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摘要: 经典的Active demons算法利用参考图像和浮动图像的梯度信息作为驱动力，并使用均化系数调节两种驱动力之间的强度.该算法克服了Demons算法单一使用参考图像的梯度信息作为驱动力的缺点，但是Active demons算法中的均化系数无法同时兼顾大形变和小形变区域的准确配准，还会导致配准的收敛速度和精确度相互制约的问题.为此，本文提出一种新的Active demons非刚性配准算法.提出的算法在Active demons扩散方程中引入一个称为平衡系数的新参数，与均化系数联合调整驱动力，不仅可以兼顾图像中同时具有的大形变和小形变区域的准确配准，而且在一定程度上缓和了收敛速度和精确度相互制约的问题.为了进一步提高配准的收敛速度和精确度，避免陷入局部极值，在新的配准算法的实现中引入由粗到细的多分辨率策略.在Checkboard测试图像、自然图像和医学图像上的实验结果表明，提出的算法较经典的Active demons算法收敛速度更快，配准精度平均提高了54.28%，接近最新的TV-L1光流场图像配准算法的配准精度，解决了Active demons算法存在的问题.
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关键词:
- 非刚性配准 /
- Active demons算法 /
- 光流场图像配准 /
- 驱动力 /
- 多分辨率策略
Abstract: Classic active demons algorithm uses gradient information of the static image and the moving image as driving forces, and uses a homogeneous coefficient to adjust their intensities. Although the algorithm overcomes the disadvantage of the demons algorithm using the gradient information of a single static image, the homogeneous coefficient of the active demons algorithm can not accurately handle registration with both large deformation and small deformation, and will cause the mutual restraint problem of convergence speed and registration accuracy. In order to solve this problem, this paper presents a non-rigid registration algorithm based on active demons algorithm, which introduces a new parameter called balance coefficient to the active demons algorithm to adjust the driving force in combination with the homogeneous coefficient. Not only can the large deformation and small deformation be taken into account at the same time, but also the mutual restraint problem of speed and accuracy can be eased to a certain extent. In order to further improve registration accuracy and convergence speed and avoid falling into local extremes, a coarse-to-fine multi-resolution strategy is introduced into the registration process. Experiments on checkboard test images, natural images and medical images demonstrate that the proposed algorithm is faster and more accurate. The registration accuracy is improved by 54.28% on average, and is close to that of the latest TV-L1 optical flow image registration algorithm. -
图 7 平衡系数对改进Active demons算法的影响
Fig. 7 The impact of balance coefficient k on the improved active demons registration algorithm
图 8 均方差与均化系数和平衡系数的关系曲线
Fig. 8 The relations of the mean square error with the α and the k
图 10 图像的配准结果与参考图像的差值
Fig. 10 The differences between the registration results and the static image
图 12 图像的配准结果与参考图像的差值
Fig. 12 The differences between the registration results and the static image
图 15 图像的配准结果与参考图像的差值图
Fig. 15 The differences between the registration results and the static image
图 17 图像的配准结果与参考图像的差值图
Fig. 17 The differences between the registration results and the static image
表 1 两种算法的配准结果均方差对比
Table 1 The comparison of two registration algorithms on the MSE
α 0.05 0.1 0.4 0.5 0.6 AD(×10−4) 3.55 4.02 6.49 8.18 10 IAD(×10−4) 2.25 2.35 3.71 4.29 5.27 α 1.0 1.5 2 2.5 3 AD(×10−4) 34 107 187 255 311 IAD(×10−4) 12 47 113 183 246 
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表 2 配准结果的客观分析
Table 2 The objective analysis of registration results
评价方法 Demons AD SIAD MIAD TV-L1 均方差(×10−4) 43 40 29 25 11 相互系数(%) 99.16 99.24 99.44 99.52 99.98 峰值信噪比 54.43 55.31 58.36 59.97 87.74 归一化互信息 1.42 1.42 1.43 1.43 0.71 结构相似度(%) 95.42 95.74 96.82 97.41 99.97
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表 3 配准结果的客观分析
Table 3 The objective analysis of registration results
评价方法 Demons AD SIAD MIAD TV-L1 均方差(×10−4) 13 8.11 6.19 2.81 4.61 相互系数(%) 96.35 97.69 98.25 99.22 99.87 峰值信噪比 66.59 71.15 73.87 81.75 91.49 归一化互信息 1.37 1.29 1.39 1.41 3.96 结构相似度(%) 88.55 90.99 92.56 96.28 99.11
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表 4 配准结果的客观分析
Table 4 The objective analysis of registration results
评价方法 Demons AD SIAD MIAD TV-L1 R 5.09 5.03 5.12 18.69 2.50 均方差(×10−5) G 5.07 5.10 5.33 17.68 2.47 B 4.69 4.79 5.01 16.71 3.20 R 99.84 99.92 99.92 99.90 99.99 相互系数(%) G 99.86 99.86 99.85 99.83 99.98 B 99.92 99.84 99.83 99.81 99.71 R 91.07 91.12 91.04 90.19 94.16 峰值信噪比 G 91.08 91.05 90.86 90.43 94.20 B 91.42 91.33 91.14 90.67 93.08 R 3.25 3.26 3.25 3.27 3.98 归一化互信息 G 3.17 3.17 3.16 3.17 4.03 B 3.02 3.02 3.00 3.01 3.63 R 98.87 97.49 97.56 97.71 99.21 结构相似度(%) G 98.99 97.46 97.41 97.44 99.27 B 98.70 97.30 97.23 97.23 98.89
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表 5 配准结果的客观分析
Table 5 The objective analysis of registration results
评价方法 Demons AD SIAD MIAD TV-L1 均方差(×10−5) 4.78 7.53 3.06 0.81 8.56 相互系数(%) 99.81 99.70 99.88 99.97 99.97 峰值信噪比 99.51 94.94 103.94 117.26 98.81 归一化互信息 1.43 1.31 1.44 1.54 3.49 结构相似度(%) 98.71 98.44 99.03 99.76 99.34
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表 6 配准结果的客观分析
Table 6 The objective analysis of registration results
评价方法 Demons AD SIAD MIAD TV-L1 均方差(×10−4) 30 19 16 14 11.4 相互系数(%) 97.21 98.26 98.50 98.75 99.06 峰值信噪比 58.08 62.81 64.29 66.05 77.56 归一化互信息 1.38 1.39 1.41 1.43 2.90 结构相似度(%) 83.55 89.27 89.61 94.40 98.77
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表 7 几种算法的配准结果均方差值比较
Table 7 The objective analysis of difference algorithms
Cases AD SIAD MIAD Pe(s) Pe(M) (×10−4) (×10−4) (×10−4) (%) (%) 1 40 29 25 27.5 37.5 2 8.11 6.19 2.81 23.00 65.00 3 0.497 0.515 1.769 16.67 53.33 4 0.753 0.306 0.081 59.32 89.28 5 19 16 14 15.79 26.32 Average — — — 28.45 54.28
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