【作者】 王锋；

【导师】 郑辉；

【作者基本信息】 南昌大学 ， 力学， 2022， 硕士

【摘要】 随着计算机技术在数字图像处理领域的大量应用,医学图像的三维重建技术取得了巨大进展。医学图像的三维重建首先需要将二维的医学断层扫描图像进行处理,进而得到目标组织外轮廓的相关数据,然后再利用各种重建算法对其进行三维重建,得到重建后的模型。重建得到的三维数字模型可用于辅助治疗、手术规划、生物力学分析,有着很大的实际应用价值。本文的主要研究内容为基于基本解法求解偏微分方程的医学图像三维重建技术。本文首先介绍了图像分割以及三维曲面重建的研究现状,然后以人体CT断层扫描图像为对象,将其在MATLAB环境下进行直方图均衡化,进而增强人体组织与图像背景的对比度,再使用高斯滤波对图像进行处理,得到降噪后的医学图像。在人体组织外轮廓的提取上,利用Canny算子能够获得单像素轮廓的这一优势,得到单向素且连续封闭的人体组织外轮廓点云数据。最后在保留人体组织完整特征的前提下,利用点云精简算法,对得到的点云数据进行精简处理,提高了后续三维重建工作的效率。本文在第四章中主要描述了基于基本解法求解偏微分方程进行隐式曲面重建的方法及其实现步骤。该方法通过基本解法求解给定边界条件的偏微分方程,得到源点强度,进而得到描述重建曲面的隐式函数,最后通过提取隐式函数中函数值与给定边值相等的等值面,完成对目标曲面的逼近。本文接着介绍了已有的调和方程以及双调和方程两种数值模型,在此基础之上,提出了一种只包含一个参数λ的改进双调和方程的数值模型,并使用上述三种数值模型分别实现了对单位立方体以及斯坦福兔的三维重建,通过分析重建效果,证明了我们提出的数值模型的可行性以及优越性。此外,我们通过数值实验确定了我们提出的数值模型中参数的取值对重建效果的影响,即当数值模型中的参数λ满足0.042 ≤λ×d_min ≤0.084时,可以有效地去除重建模型上的杂散曲面,得到良好的重建效果。最后,我们分别使用双调和方程以及改进双调和方程的数值模型实现了一系列CT图像的三维重建。结果表明,当合理取值参数λ时,我们提出的改进双调和方程的数值模型重建效果优于双调和方程的数值模型,可以有效地去除重建曲面上的杂散曲面,而当参数λ取值过大时,重建曲面上将产生可预测的分解。更多还原

【Abstract】 With the extensive application of computer technology in the field of digital image processing,great progress has been made in 3D reconstruction of medical images.The 3D reconstruction of medical images first needs to process the 2D medical tomographic images to obtain the relevant data of the outer contour of the target tissue,and then use various reconstruction algorithms to reconstruct it in 3D to obtain the reconstructed model.The reconstructed 3D digital model can be used for various purposes such as adjuvant therapy,surgical planning,and biomechanical analysis,and has great practical application value.The main research content of this paper is the 3D reconstruction technology of medical images based on the basic solution method to solve partial differential equations.This paper first introduces the research status of image segmentation and 3D surface reconstruction,and then takes the human CT tomography image as the object,performs histogram equalization in the MATLAB environment,and then enhances the contrast between the human tissue and the image background,and then uses Gaussian filtering.The image is processed to obtain a denoised medical image.In the extraction of the outer contour of human tissue,the Canny operator can be used to obtain the advantage of single-pixel contour,and the point cloud data of the outer contour of human tissue with unidirectional elements and continuous closure can be obtained.Finally,on the premise of retaining the complete characteristics of human tissue,the point cloud reduction algorithm is used to simplify the obtained point cloud data,which improves the efficiency of subsequent 3D reconstruction work.In the fourth chapter,this paper mainly describes the method and implementation steps of implicit surface reconstruction based on the method of fundamental solutions to solve partial differential equations.This method solves the partial differential equation of the given boundary condition through the method of fundamental solutions,obtains the intensity of the source point,and then obtains the implicit function describing the reconstructed surface.Complete the approximation to the target surface.This paper then introduces two existing numerical models of harmonic equations and biharmonic equations.On this basis,a numerical model of improved biharmonic equations containing only one parameter λ is proposed,and the above three numerical models are used respectively.The three-dimensional reconstruction of the unit cube and the Stanford Rabbit is realized,and the feasibility and superiority of the numerical model proposed by us are proved by analyzing the reconstruction effect.In addition,we have determined the influence of the values??of the parameters in our proposed numerical model on the reconstruction effect through numerical experiments,that is,when the parameter λ in the numerical model is satisfied,the stray surfaces on the reconstructed model can be effectively removed,and a good Rebuild effect.Finally,we achieved 3D reconstruction of a series of CT images using the biharmonic equation and the numerical model of the improved biharmonic equation,respectively.The results show that when the parameter λ is reasonably selected,the numerical model reconstruction effect of our improved biharmonic equation is better than the numerical model of the biharmonic equation,and the stray surfaces on the reconstructed surface can be effectively removed.When too large,a predictable decomposition will be produced on the reconstructed surface.更多还原