基于细分曲面的医学假体CAD关键造型技术研究
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摘要
随着科技的进步与生活水平的提高,现代外科医学中精确设计制造人工假体来修复病损器官的案例日益增多,这对CAD/CAM技术提出了面向生物医学的特殊要求,也将刺激与推动CAD/CAM技术本身的创新。本文的研究以基于分片光滑细分曲面表示的医学假体CAD系统的开发为目标,从医学图像的输入到假体制造接口的输出,研究了医学图像的三维重建、三角网格模型处理、细分曲面拟合、基于细分曲面的实体造型与RP加工接口表示等关键造型技术,主要研究内容和成果如下:
(1)建立了基于细分曲面表示的医学假体CAD系统的总体架构,分别从技术体系与功能模块两个角度来阐述。技术体系包括基础理论、实现工具与临床应用三个层次,为进一步的研究指明了方向;功能模块从软件实现的角度描述了医学假体CAD系统的总体框架,为系统持续开发与完善打下了坚实的基础。
(2)研究了医学图像三维重建之MC算法的拓扑稳健与高效运行的实现方法。实现了无拓扑歧义的MC算法;为了提高原MC算法的效率,将区域增长分割的思想纳入到MC算法中,提出了一种基于相邻立方体跟踪的MC算法。
(3)研究了面向细分曲面拟合的三角网格简化与形状优化技术。为了得到细分曲面拟合所需要的尽量简单而又形状优良的基网格,现有算法与软件都难以单独奏效,本文采用了多种策略来达此目的。首先在QEM简化算法的边折叠代价计算公式基础上添加了形状优化项,用系数α来控制该项的影响大小,称为αShape-QEM简化算法;其次,将基于切向Laplace平滑的顶点几何优化以及基于边折叠与边交换的网格拓扑优化集成到总体简化过程中,提出了迭代式网格简化优化算法。
(4)提出了基于交互式优化的细分曲面拟合算法,可在计算效率与拟合精度之间取得最佳平衡。首先对输入原始网格M_O用前述方法简化优化得到基网格M_B,再用M_B对M_O进行若干次细分重网格化(Remeshing)得到逼近原始网格M_O的细分网格M R,对M R进行细分拟合得到控制网格M_C,使得M_C的细分极限曲面M_∞与原始网格M_O互相贴合。
(5)提出了“支持细分曲面的构造实体边界表示(Constructive Solid Boundary Representation with Subdivision Surfaces,CSBrepSS)”实体造型方法。该方法采用混合CSG/Brep表示,实体模型在整体上用CSG树表示,整个模型为基本边界表示的叶节点的组合,叶结点可以是三角网格、细分曲面控制网格或参数表示的基本几何体。
(6)提出了一种基于细分曲面的RP加工接口表示方法。RP系统可以用内嵌的细分曲面造型模块读入细分曲面控制网格表示的CAD模型,按照模型中指定的细分规则与特征标记对控制网格进行细分,然后再对细分结果作切片处理与分层加工。这样可以用紧凑的细分控制网格来表示形状复杂的光滑曲面,为大型复杂假体的网络化制造铺平了道路。
With the development of advanced technologies and improvement of life quality, accurately designed and manufactured artificial prosthesis for sick organ repairing is applied more and more often in modern surgery. This needs to adapt traditional CAD/CAM systems to the particular requirement of bio-medicine application, also will impulse the innovation of CAD/CAM technology itself.
The research of this dissertation aims at the development of a medical prosthesis CAD system based on piece-wise subdivision surfaces. Thus, the research objects are the key modeling technologies for the system, from the medical image input to the manufacturing interface output, including medical image three-dimensional reconstruction, triangular mesh processing, subdivision surfaces fitting, subdivision surfaces based solid modeling and rapid prototyping manufacturing interface representation, etc. The main research contents and achievements are as following in detail:
(1) An overall architecture of medical prosthesis CAD system based on subdivision surfaces is established, which is described in the two viewports: technological hierarchy and functional modules. The technological hierarchy consistes three levels: fundamental theory, realization tool and clinic applications, which is a good guide for further research. The functional modules describe how to implement the system, which paves the way for the system lasting development.
(2) The topology robust and efficient Marching Cube algorithm for medical image 3D reconstruction is implemented. An ambiguity resolved MC algorithm is implemented; to improve the efficiency of the original MC algorithm, the idea of Region Growing Segmentation is put into MC algorithm, and the Neighbor Cubes Tracing based MC algorithm is put forward.
(3) The method of triangular mesh smoothing, simplification and shape optimization for subdivision surfaces fitting is implemented. To get the base mesh well shaped and as compact as possible for subdivision surfaces fitting, none available algorithms and software can succeed along. In this dissertation, multi-policies are adopted to achieve the goal. First, a shape optimization item is added to the edge collapse cost computation formula of the original QEM algorithm, and a coefficientαis used for controlling the shape item’s effect on the overall cost, the method is calledαShape-QEM simplification algorithm. Second, the Tangent Laplace Smoothing based mesh vertex geometric optimization and the Local Topology Adjusting based mesh topology optimization is integrated into the overall simplification process, thus the Iterative Mesh Simplification and Optimization algorithm is put forward.
(4) The Interactive Optimization based Subdivision surface Fitting algorithm is put forward, by which the computational efficiency and fitting accuracy can be balanced best. First, the inputted original mesh M_O is simplified and optimized to base mesh M_B, which is Subdivision Remeshed several times to get M R that fitted to M_O, then M R is subdivision fitted to control mesh M_C, from which the subdivision limit mesh M_∞that fits M_O is gotten.
(5) The solid modeling method of“Constructive Solid Boundary Representation with Subdivision Surfaces (CSBrepSS)”is put forward. Using hybrid CSG/Brep representation, the whole solid model is a CSG tree made of leaf nodes with basic Brep, which include triangular mesh, subdivision surface control mesh and basic geometries with parametric representation.
(6) A subdivision surfaces based RP interface representation method is put forward. Using the embedded subdivision surface modeling module, RP equipments can read CAD models represented with subdivision control mesh, subdivide the control mesh to generate smooth models with the subdivision rule and feature tags provided in the control mesh, then slice the result mesh and generate machining code. Thus, complex smooth surface can be represented with compact subdivision control mesh, and it paves the way of networked manufacturing of large complex prostheses.
(1)建立了基于细分曲面表示的医学假体CAD系统的总体架构,分别从技术体系与功能模块两个角度来阐述。技术体系包括基础理论、实现工具与临床应用三个层次,为进一步的研究指明了方向;功能模块从软件实现的角度描述了医学假体CAD系统的总体框架,为系统持续开发与完善打下了坚实的基础。
(2)研究了医学图像三维重建之MC算法的拓扑稳健与高效运行的实现方法。实现了无拓扑歧义的MC算法;为了提高原MC算法的效率,将区域增长分割的思想纳入到MC算法中,提出了一种基于相邻立方体跟踪的MC算法。
(3)研究了面向细分曲面拟合的三角网格简化与形状优化技术。为了得到细分曲面拟合所需要的尽量简单而又形状优良的基网格,现有算法与软件都难以单独奏效,本文采用了多种策略来达此目的。首先在QEM简化算法的边折叠代价计算公式基础上添加了形状优化项,用系数α来控制该项的影响大小,称为αShape-QEM简化算法;其次,将基于切向Laplace平滑的顶点几何优化以及基于边折叠与边交换的网格拓扑优化集成到总体简化过程中,提出了迭代式网格简化优化算法。
(4)提出了基于交互式优化的细分曲面拟合算法,可在计算效率与拟合精度之间取得最佳平衡。首先对输入原始网格M_O用前述方法简化优化得到基网格M_B,再用M_B对M_O进行若干次细分重网格化(Remeshing)得到逼近原始网格M_O的细分网格M R,对M R进行细分拟合得到控制网格M_C,使得M_C的细分极限曲面M_∞与原始网格M_O互相贴合。
(5)提出了“支持细分曲面的构造实体边界表示(Constructive Solid Boundary Representation with Subdivision Surfaces,CSBrepSS)”实体造型方法。该方法采用混合CSG/Brep表示,实体模型在整体上用CSG树表示,整个模型为基本边界表示的叶节点的组合,叶结点可以是三角网格、细分曲面控制网格或参数表示的基本几何体。
(6)提出了一种基于细分曲面的RP加工接口表示方法。RP系统可以用内嵌的细分曲面造型模块读入细分曲面控制网格表示的CAD模型,按照模型中指定的细分规则与特征标记对控制网格进行细分,然后再对细分结果作切片处理与分层加工。这样可以用紧凑的细分控制网格来表示形状复杂的光滑曲面,为大型复杂假体的网络化制造铺平了道路。
With the development of advanced technologies and improvement of life quality, accurately designed and manufactured artificial prosthesis for sick organ repairing is applied more and more often in modern surgery. This needs to adapt traditional CAD/CAM systems to the particular requirement of bio-medicine application, also will impulse the innovation of CAD/CAM technology itself.
The research of this dissertation aims at the development of a medical prosthesis CAD system based on piece-wise subdivision surfaces. Thus, the research objects are the key modeling technologies for the system, from the medical image input to the manufacturing interface output, including medical image three-dimensional reconstruction, triangular mesh processing, subdivision surfaces fitting, subdivision surfaces based solid modeling and rapid prototyping manufacturing interface representation, etc. The main research contents and achievements are as following in detail:
(1) An overall architecture of medical prosthesis CAD system based on subdivision surfaces is established, which is described in the two viewports: technological hierarchy and functional modules. The technological hierarchy consistes three levels: fundamental theory, realization tool and clinic applications, which is a good guide for further research. The functional modules describe how to implement the system, which paves the way for the system lasting development.
(2) The topology robust and efficient Marching Cube algorithm for medical image 3D reconstruction is implemented. An ambiguity resolved MC algorithm is implemented; to improve the efficiency of the original MC algorithm, the idea of Region Growing Segmentation is put into MC algorithm, and the Neighbor Cubes Tracing based MC algorithm is put forward.
(3) The method of triangular mesh smoothing, simplification and shape optimization for subdivision surfaces fitting is implemented. To get the base mesh well shaped and as compact as possible for subdivision surfaces fitting, none available algorithms and software can succeed along. In this dissertation, multi-policies are adopted to achieve the goal. First, a shape optimization item is added to the edge collapse cost computation formula of the original QEM algorithm, and a coefficientαis used for controlling the shape item’s effect on the overall cost, the method is calledαShape-QEM simplification algorithm. Second, the Tangent Laplace Smoothing based mesh vertex geometric optimization and the Local Topology Adjusting based mesh topology optimization is integrated into the overall simplification process, thus the Iterative Mesh Simplification and Optimization algorithm is put forward.
(4) The Interactive Optimization based Subdivision surface Fitting algorithm is put forward, by which the computational efficiency and fitting accuracy can be balanced best. First, the inputted original mesh M_O is simplified and optimized to base mesh M_B, which is Subdivision Remeshed several times to get M R that fitted to M_O, then M R is subdivision fitted to control mesh M_C, from which the subdivision limit mesh M_∞that fits M_O is gotten.
(5) The solid modeling method of“Constructive Solid Boundary Representation with Subdivision Surfaces (CSBrepSS)”is put forward. Using hybrid CSG/Brep representation, the whole solid model is a CSG tree made of leaf nodes with basic Brep, which include triangular mesh, subdivision surface control mesh and basic geometries with parametric representation.
(6) A subdivision surfaces based RP interface representation method is put forward. Using the embedded subdivision surface modeling module, RP equipments can read CAD models represented with subdivision control mesh, subdivide the control mesh to generate smooth models with the subdivision rule and feature tags provided in the control mesh, then slice the result mesh and generate machining code. Thus, complex smooth surface can be represented with compact subdivision control mesh, and it paves the way of networked manufacturing of large complex prostheses.
引文
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