【作者】 成思源；

【导师】 张湘伟；

【作者基本信息】 重庆大学 ， 固体力学， 2003， 博士

【摘要】 轮廓提取与表面重建是计算机视觉中的重要研究课题，其在虚拟现实、自控车辆、机器人环境分析、监控系统中的物体跟踪与识别、生物医学图像处理、工业在线自动检测、形状反求等方面有着广泛的应用前景。基于断层数据的三维重建是通过提取被测物体的截面轮廓曲线以实现被测对象的三维反求和重构的一种测量方法，是目前国内外研究的热点。根据断层图像提取的实体轮廓可以通过表面重建得到物体的CAD模型，或直接应用于快速成形系统。在此过程中，从断层测量图像中提取实体轮廓是关键的一步。近年来，将物理原理引入物体的形状恢复吸引了学者们的研究兴趣，基于可变形模型的轮廓提取与表面重建就是其中的一类。可变形模型可视为在内力和外力作用下的能量极小化样条模型，内力来自几何模型，约束它的形状；外力来自图像特征，引导它的行为，将其吸引至图像特征处。可变形模型的提出给传统的计算机视觉理论及应用研究带来了新的观点和思维方式，已经被越来越多的研究者成功地应用于图像分割、运动跟踪、3D重建、立体匹配等许多领域，并已发展成为计算机视觉与模式识别中最为活跃和成功的研究领域之一。因此，基于可变形模型的断层图像轮廓提取与表面重建研究，在科学研究及工程应用中有着重要的意义。本论文主要针对医学断层图像的轮廓提取与表面重建，重点对B样条可变形模型进行了研究。本文在系统地分析了国内外关于可变形模型理论与应用研究的基础上，提出了一种基于有限元法的B样条主动轮廓模型；并将其应用于由断层图像导出的截面轮廓数字曲线的拟合，利用自适应有限元技术提高拟合精度；最后将其推广到三维，提出了基于有限元法的B样条主动曲面模型。本文主要工作和结论如下：（1）对可变形模型的基础理论进行了论述，并从弹性理论的观点对可变形模型的物理本质进行讨论分析；然后从几何表达、能量方程及优化方法三个方面对可变形模型的理论研究与发展进行了综述，指出了可变形模型理论上存在的问题及进一步研究的方向。（2）提出了一种基于有限元法的B样条主动轮廓模型。B样条方法是当前自由曲线曲面造型最为流行的方法，而有限元法是一种有效地求解泛函极值问题的数值方法。该模型以三次B样条曲线段作为有限单元，运用有限元法对B样条主动轮廓的能量泛函极值问题进行求解，从而实现对图像的轮廓提取。该模型结合了B样条方法与有限元法的优点，可快速稳定地收敛到目标轮廓，得到的B样条轮廓有利于进一步的表面重建处理。 <WP=6>（3）提出了基于自适应有限元的B样条主动轮廓模型，并将其应用于基于断层图像的表面重建。首先对断层图像的边缘提取方法进行了论述，针对得到的截面轮廓数字曲线，提出了一种基于自适应B样条主动轮廓拟合方法。该方法避免了传统插值、近似方法中的采样点数量、分布及参数化过程所带来的问题，通过在拟合过程中插入新的控制点，提高拟合精度，实现对数字轮廓的整体逼近。最后，由各断层截面的B样条轮廓重构出物体的三维模型。（4）将二维的B样条主动轮廓模型扩展到三维，提出了基于有限元法的B样条主动曲面模型。通过在数据点与模型之间连接虚拟弹簧，建立光顺模型，并以双三次B样条曲面片作为单元，运用有限元法对模型在虚拟弹簧作用下的变形问题进行求解，得到光顺后的B样条曲面；并在此基础上，提出了一种新的基于断层数据的表面重建方法，可很好地解决不均匀截面族的曲面生成问题。更多还原

【Abstract】 Contour extraction and surface reconstruction is an important problem in computer vision, and can be used extensively in many fields such as virtual reality, autonomous guided vehicles, robot environment analysis, object tracking and recognition in monitor system, biology medical image processing, industry online automatic checking and reverse engineering etc. 3D reconstruction based on layer data has been a hot point of research and new direction of reverse engineering. The contours extracted from cross-sections can be used to surface reconstruction to obtain the object’s CAD model, or can be used directly to prototyping system. During this process, contour extraction form cross-section is the key step.In the last few years, introducing physics principle into shape recovery has attracted researchers’ attention, and deformable model based contour extraction and shape reconstruction is one kind. A deformable model is an energy-minimizing spline model controlled by internal forces and external forces. Internal forces come from geometry model which constrain its shape, and external forces come from image data which guide its movement and pull it toward image feature. Deformable models which bring a new viewpoint to traditional computer vision have been successfully applied to many fields in computer vision such as image segmentation, motion tracking, 3D reconstruction and stereo matching etc., and have become one of the most active and successful fields in computer vision and pattern recognition.Therefore, cross-sectional contour extraction and surface reconstruction based on deformable models is important signification of theory and application. Aim at medical cross-sections, the research work of this dissertation put emphasis on B-spline deformable model. In this dissertation, based on the systematically analysis of theory and application research on deformable model, a new B-spline active contour based on the finite element method (FEM) is proposed; then B-spline active contour is applied to fitting the digital curve cross-sectional contour, and adaptive FEM is adopted to improve the precision; lastly the model is generalized to 3D, and a B-spline active surface model based on FEM is proposed. The main work and conclusions in this dissertation are as follows:(1) The basic theory of deformable model is expatiated and the physical essence of deformable model is discussed from the viewpoint of elasticity theory. The research, <WP=8>development and application of deformable model is reviewed from geometry representation, energy function and optimization method, and the existing problems and possible future research orientations are presented. (2) A B-spline active contour model based on FEM is presented. B-spline is the most popular method to represent free-form curve and surface, and FEM provides an efficient way to solve the functional minima problem. In this model, a cubic B-spline curve segment is used as one element, and the FEM is adopted to find the B-spline active contour which minimize its energy. Experiment results showes that this medel could effectively combine the merits of B-spline and EFM for active contour model, yielding stable, accurate and faster convergence, and its result is favorable for surface reconstruction.(3) A B-spline active contour model based on adaptive FEM is presented and applied to surface reconstruction from layer data. Firstly edge detection method for cross-sections is expatiated, and a B-spline active contour based on adaptive FEM is proposed to fit the digital contour curve. This method can avoid the sampling and parametrization problems result from traditional interpolation and approximation methods and improve fitting accuracy is gradually improved during fitting process by insert new control points to realize the satisfying result. Lastly 3D model is reconstructed from a set of planar B-spline contour. (4) To generalize the B-spline active contour to 3D, a B-spline active surface model based on FEM is proposed. By anchoring an imaginary spring between each data p更多还原