薄板样条函数在空间数据插值中的应用

薄板样条函数是空间数据插值中一种重要的方法,介绍了该方法的基本原理,并以珠江河道地形数据为例,借助地理信息系统的二次开发功能,将薄板样条函数应用于空间插值,通过与测试样本点以及克里金插值在最大值、标准误等方面的比较分析,证明薄板样条函数是一种有效的空间数据插值方法。     

基于薄板样条插值算法的巨幅影像分块并行处理

薄板样条函数是空间插值中的一种重要方法。对于巨幅影像数据使用薄板样条函数进行空间插值时,可能会出现运行时间太长,以及计算机内存空间不足或程序运行无响应的问题。针对这些问题,根据薄板样条函数光滑、连续的特点,基于GDAL开源函数库,提出对巨幅影像数据的分块读取,在块内利用并行技术求解线性方程组,确定薄板样条函数,最后进行空间插值的方法。结果表明,该方法可以有效的解决这些问题。     

薄板样条插值函数的改进与应用

薄板样条插值是应用较多的弹性配准方法.本文深入研究了这种方法,并就此方法的不足之处进行了详细的分析.针对薄板样条插值方法的不足,提出了两种新的处理方法,使薄板样条插值具有平滑性和紧支撑性,大大提高了配准的鲁棒性和适用性.     

混合插值法重构近地表模型

当控制点多和网格稠密时,基于薄板样条(TPS)插值的近地表模型重构往往很耗时,影响了静校正中近地表建模的效率.针对此问题,采用一种TPS插值和三次样条插值相结合的混合插值法重构近地表模型.首先利用矩阵递归LU分解及GPU加速的LU分解算法求解大型线性方程组,建立TPS插值函数;然后在X和Y方向上使用适当的步长对网格进行抽稀,运用TPS插值函数计算稀疏网格点的值,再通过稀疏网格点建立三次样条插值函数并计算剩余网格点的值;最后用OpenGL实现近地表模型的三维可视化.实验结果表明,文中算法提高了近地表模型重构的速度,其精度接近TPS插值精度.     

基于多分辨率策略的弹性配准方法

提出了一种基于多分辨率策略的医学图像弹性配准方法.首先通过使用多分辨率C-V模型来加快边界提取的速度,接着采用模拟退火结合薄板样条插值的方法来配准边界点.为了增强边界点配准算法的鲁棒性和速度,在退火过程中使用多分辨率策略来构造点集数据.最后利用薄板样条插值函数完成弹性变换.实验结果表明,算法对于大形变的情况依然具有很好的效果.     

薄板样条法和泛克里金法在理论和

研究插值方法以建立变量的数据场模型是科学计算可视化的重要内容。文中首先给出了薄板样条法和泛克里金法的插值原理,推导得出了泛克里金法的对偶形式,并论证了薄板样条法是泛克里金法的特例;然后对这两种方法在理论形式和实际应用方面进行了比较,得出的结论为泛克里金法的插值效果要优于薄板样条法的效果。     

薄板样条法和泛克里金法在理论和应用方面的比较

研究插值方法以建立变量的数据场模型是科学计算可视化的重要内容。文中首先给出了薄板样条法和泛克里金法的插值原理,推导得出了泛克里金法的对偶形式,并论证了薄板样条法是泛克里金法的特例;然后对这两种方法在理论形式和实际应用方面进行了比较,得出的结论为泛克里金法的插值效果要优于薄板样条法的效果。     

周期B样条基函数系数的并行算法

在现有周期B样条插值方法中,需要用迭代算法确定B样条基函数系数。针对现有方法的不足,建立B样条基函数系数的并行算法。首先构造周期区域的正交B样条基,得出正交B样条基函数系数的并行算法;进一步利用正交B样条基函数系数与B样条基函数系数的关系,得出B样条基函数系数的并行算法;最后推导二阶、三阶、四阶周期插值B样条基函数系数及插值点函数值的显式算式。实验证明了该方法在实现B样条基函数系数快速并行算法的同时保持了B样条基函数简单的函数关系。     

连续等距区间上积分值的二次样条插值

目的 在现实中,某些插值问题结点处的函数值往往是未知的,而仅仅已知一些区间上的积分值。为此提出一种给定已知函数在连续等距区间上的积分值构造二次样条插值函数的方法。方法 首先,利用二次B样条基函数的线性组合去满足给定的积分值和两个端点插值条件,该插值问题等价于求解n+2个方程带宽为3的线性方程组。然后,运用算子理论给出二次样条插值函数的误差估计,继而得到二次样条函数逼近结点处的函数值时具有超收敛性。最后,通过等距区间上积分值的线性组合逼近两个端点的函数值方法实现了不带任何边界条件的积分型二次样条插值问题。结果 选取低频率函数,对积分型二次样条插值方法和改进方法分别进行数值测试,发现这两种方法逼近效果都是良好的。同样,选取高频率函数对积分型二次样条插值方法进行数值实验,得到数值收敛阶与理论值相一致。结论 实验结果表明,本文算法相比已有的方法更简单有效,对改进前后的二次样条插值函数在逼近结点处的函数值时的超收敛性得到了验证。该方法对连续等距区间上积分值的函数重构具有普适性。     

带参数的C~3连续分段七次Hermite插值样条

针对分段三次Hermite插值样条在形状调控与连续性方面的不足,提出带2个参数的C~3连续分段七次Hermite插值样条.首先构造一组带2个参数的七次Hermite基函数;然后基于该组基函数定义分段七次Hermite参数样条曲线,并讨论样条曲线所带参数的选取方案;最后研究对应的分段七次Hermite样条插值函数,并给出其插值余项及最佳插值函数的确定方法.实例结果表明,当插值条件保持不变时,分段七次Hermite参数样条曲线不仅达到C~3连续,而且还可利用所带的参数实现对曲线形状的调控;通过确定所带参数的最佳取值,可使得分段七次Hermite样条插值函数获得较好的插值效果.     

利用Principal Warps评估颅面几何相似度

针对目前颅面相似度评估主要依靠主观验证、缺乏衡量相似度的物理量等问题,提出一种3维颅面几何相似度评估方法。将颅面相似度评估看做是待比较颅面到数据库中其余颅面的弯曲变形,计算出待比较颅面的Principal Warps作为新的基,给出颅面间对应全局特征点的选择方法,并利用薄板样条函数建立映射,从而计算出相应的弯曲变形矩阵,将该矩阵表示为基与系数矩阵的乘积。实现了在待比较颅面固定的情况下,用系数矩阵来衡量颅面间的变形程度,并在此基础上定义了颅面间几何相似度距离,给出了具体比较方法。实验结果验证了该方法的有效性。     

某型舰炮炮口冲击波等压场测试方法

针对现有军标中规定的炮口冲击波等压场测试方法不适用于某型舰炮炮口冲击波压力场的测试情况,提出了以极坐标布放传感器的测试方案,并测试了各点位的冲击波超压值。其次,提出采用三次样条函数方法对测试数据进行插值;最后,使用Delaunay三角划分方法对插值后的数据进行网格划分和等压线绘制,得到了某型舰炮的炮口冲击波等压场。     

Moving least squares interpolation with thin-plate splines and radial basis functions

Moving least-squares methods for interpolation or approximation of scattered data are well known, and can suffer from defects, such as flat spots in the Shepard method, and edge effects inherited from a polynomial basis in the higher degree cases. We investigate methods based on thin-plate splines and on other radial basis functions. It turns out that a small support of the weight function leads to a small support for the “spline basis” and associated efficiency in the evaluation of the approximant. The edge effects seem minimal and good interpolants of scattered data can be obtained.     

基于格网模型的等高线算法

提出了一种通过格网模型生成等高线的方法.通过计算规则格网模型中顶点的符号来确定等高线与格网中棱的交点数目,根据交点的数目和格网中心点的符号确定等高线的跟踪方向,对等高线上的点用样条曲线连接可得等高线.实验结果表明,此算法正确、有效,运行效率高.     

结合变形函数和幂函数权重的图像拼接

针对图像拼接算法存在效率低下、特征点错误匹配、重影和拼接缝等问题，提出一种基于尺度不变特征变换、薄板样条函数和幂函数的图像拼接方法。该方法通过对输入图像进行采样匹配，计算输入图像间的点映射关系和重合区域，使用点映射关系对重合区域内的特征点进行定向配准，利用特征点集合计算出图像的局部扭曲模型，使用图像插值方法对图像进行变形映射；采用幂函数权重模型对变形图像中的像素进行平滑过渡，完成图像拼接。实验结果表明，在拼接相同图像的情况下，所提方法与传统的尺度不变特征变换算法相比，特征点配准效率提高了约59.78%，而且得到了更多的特征点对；与经典的图像拼接算法相比，该方法解决了图像的重影和拼接缝的问题，同时提高了图像的质量评估指标的得分。     

A Blend of Subdivision Surfaces and NURBS

In present paper, the contour deletion method is developed both to blend surfaces and to fill N-sided holes, which is used for subdividing the NURBS surface. First, according to the non-uniform Catmull-Clark subdivision principle, surfaces are blended. The non-uniform Catmull-Clark subdivision method is constructed, which build the surface through interpolating corner vertices and boundary curves. Then the contour deletion method is adapted to remove the controlling mesh boundary contour in the process of segmentation iteration. Last, N sided-hole is filled to generate a integral smooth continuous surface. This method not only guarantee that the blending surface and base surface patches have C2 continuity at the boundary, but also greatly improve the smoothness of the N-side hole filling surface. The results show that, this method simplifies the specific computer-implemented process, broads the scope of application of subdivision surfaces, and solves the incompatible problem between the subdivision surface and classical spline. The resulting surface has both advantages of the subdivision surface and classical spline, and also has better filling effect.     

Design of walking gaits for Tao-Pie-Pie,a small humanoid robot

A new way for multi-axis robot trajectory planning using a single cubic spline incorporating velocity and acceleration clipping is presented. Equations for velocity and acceleration clipping employing the cubic spline function for a single axis are derived. A robot tool-tip velocity vector magnitude clipping algorithm is proposed. Implementation for a fly-by and contour following trajectory control is discussed.     

Contour reconstruction using recursive smoothing splines - Algorithms and experimental validation

In this paper, a recursive smoothing spline approach for contour reconstruction is studied and evaluated. Periodic smoothing splines are used by a robot to approximate the contour of encountered obstacles in the environment. The splines are generated through minimizing a cost function subject to constraints imposed by a linear control system and accuracy is improved iteratively using a recursive spline algorithm. The filtering effect of the smoothing splines allows for usage of noisy sensor data and the method is robust to odometry drift. The algorithm is extensively evaluated in simulations for various contours and in experiments using a SICK laser scanner mounted on a PowerBot from ActivMedia Robotics.     

Intrinsic Random Fields and Image Deformations

The stochastic structure of images, especially individual medical images as they are reconstructed nowadays from arrays of medical imaging sensors, is becoming steadily better understood. Less attention has been paid to the parallel notion of estimation error for the deformations that convey relations among these images, such as localized abnormality or growth prediction. The dominant current formalism for the biostatistics of deformations deals solely with the shape of a set of landmarks parameterizing the deformation, not otherwise with its behaviour inbetween the landmarks. This paper attempts to fit a rigorous stochastic model for a deformation between landmarks and to assess the error of the fitted deformation. The relation between two images is modelled as a stochastic deformation, i.e. as an identity map plus a stochastic process whose value at every point is a vector-valued displacement. There are two common strategies for fitting deformations given information at a set of landmarks. One involves minimizing a roughness penalty, e.g. for a thin-plate spline, and another involves prediction for a stochastic process, e.g. for a self-similar intrinsic random field. The stochastic approach allows parameter estimation and confidence limits for the predicted deformation. An application is presented from a study of breast images and how they deform as a function of the imaging procedure.     

一种非刚体医学图像配准算法应用研究

刚体配准在许多情况下不能满足临床需要,因为很多形变的性质是非刚体、非线性的。为此,提出一种薄板样条函数点约束和互信息相结合的配准算法,先全局粗配准,然后用互信息技术局部校正。实验证明该算法具有较好的配准效果。