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中国工业与应用数学学会会刊
主管：中华人民共和国教育部
主办：西安交通大学
ISSN 1005-3085  CN 61-1269/O1
工程数学学报

工程数学学报 ›› 2024, Vol. 41 ›› Issue (3): 421-431.doi: 10.3969/j.issn.1005-3085.2024.03.003

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基于局部高斯分布模型的图像配准方法

张  婧,  全婷婷   

  1. 天津城建大学理学院，天津 300384
  • 收稿日期:2021-11-22 接受日期:2023-06-08 出版日期:2024-06-15 发布日期:2024-08-15
  • 基金资助:
    国家自然科学基金 (11802200).

A Local Gaussian Distribution Model for Image Registration

ZHANG Jing,  QUAN Tingting   

  1. School of Science, Tianjin Chengjian University, Tianjin 300384
  • Received:2021-11-22 Accepted:2023-06-08 Online:2024-06-15 Published:2024-08-15
  • Supported by:
    The National Natural Science Foundation of China (11802200).

摘要：

提出了一种基于统计和变分相结合的非刚体图像配准新模型。假设残差图像服从具有不同均值和方差的局部高斯分布，由此得到一个双重能量泛函，再结合变分的正则化方法，得到了一种配准新模型。该方法的新颖之处在于，保真项中引入了权重函数和一些控制参数。其中权重函数可以自动有效地区分残差图像中灰度对比度不同的区域，控制参数的引入提高了算法的鲁棒性。合成图像、二维肺部CT及三维大脑MRI图像的配准结果证明了这一方法的有效性和准确性。

关键词: 非刚体图像配准, 局部高斯分布, 加性算子分裂, 交替极小化算法

Abstract:

This paper proposes a new non-rigid image registration model based on the combination of statistical and variational methods. Assuming that the residual image obeys a local Gaussian distribution with different means and variances, a dual energy functional is obtained. Combined with the variational regularization method, a new registration model is obtained in this paper. The novelty of this method lies in the introduction of weighting functions and some control parameters in the fidelity term. The weighting functions can automatically and effectively distinguish regions with different grayscale contrasts in residual image, and the control parameters improve the robustness of the algorithm. The registration results of synthetic images, two-dimensional lung CT, and three-dimensional brain MRI images demonstrate the effectiveness and accuracy of this method.

Key words: non-rigid image registration, local Gaussian distribution, additive operator splitting, alternating minimization algorithim

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