \varOmega _{2,2}^0 $ 0 0 2 1 0 2 0 2 0 1 2 0 2 0 0 2 1 0 $ \varOmega _{2,2}^1 $ 1 0 1 0 0 3 0 1 1 $ \varOmega _{3,3}^0 $ 0 0 3 $ \varOmega _{2,2}^2 $ 0 2 0 0 2 1 1 1 0 2 0 1 2 0 0 $ \Omega _{3,3}^1 $ 0 1 2 $ \varOmega _{3,1}^0 $ 0 0 1 0 3 0 0 0 3 1 0 2 0 2 1 1 2 0 2 0 1 2 1 0 $ \varOmega _{3,3}^3 $ 0 1 0 3 0 0 1 0 2 $ \varOmega _{3,3}^2 $ 0 2 1 0 3 0 1 1 1 1 0 0 2 0 1 
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表 4 各阶次描述子编号
编号 描述子 1~2 ${F_{2,0}},{F_{2,2}}$ 3~4 ${F_{3,1}},{F_{3,3}}$ 5~7 ${F_{4,0}},{F_{4,2}},{F_{4,4}}$ 8~10 ${F_{5,1}},{F_{5,3}},{F_{5,5}}$ 11~14 ${F_{6,0}},{F_{6,2}},{F_{6,4}},{F_{6,6}}$ 15~18 ${F_{7,1}},{F_{7,3}},{F_{7,5}},{F_{7,7}}$ 19~23 ${F_{8,0}},{F_{8,2}},{F_{8,4}},{F_{8,6}},{F_{8,8}}$ 24~28 ${F_{9,1}},{F_{9,3}},{F_{9,5}},{F_{9,7}},{F_{9,9}}$ 29~34 ${F_{10,0}},{F_{10,2}},{F_{10,4}},{F_{10,6}},{F_{10,8}},{F_{10,10}}$
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表 5 噪声标准差5 m情况下的匹配概率
转角 精确匹配概率/% 全阶 奇数阶 偶数阶 0° 94.1 99.0 80.6 15° 75.9 88.8 49.5 30° 78.3 88.2 51.7 45° 69.6 82.0 42.2
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[1] FLUSSER J, ZITOVA B, SUK T. Moments and moment invariants in pattern recognition[M]. Hoboken: John Wiley and Sons, 2009: 186-208. [2] 胡修林, 车龙, 叶斌. 3D Zernike矩在三维地形匹配中应用[J]. 测绘科学, 2007, 32(1): 107-108, 164. DOI: 10.3771/j.issn.1009-2307.2007.01.041 [3] NOVOTNI M, KLEIN R. 3D Zernike descriptors for content based shape retrieval[C]//The 8th ACM Symposium on Solid Modeling and Applications, 2003: 216-225. DOI: 10.1145/781606.781639 [4] POZO J M, VILLA-URIOL M C, FRANGI A F. Efficient 3D geometric and Zernike moments computation from unstructured surface meshes[J]. IEEE transactions on pattern analysis and machine intelligence, 2011, 33(3): 471-484. DOI: 10.1109/TPAMI.2010.139 [5] HOSNY K M, HAFEZ M A. An algorithm for fast computation of 3D Zernike moments for volumetric images[J]. Mathematical problems in engineering, 2012(2): 1-17. DOI: 10.1155/2012/353406 [6] Al-RAWI M S. 3D (pseudo) Zernike moments: fast computation via symmetry properties of spherical harmonics and recursive radial polynomials[C]//The 19th IEEE International Conference on Image Processing, 2012: 2353-2356. DOI: 10.1109/ICIP.2012.6467369 [7] WANG K D, ZHU T Q, GAO Y F, et al. Efficient terrain matching with 3-D Zernike moments[J]. IEEE transactions on aerospace and electronic systems, 2019, 55(1): 226-235. DOI: 10.1109/TAES.2018.2849921 -
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