Medical Image Non-rigid Registration Based on Adaptive Fractional Order
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摘要: 现有的医学图像配准算法对于灰度均匀、弱边缘以及弱纹理图像易陷入局部最优从而导致配准精度低下、收敛速度缓慢. 分数阶主动Demons (Fractional active Demons, FAD)算法是解决该问题的有效方法, 并且适用于图像的非刚性配准. 但FAD中的最佳分数阶阶次是人工交互选取, 并且对整幅图像都是固定不变的. 为了解决该问题, 提出一种阶次自适应的主动Demons算法并将其应用到医学图像的非刚性配准中. 算法首先根据图像的局部特征建立分数阶阶次自适应的数学模型, 并逐像素计算最优阶次, 基于该阶次构造Riemann-Liouvill (R-L)分数阶微分动态模板; 然后将自适应R-L分数阶微分引入到Active Demons算法, 在一定程度上缓解了图像配准在弱边缘和弱纹理区域易陷入局部最优问题, 从而提高了配准精度. 通过在两个医学图像库上进行实验验证, 实验结果表明该方法可以处理灰度均匀、弱纹理和弱边缘的医学图像非刚性配准, 配准精度得到较大提升.
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关键词:
- 自适应分数阶 /
- 主动Demons算法 /
- 自适应模型 /
- 非刚性配准 /
- 医学图像
Abstract: The existing medical image registration methods have limitation in registration images with intensity uniformity, weak edges and weak texture, troubled by inclining to local minimum, which always result in low registration accuracy and efficiency. Active Demons algorithm with fractional differential has been proved to be effective for non-rigid image registration. However, it searches the optimal order of fractional differential manually, lack of order adaptive in images registration. To address the problem, this paper applies multi-resolution and adaptive fractional differential to active Demons, and proposes a novel images registration method for 3D medical images registration. Firstly, a mathematical model of adaptive order for fractional differential is constructed, which adopts local image features such as gradient magnitude and information entropy, therefore the optimal order and differential dynamic template are adjusted adaptively; Secondly, multi-resolution strategy is introduced to adaptive fractional differential active Demons algorithm, optimization falling into local minimum is avoided, therefore the registration accuracy is improved once more. Lastly, extensive experiments show that the proposed algorithm is capable of registration images with intensity uniformity and weak texture. And the optimal order of fractional differential can be calculated adaptively. Furthermore, the presented methods is capable of avoiding falling into local optimum, thus the registration accuracy can be improved greatly. -
图 2 不同切片层的BrainWeb图像配准结果
Fig. 2 Registration result of BrainWeb image of different slice layers
表 3 冠状面配准精度对比
Table 3 Comparison of registration accuracy of coronal plane
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表 4 矢状面配准精度对比
Table 4 Comparison of registration accuracy of sagittal plane
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表 5 横切面配准精度对比
Table 5 Comparison of registration accuracy of transverse plane
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表 6 不同算法的时间对比(s)
Table 6 Time comparison of two methods (s)
不同切片层的图像 文献 [13] 的方法 (不同的阶次) 本文方法 $ \alpha $ = 0.1$ \alpha $ = 0.2$ \alpha $ = 0.3$ \alpha $ = 0.4$ \alpha $ = 0.5$ \alpha $ = 0.6$ \alpha $ = 0.7$ \alpha $ = 0.8$ \alpha $ = 0.9总计时间 I 3.21 3.14 2.98 2.76 3.03 2.89 2.92 2.67 2.58 26.18 17.69 II 3.72 3.65 3.37 3.54 3.68 3.03 3.29 3.21 3.16 30.65 19.08 III 4.64 4.61 4.53 4.57 4.65 4.06 4.52 4.18 4.49 40.25 26.83
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表 7 两种策略的时间对比(s)
Table 7 Time comparison of two strategies (s)
图像 不采用多分辨率 采用多分辨率 I 30.25 17.69 II 28.04 19.08 III 40.63 26.83
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