计算机科学

计算机科学 ›› 2024, Vol. 51 ›› Issue (6): 206-214.doi: 10.11896/jsjkx.230400090

• 计算机图形学&多媒体 • 上一篇    下一篇

基于加权有界形变函数的可形变图像配准模型

闵莉花, 丁田中, 金正猛   

  1. 南京邮电大学理学院 南京 210023
  • 收稿日期:2023-04-13 修回日期:2023-10-13 出版日期:2024-06-15 发布日期:2024-06-05
  • 通讯作者: 金正猛(jinzhm@njupt.edu.cn)
  • 作者简介:(mlh@njupt.edu.cn)
  • 基金资助:
    国家自然科学基金面上项目(12271262);南京邮电大学自然科学基金(NY221097)

Deformable Image Registration Model Based on Weighted Bounded Deformation Function

MIN Lihua, DING Tianzhong, JIN Zhengmeng   

  1. School of Science,Nanjing University of Posts and Telecommunications,Nanjing 210023,China
  • Received:2023-04-13 Revised:2023-10-13 Online:2024-06-15 Published:2024-06-05
  • About author:MIN Lihua,born in 1986,Ph.D,asso-ciate professor.Her main research interests include partial differential equations,numerical optimization and image processing.
    JIN Zhengmeng,born in 1982,Ph.D,professor,Ph.D supervisor.His main research interests include partial diffe-rential equations,numerical optimization and image processing.
  • Supported by:
    National Natural Science Foundation of China(12271262) and Natural Science Foundation of Nanjing University of Posts and Telecommunications(NY221097).

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摘要： 可形变图像配准是图像处理领域中一个非常重要的课题,是计算机视觉中最基本的问题之一,也是医学图像分析的一个难题。文中研究了两幅单模态灰度图像之间的图像配准问题,充分考虑了参考图像的边缘信息,提出了一个新的基于加权有界形变函数的可形变图像配准模型。首次提出了加权的有界形变函数空间,给出了该空间的定义及相关结论,并从理论上证明了所提模型解的存在性。同时,利用梯度下降法设计了有效的算法进行数值求解,分别在合成图像和医学图像上进行数值实验。实验结果和定量评估结果表明,与对比模型相比,所提模型由于引入了控制函数且将加权有界形变函数作为正则项,得到了更精确的配准结果,特别是在图像边缘及一些细节处配准效果有明显提高。

关键词: 可形变图像配准, 加权有界形变函数, 变分方法, 梯度下降法

Abstract: Deformable image registration is a very important topic in the field of image processing.It is one of the most basic problems in computer vision,and also a difficult point in medical image analysis.In this paper,we study the image registration of two uni-modal grayscale images.A new deformable image registration model based on the weighted bounded deformation function is proposed by fully considering the edge information of the reference image.In addition,the paper firstly proposes a weighted bounded deformation function space in which the definition and related conclusions are given.Theoretically,we prove the exis-tence of solutions to the proposed model.Furthermore,an effective algorithm is designed based on the gradient descent method to numerically solve the model.Moreover,numerical experiments which are also performed on synthetic images and medical images respectively show that,compared with other comparison models,the proposed model can obtain more accurate registration results by introducing control functions and using weighted bounded deformation functions as regular terms,especially in the image edge.

Key words: Deformable image registration, Weighted bounded deformation function, Variation method, Gradient descent method

中图分类号: 

  • TN911.73
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