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摘要: 针对多视角点云配准问题，本文设计了一个合理的目标函数，便于将多视角配准问题分解成多个双视角配准问题，并考虑了两个要素：1）各帧点云均具有其他所有点云所未覆盖的区域；2）基准帧点云的重要程度高于其他点云.为了求解该目标函数，本文提出了逐步求精的解决策略：根据给定的配准初值构造初始模型，依次取出基准帧以外的每帧点云，利用所提出的双视角配准算法计算该帧点云的配准参数，并修正模型，以便进一步计算后续点云的配准参数.遍历完全部点云构成一次完整的循环，多次循环后可获得精确的多视角配准结果.公开数据集上的实验结果表明，本文所提出的方法能够精确、可靠地实现多视角点云配准.Abstract: For registration of multi-view point sets, this paper designs a reasonable objective function. This objective function allows to easily decompose the multi-view registration problem into several pair-wise registration problems. It also considers two important factors:1) each point set contains regions, which are non-overlapping to all other point sets; 2) the point set attached to the reference frame is more important than other point sets. To solve this function, it then proposes a strategy of stepwise refinement:Given the initial registration parameters, the pair-wise registration algorithm sequentially aligns each point set with the coarse model, which is reconstructed by other initially aligned point sets. Then the pair-wise registration results can be immediately returned to refine the coarse model for registration of other point sets. Accurate results for registration can be obtained by multiple loops, where each complete loop is comprised by traversing all point sets. Experimental results carried on public data sets demonstrate its superiority to achieve registration of multi-view point sets.1) 本文责任编委 黄庆明
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图 2 逐步求精的多视角点云配准方法原理图
Fig. 2 The framework of stepwise refinement approach for the registration of multi-view point sets
图 3 逐步求精的多视角点云配准方法原理图
Fig. 3 The framework of stepwise refinement approach for the registration of multi-view point sets
图 4 不同噪声水平下的各多视角点云配准方法对比结果
Fig. 4 Comparison results of competed approaches under different noise levels
图 5 基于多视角点云配准方法的三维场景重建结果
Fig. 5 3D reconstructed result of scene based on the multi-view registration approach
表 1 复杂度分析结果
Table 1 Complexity analysis results
操作 计算复杂度 执行次数 构造不完整模型 O$(M_i)$ 1 创建$k$-d树 O$({M{'}}\lg {M{'}})$ 1 建立点对关系 O$({M_{i}}\lg {M{'}})$ $\le K$ 计算权重 O$({M_{i}})$ $\le K$ 计算刚体变换 O$({M_{i}})$ $\le K$ 更新模型 O$(M_i)$ 1 
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表 2 测试数据集的基本信息
Table 2 The basic information of testing datasets
Armadillo Buddha Bunny Dragon 点云帧数 12 15 10 15 总点数 307 625 1 099 005 362 272 469 193
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表 3 各种逐步求精策略的配准结果
Table 3 Registration results of different stepwise refinements
数据集 初始 SRICP SRbICP SReICP SRwICP ${e_{{R}}}$ ${e_{ t}}$ ${e_{{R}}}$ ${e_{ t}}$ ${e_{{R}}}$ ${e_{ t}}$ ${e_{{R}}}$ ${e_{ t}}$ ${e_{{R}}}$ ${e_{ t}}$ Bunny 0.0588 1.3296 0.0114 0.9066 0.0148 1.1977 0.0085 0.8186 0.0071 0.4539 Dragon 0.0400 1.5015 0.0210 1.7705 0.0102 0.9778 0.0100 0.8231 0.0071 0.8042
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表 4 不同多视角点云配准方法的实验对比结果
Table 4 Results of different multi-view registration approaches
数据集 初始 MA[20] LRS[21] 本文算法 ${e_{{R}}}$ ${e_{ t}}$ ${e_{{R}}}$ ${e_{ t}}$ 时间(min) ${e_{{R}}}$ ${e_{ t}}$ 时间(min) ${e_{{R}}}$ ${e_{ t}}$ 时间(min) Armadillo 0.0509 0.9856 0.0318 1.8868 0.1811 0.0188 3.0913 0.3290 0.0039 0.9247 0.7000 Buddha 0.0382 1.4313 0.0127 0.9337 0.6772 0.0102 0.8960 1.7947 0.0066 0.9834 3.9372 Bunny 0.0588 1.3296 0.0110 0.6797 0.1896 0.0116 0.9009 0.6883 0.0071 0.4539 0.5684 Dragon 0.0400 1.5015 0.0170 1.1386 0.2446 0.0244 1.5335 0.4572 0.0071 0.8042 0.2930
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