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摘要: 提出一种基于混合特征的非刚性点阵配准算法.该算法包含了对应关系评估与空间变换更新两个相互交替的步骤.首先定义了两个特征描述法用于描述两个点阵之间的全局和局部几何结构特征差异，随后合并这两个特征描述法建立一个基于混合特征的能量优化方程.该能量优化方程可以利用线性分配技术进行求解，同时可以灵活地选择使用最小化全局结构特征差异或最小化局部结构特征差异来评估两个点阵之间的对应关系.为了增强前述两个步骤之间的协调性，我们利用能量权重调节在整个配准过程中控制能量优化从最小化局部结构特征差异逐步转变为最小化全局结构特征差异，同时控制用于空间变换的薄板样条函数（Thin plate spline）的更新从刚性变换逐步转变为非刚性变换.我们在二维轮廓配准、三维轮廓配准、序列图像配准和图像特征点配准下对本文算法进行了各项性能测试，同时也与当前8种流行算法进行了性能比较.本文算法展现了卓越的非刚性配准性能，并在大部分实验中超越了当前的相关算法.Abstract: We present a novel non-rigid point set registration method with mixed features. The proposed method is designed by an alternating two-step process: correspondence estimation and transformation updating. We first design a global and a local feature descriptors for assessing the global and local structural differences between two point sets, respectively. The two feature descriptors are then combined for forming a mixed feature based energy function, so as to provide a flexible way to estimate correspondences by minimizing global or local structural differences using a linear assignment solution. To improve the interactions between the two steps, a tradeoff of energy adjustment is used to gradually adjust the energy minimization from local to global structural differences and the thin plate spline transformation from rigid to non-rigid during registration. We evaluate the performances of our method in contour registration, sequence images and real images; through comparision with other eight state-of-the-art methods, our method shows the best alignments in most deformation and rotation scenarios.
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图 1 二维轮廓点阵配准下的性能对比(误差线表示了100次随机测试中平均误差的标准偏差值.从第1行至第4行分别为点阵Line,Fish 1,Chinese character以及Fish2的实验结果.
Fig. 1 Comparison of our results against CPD,TPS-RPM and GMMREG on 2D contour point set registration (The error bars indicate the standard deviations of the mean errors in100 random experiments. From the top row to bottom row are: Line,Fish 1,Chinese character and Fish 2,respectively.
图 4 本文算法的配准实例: Chinese character
Fig. 4 Registration examples on Chinese character point set
图 6 三维Face轮廓点阵配准下的性能对比 (误差线表示了100次随机测试中平均误差的标准偏差值.)
Fig. 6 Comparison of our results against CPD and GMMREG on3D face contour point set registration (The error bars indicate the standard deviations of the mean errors in 100 random experiments.)
图 10 不同能量权重调节参数设定下的配准性能
Fig. 10 Relationships between performances and different energy tradeoff adjustment parameter settings
表 1 本文算法与相关算法的不同
Table 1 Methodological differences between our method and the current methods
算法 对应关系评估 空间变换更新 使用的特征 对应关系 约束条件 空间变换方程 本文算法 混合特征 B TPS 能量方程 1 TPS TPS-RPM 高斯概率密度 F TPS 能量方程 2 TPS CPD 高斯概率密度 F MCC-NLL GRBF GMMREG 高斯概率密度 F 最小化 L2 距离 TPS Ma 等[29] Shape context B L2E 评估子[30] RKHS Wang 等[31] MoAG F 最小化 L2 距离 RKHS 注: B: 二值对应; F: 模糊对应; GRBF (Gaussian radial basis function): 高斯径向基函数; TPS: 薄板样条函数; MCC-NLL(Motion coherence constraint based negative log-likelihod):基于运动一致性的负对数似然; RKHS (Reproducing kernel Hilbert space): 再生核Hilbert空间; MoAG (Mixture of asymmetric Gaussian model): 混合非对称高斯模型; 在TPS能量方程 2中, $λ_{2}\textrm{tr}(d-I)^{\rm T}(d-I)$ 被加到了式(7) (TPS能量方程 1) 来控制仿射变换. 
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表 2 CMU house和CMU hotel序列图像中所有可能的图像配准结果 (%)
Table 2 Matching rates on the CMU house and CMU hotel for all possible image pairs (%)
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表 3 汽车与摩托车图像库的配准结果 (%)
Table 3 Matching rates on cars and motorbikes (%)
本文算法 CPD GMMREG A B 93 80 82 80 80
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表 4 Jonker-Volgenant 算法性能 (测试矩阵由 Matlab 的 rand 函数自动生成.)
Table 4 Performance of Jonker-Volgenant algorithm (The cost matrices were generated by Matlab rand function.)
矩阵大小 200 500 1 000 2 000 3 000 所需时间 (秒) 0.002 0.016 0.100 0.316 0.588
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