Functional data analysis in shape analysis

Mid-level processes on images often return outputs in functional form. In this context the use of functional data analysis (FDA) in image analysis is considered. In particular, attention is focussed on shape analysis, where the use of FDA in the functional approach (contour functions) shows its superiority over other approaches, such as the landmark based approach or the set theory approach, on two different problems (principal component analysis and discriminant analysis) in a well-known database of bone outlines. Furthermore, a problem that has hardly ever been considered in the literature is dealt with: multivariate functional discrimination. A discriminant function based on independent component analysis for indicating where the differences between groups are and what their level of discrimination is, is proposed. The classification results obtained with the methodology are very promising. Finally, an analysis of hippocampal differences in Alzheimer’s disease is carried out.     

Interpolating meshes of boundary intersecting curves by subdivision surfaces

C ⁰ (creases) or C ¹ continuity across the interpolated curves.     

基于椭圆曲线的数字签名方案研究

该文提出了一种新的基于椭圆曲线的数字签名方案。该数字签名方案的安全性是基于椭圆曲线离散对数难题上的。作者对该方案进行了安全性分析,发现该方案能有效防止伪造攻击。同时,该方案具有通信成本低、通信速度快、安全性高等特点,适合应用于小型身份认证系统。     

基于图像处理的显微外科手术质量评价研究*

目前显微外科手术质量评定仍采用测角计进行手工测量,测量中有一定的随意性,测量误差大。针对该问题,提出了应用图像处理技术对显微外科接指手术进行分析和质量评价的方法。通过与手工测量进行对比,图像处理方法评价客观,测量精度高,得到了满意的结果。     

逆向工程中基于精确截面信息的曲面拟合*

针对带有精确截面信息的有序离散点的三维曲面重构问题,提出了一种NURBS曲面快速重构方法。该方法有效地减少了运算数据量,提高了运算效率,同时改进了传统曲面拟合在处理非均匀截面数据点时曲线曲面形状的失真和运算的不稳定现象,最后应用三维图形标准以及图形函数库在实际系统中验证了该方法的有效性。     

Error estimation in reconstruction of quadratic curves in 3D space

Many natural and man-made objects have planar and curvilinear surfaces. The images of such curves do not usually have sufficient distinctive features to apply conventional feature-based reconstruction algorithms. In this paper, we describe a method for the reconstruction of various kinds of quadratic curves in 3D space as an intersection of two cones containing the respective projected digitized curve images in the presence of Gaussian noise. The advantage of this method is that it overcomes the correspondence problem that occurs in pairs of projections of the curve. Using nonlinear least-squares curve fitting, the parameters of a curve in 2D digitized image planes are determined. From this we reconstruct the 3D quadratic curve. Relevant mathematical formulations and analytical solutions for obtaining the equation of the reconstructed curve are given. Simulation studies have been conducted to observe the effect of noise on errors in the process of reconstruction. Results for various types of quadratic curves are presented using simulation studies. These are the main contributions of this work. The angle between the reconstructed and the original quadratic curves in 3D space has been used as the criterion for the measurement of the error. The results of this study are useful for the design of a stereo-based imaging system (such as the LBW decision in cricket, the path of a missile, robotic vision, path planning, etc.) and for the best reconstruction with minimum error.     

Improving the Parameterization of Approximate Subdivision Surfaces

We provide a method for improving the parameterization of patching schemes that approximate Catmull‐Clark subdivision surfaces, such that the new parameterization conforms better to that of the original subdivision surface. We create this reparameterization in real‐time using a method that only depends on the topology of the surface and is independent of the surface's geometry. Our method can handle patches with more than one extraordinary vertex and avoids the combinatorial increase in both complexity and storage associated with multiple extraordinary vertices. Moreover, the reparameterization function is easy to implement and fast.     

暴雨衰减指数为函数型的暴雨强度公式确定方法

暴雨强度公式是城镇排水工程设计的基本依据之一。为提高暴雨衰减指数随重现期显著变化时暴雨强度公式的拟合精度,结合实例研究了采用麦夸尔特法确定衰减指数为函数型的五参数暴雨强度公式的方法。计算结果表明,五参数暴雨强度公式能显著提高拟合精度,由该公式计算的残差平方和及各重现期的绝对均方差(即标准差)均明显小于四参数公式的计算结果,其各重现期的绝对均方差均小于0.05mm/min。该方法能有效降低重现期较小与较大时的绝对均方差。此外,给出了麦夸尔特法的计算程序框图,为编写计算程序代码奠定基础。     

基于ECDSA的三方口令认证密钥交换协议

提出一种基于椭圆曲线数字签名算法(ECDSA)的三方口令认证密钥交换协议。将ECDSA分为公钥生成、签名过程和验证过程 3个阶段,在此基础上,设计协议过程、双向认证机制,使任意2个用户通过服务器能进行身份认证和密钥交换。分析结果表明,该协议能降低计算难度和存储开销,抵抗字典攻击和服务器泄露攻击。     

C~1插值二次B样条曲线曲面

利用二次均匀B样条曲线的端点性质,导出了构造插值二次均匀B样条曲线曲面的一种新的基函数―BB基函数。由BB基函数构造了C1保形插值二次均匀B样条曲线,构造了C1双二次均匀B样条插值曲面。