隐式表达三维模型流水线的关键技术研究
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摘要
作为国家自然科学基金项目(项目号:60275012),广东省普通高校自然科学研究重点项目(项目号:04Z010),以及深圳市科技计划项目(项目号:200341)的重要研究内容之一,本论文旨在隐式表达的框架下,围绕三维数字成像及造型流水线中涉及的三个核心技术,即三维系统标定、多视点深度图像的匹配以及多视点深度图像的合成,从理论上和实践上进行深入系统的研究与探讨。
论文的主要研究内容和取得的主要研究进展有:
1.分析并论证了根据径向基函数插值构造变分隐式曲面进行曲面重建的优缺点,并在此基础上确定了基于隐式表达的匹配和合成多视点深度图像的研究方案。以实验室搭建的三维扫描器为工具实现三维建模流水线的标定、匹配和合成三个过程。
2.设计点阵图案,利用位错点阵成像原理和基准传递概念标定三维扫描器,为重建三维模型提供精确数据。实验结果表明,经过标定的三维扫描器,对300×300×80mm~3的测量体积内,可以获得X方向的标准差为0.288mm,Y方向的标准差为0.238mm和Z方向的标准差为0.292mm的测量精度。
3.估计三维扫描器在多个视点的位置姿态,以此作为多视点深度图像匹配的初值。将数字投影仪的投射过程,当作摄像机成像的逆过程。提出了“相位-坐标”的变换方法,利用投射正交的条纹图,快速寻找成像平面和投影平面上的对应点。将极线几何约束原理应用于主动三维视觉系统,并在考虑到采样数据受噪声影响的条件下建立了优化多视点位姿估计的数学模型。通过求解所建立的数学模型可以获得三维扫描器在多视点的位置姿态的优化估计。同时,此模型还可以应用于同步自标定三维扫描器的设备参数。这种方法不需要任何已知三维坐标的标定参照物,改善和提高了三维扫描器的实用性。
4.针对同类合成方法中经常用到的符号距离函数,在向量空间进行了严格和系统的数学公式化证明和明确的几何解释,并在此基础上利用“最小二乘逼近深度曲面上的点到等值面上的对应点的距离”和“空间向量图解”的方法建立一个广义且规范的隐式曲面方程。重新解释设置“权函数”的标准以及隐式曲面造型中的其他一些几何关系,将相邻视点间的关系和深度图像采样点的可靠性考虑到权函数里,合成多个视点生成的变分隐式曲面。
As important research contents of the National Natural Science Foundation of China (Grant No. 60275012), the Natural Science Research Grant of Higher Education of Guangdong province (Grant No. 04Z010), and the Science & Technology Bureau of Shenzhen (Grant No. 200341), this thesis focuses on the three key issues of three dimensional pipeline-modeling based on implicit representation. Those issues involve in the calibration method for three dimensional vision system, the registration method for multi-view range images and the integration method for multi-view range images. Both theoretical and experimental aspects are considered, and some innovative research outcomes have been accomplished.
The main research contents and contributions made by this thesis are summarized as follows:
1. The surface reconstruction method using variational implicit surface with radial basis function interpolation was exploited in detail. On the basis of this analysis, we developed an efficient scheme for the registration and the integration of multiple range images. Moreover, we built up an in-house 3D scanner with which we demonstrated our approaches.
2. With the concept of benchmark transmission and shifted point array encoding we developed a method for calibrating our 3D scanner. Experiment results showed that after the proposed calibration procedure the 3-D vision system was able to achieve such an accuracy as the standard deviation in X direction was 0.288mm, 0.238mm in Y direction, and 0.292mm in Z direction, respectively, for a measuring volume of 300×300×80mm~3.
3. To register multiple range images, we presented a method for the pose estimation for 3D scanner based on the principle of fringe projection. The projector could be conceptually regarded as a camera that works in a reversed mode. To determine homologous points in the proposed camera/projector configuration, the phase map was converted to the u, v coordinates using two orthogonal fringe sequences. Taking epipolar geometry into account, this approach could further realize the estimation of arbitrary pose of view point and achieve a self-calibration of the 3D scanner by minimizing the squared distances between those imaging points and their corresponding epipolar lines. With this procedure, we were able to simultaneously calculate the parameters of the orientation and the system structure. Parameters with moderate accuracy could be estimated even if the input data deteriorated with the noise was presented. Because this procedure didn’t need a priori 3D calibration reference, the practicability of the 3D scanner had been therefore improved.
4. The signed-distance function has been used frequently in most of integration methods based on implicit representation. In this thesis, we expanded the definition of signed-distance function in a vector space. Furthermore we developed a generalized implicit equation (GIE) by virtue of a strict mathematical formulation and a geometric reasoning. The GIE was a canonical implicit equation and was constructed by using least-mean-square approximation and vector-map reasoning. With the GIE, we could reexplain how to establish a weighted function and other geometric relations. Finally, we integrated multiple range images with the technique of variational implicit surfaces. In this process, the embedded relationship among the neighboring viewpoints and reliability of data points used in the weighted function should be considered.
论文的主要研究内容和取得的主要研究进展有:
1.分析并论证了根据径向基函数插值构造变分隐式曲面进行曲面重建的优缺点,并在此基础上确定了基于隐式表达的匹配和合成多视点深度图像的研究方案。以实验室搭建的三维扫描器为工具实现三维建模流水线的标定、匹配和合成三个过程。
2.设计点阵图案,利用位错点阵成像原理和基准传递概念标定三维扫描器,为重建三维模型提供精确数据。实验结果表明,经过标定的三维扫描器,对300×300×80mm~3的测量体积内,可以获得X方向的标准差为0.288mm,Y方向的标准差为0.238mm和Z方向的标准差为0.292mm的测量精度。
3.估计三维扫描器在多个视点的位置姿态,以此作为多视点深度图像匹配的初值。将数字投影仪的投射过程,当作摄像机成像的逆过程。提出了“相位-坐标”的变换方法,利用投射正交的条纹图,快速寻找成像平面和投影平面上的对应点。将极线几何约束原理应用于主动三维视觉系统,并在考虑到采样数据受噪声影响的条件下建立了优化多视点位姿估计的数学模型。通过求解所建立的数学模型可以获得三维扫描器在多视点的位置姿态的优化估计。同时,此模型还可以应用于同步自标定三维扫描器的设备参数。这种方法不需要任何已知三维坐标的标定参照物,改善和提高了三维扫描器的实用性。
4.针对同类合成方法中经常用到的符号距离函数,在向量空间进行了严格和系统的数学公式化证明和明确的几何解释,并在此基础上利用“最小二乘逼近深度曲面上的点到等值面上的对应点的距离”和“空间向量图解”的方法建立一个广义且规范的隐式曲面方程。重新解释设置“权函数”的标准以及隐式曲面造型中的其他一些几何关系,将相邻视点间的关系和深度图像采样点的可靠性考虑到权函数里,合成多个视点生成的变分隐式曲面。
As important research contents of the National Natural Science Foundation of China (Grant No. 60275012), the Natural Science Research Grant of Higher Education of Guangdong province (Grant No. 04Z010), and the Science & Technology Bureau of Shenzhen (Grant No. 200341), this thesis focuses on the three key issues of three dimensional pipeline-modeling based on implicit representation. Those issues involve in the calibration method for three dimensional vision system, the registration method for multi-view range images and the integration method for multi-view range images. Both theoretical and experimental aspects are considered, and some innovative research outcomes have been accomplished.
The main research contents and contributions made by this thesis are summarized as follows:
1. The surface reconstruction method using variational implicit surface with radial basis function interpolation was exploited in detail. On the basis of this analysis, we developed an efficient scheme for the registration and the integration of multiple range images. Moreover, we built up an in-house 3D scanner with which we demonstrated our approaches.
2. With the concept of benchmark transmission and shifted point array encoding we developed a method for calibrating our 3D scanner. Experiment results showed that after the proposed calibration procedure the 3-D vision system was able to achieve such an accuracy as the standard deviation in X direction was 0.288mm, 0.238mm in Y direction, and 0.292mm in Z direction, respectively, for a measuring volume of 300×300×80mm~3.
3. To register multiple range images, we presented a method for the pose estimation for 3D scanner based on the principle of fringe projection. The projector could be conceptually regarded as a camera that works in a reversed mode. To determine homologous points in the proposed camera/projector configuration, the phase map was converted to the u, v coordinates using two orthogonal fringe sequences. Taking epipolar geometry into account, this approach could further realize the estimation of arbitrary pose of view point and achieve a self-calibration of the 3D scanner by minimizing the squared distances between those imaging points and their corresponding epipolar lines. With this procedure, we were able to simultaneously calculate the parameters of the orientation and the system structure. Parameters with moderate accuracy could be estimated even if the input data deteriorated with the noise was presented. Because this procedure didn’t need a priori 3D calibration reference, the practicability of the 3D scanner had been therefore improved.
4. The signed-distance function has been used frequently in most of integration methods based on implicit representation. In this thesis, we expanded the definition of signed-distance function in a vector space. Furthermore we developed a generalized implicit equation (GIE) by virtue of a strict mathematical formulation and a geometric reasoning. The GIE was a canonical implicit equation and was constructed by using least-mean-square approximation and vector-map reasoning. With the GIE, we could reexplain how to establish a weighted function and other geometric relations. Finally, we integrated multiple range images with the technique of variational implicit surfaces. In this process, the embedded relationship among the neighboring viewpoints and reliability of data points used in the weighted function should be considered.
引文
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