A Semi‐Lagrangian Closest Point Method for Deforming Surfaces

We present an Eulerian method for the real‐time simulation of intrinsic fluid dynamics effects on deforming surfaces. Our method is based on a novel semi‐Lagrangian closest point method for the solution of partial differential equations on animated triangle meshes. We describe this method and demonstrate its use to compute and visualize flow and wave propagation along such meshes at high resolution and speed. Underlying our technique is the efficient conversion of an animated triangle mesh into a time‐dependent implicit representation based on closest surface points. The proposed technique is unconditionally stable with respect to the surface deformation and, in contrast to comparable Lagrangian techniques, its precision does not depend on the level of detail of the surface triangulation.     

点模型曲面的调和映射参数化

利用调和映射的平面和球面中值性质,提出了确定点模型曲面参数化映射中有关权因子的两种新方法,设计了能够达到内在变形较小的相应参数化方法,并将参数化方法应用于点模型曲面上的纹理映射．实验和统计结果表明,文中方法是比较有效的点模型曲面的参数化方法．     

Multi-Level Partition of Unity Algebraic Point Set Surfaces

We present a multi-level partition of unity algebraic set surfaces (MPU-APSS) for surface reconstruction which can be represented by either a projection or in an implicit form. An algebraic point set surface (APSS) defines a smooth surface from a set of unorganized points using local moving least-squares (MLS) fitting of algebraic spheres. However, due to the local nature, APSS does not work well for geometry editing and modeling. Instead, our method builds an implicit approximation function for the scattered point set based on the partition of unity approach. By using an octree subdivision strategy, we first adaptively construct local algebraic spheres for the point set, and then apply weighting functions to blend together these local shape functions. Finally, we compute an error-controlled approximation of the signed distance function from the surface. In addition, we present an efficient projection operator which makes our representation suitable for point set filtering and dynamic point resampling. We demonstrate the effectiveness of our unified approach for both surface reconstruction and geometry modeling such as surface completion.     

Feature Preserving Point Set Surfaces based on Non-Linear Kernel Regression

Moving least squares (MLS) is a very attractive tool to design effective meshless surface representations. However, as long as approximations are performed in a least square sense, the resulting definitions remain sensitive to outliers, and smooth-out small or sharp features. In this paper, we address these major issues, and present a novel point based surface definition combining the simplicity of implicit MLS surfaces [ SOS04 , Kol05 ] with the strength of robust statistics. To reach this new definition, we review MLS surfaces in terms of local kernel regression, opening the doors to a vast and well established literature from which we utilize robust kernel regression. Our novel representation can handle sparse sampling, generates a continuous surface better preserving fine details, and can naturally handle any kind of sharp features with controllable sharpness. Finally, it combines ease of implementation with performance competing with other non-robust approaches.     

Dynamic Sampling and Rendering of Algebraic Point Set Surfaces

Algebraic Point Set Surfaces (APSS) define a smooth surface from a set of points using local moving least‐squares (MLS) fitting of algebraic spheres. In this paper we first revisit the spherical fitting problem and provide a new, more generic solution that includes intuitive parameters for curvature control of the fitted spheres. As a second contribution we present a novel real‐time rendering system of such surfaces using a dynamic up‐sampling strategy combined with a conventional splatting algorithm for high quality rendering. Our approach also includes a new view dependent geometric error tailored to efficient and adaptive up‐sampling of the surface. One of the key features of our system is its high degree of flexibility that enables us to achieve high performance even for highly dynamic data or complex models by exploiting temporal coherence at the primitive level. We also address the issue of efficient spatial search data structures with respect to construction, access and GPU friendliness. Finally, we present an efficient parallel GPU implementation of the algorithms and search structures.     

基于Level Set曲面的蛋白质分子场特征分析

阐述了利用Level Set模型抽取并分析蛋白质分子场特征方面的工作.从蛋白质分子结构出发,基于分子力学和分子动力学理论计算得到蕴含丰富生化信息的分子场数据;设计了一种有效的Level Set模型揭示分子场能量突变区域;进而构造体特征函数,抽取并分析Level Set曲面的拓扑结构特征;最后对同一蛋白质不同状态下的LevelSet曲面进行多属性比对.采用文中方法可成功地抽取蛋白质分子场的重要特征,所抽取的特征与已有生物学结论一致,如DPS蛋白质与铁离子结合的空腔区域、HIV-1蛋白酶内部的水分子排出通道,以及HIV-1蛋白酶在水溶液中进行SMD模拟时的生物活性变化等.     

隐式曲面多相图像分割的变分水平集方法

基于隐式曲面的水平集表达、隐式曲面上的内蕴梯度概念和图像分割的标记函数方法,建立了隐式曲面上多相图像分割的水平集模型,并设计了相应的Split Bregman方法.首先,将分段常值与光滑平面图像两相分割的Chan-Vese模型推广到隐式曲面上图像分割的变分水平集模型,并根据图像分割的二值标记函数和凸松弛的概念将该模型转化为全局凸优化的极值问题;然后借助n-1个水平集函数划分n个区域的区域特征函数,将隐式曲面上两相图像分割变分模型推广到了多相图像分割,并利用凸优化方法将该模型的变分问题松弛为一系列凸子优化过程.通过引进辅助变量和Bregman迭代参数设计的Split Bregman方法,将每个子优化问题转化为简单的Poisson方程求解和解析的软阈值公式.数值算例结果表明,文中方法在计算效率方面要优于传统的方法.     

基于窄带的自适应Level Set方法

Level Set模型将运动界面表示为高维场函数的零等值面,自然而鲁棒地解决了界面演化中拓扑结构改变的问题,但计算效率不高.文中提出了基于窄带的自适应Level Set方法.自适应方法首先构建粗网格满足界面演化的整体需求,同时估算粗网格点的曲率值,使用快速扩散法聚类高曲率点,通过主元分析估算点集朝向,构建细网格捕捉演化中的细节区域.粗、细网格均为独立的计算单元,定义为存储网格中的有向包围盒.这种数据结构可以有效避免频繁的坐标变换和插值操作,同时保证了数值解的精度.实验结果与误差分析表明,自适应方法能有效减少计算量,达到更好的界面跟踪效果.     

基于变分Level Set方法的图像分割

文章主要利用levelset函数隐式地追踪图像的边界来实现图像分割。在该文中首先给出了一个变分问题以及相应的Euler-Lagrange方程,并且提出了一种求解该方程的数值算法,使得计算速度有了很大的提高。数值算例表明,该水平集算法具有数值稳定性,不会出现振荡现象,可以很好地处理拓扑结构的变化。     

On Geodesic Curvature Flow with Level Set Formulation Over Triangulated Surfaces

The geodesic curvature flow is an important concept in Riemannian geometry. The flow with level set formulation has many applications in image processing, computer vision, material sciences, etc. The existing discretizations on triangulated surfaces are based on either finite volume method or finite element method with piecewise linear function space, which are suitable for vertex-based two-phase problems. The contour (zero level set) in existing methods passes through triangles of the mesh. However, in some graphic applications, such as mesh segmentation (to divide a whole mesh into several sub-meshes without ambiguous triangular stripes), the cutting contour is needed to be along the edges of the mesh. Moreover, multi-phase segmentation by a single level set function is a difficult problem for a long time. In this paper, we try to tackle these two problems. We propose a new discretization which has simpler formulation and more sparse coefficient matrix. We prove the existence and uniqueness, regularization behavior and maximum–minimum principle of our discrete flow. Therein the maximum–minimum principal has not been presented before. Lots of experiments show that, the limit of the flow would be a piecewise constant solution with ’discontinuity set’ to be the closed geodesics of the surface. We therefore propose a constrained discrete geodesic curvature flow, which is also analyzed theoretically. The linear system of the constrained flow can be equivalently reformulated into a much smaller one (especially in the narrow band algorithm), which dramatically reduces the computation cost. Combined with a narrow band algorithm, the constrained flow with topologically correct initializations (easy to be got by simple existing methods or manual inputs) yields a multi-phase segmentation method by a single level set function. We test our two flows in closed curve evolution and multi-region segmentation applications. The numerical experiments are given to demonstrate the effectiveness.     

Surface Representation with Closest Point Projection in the X-FEM

Mathematical Models and Computer Simulations - At present, the eXtended Finite Element Method (X-FEM) is a common generalization of the classical finite element method for solving problems of...     

A High-Order Kernel Method for Diffusion and Reaction-Diffusion Equations on Surfaces

In this paper we present a high-order kernel method for numerically solving diffusion and reaction-diffusion partial differential equations (PDEs) on smooth, closed surfaces embedded in $\mathbb{R }^d$ . For two-dimensional surfaces embedded in $\mathbb{R }^3$ , these types of problems have received growing interest in biology, chemistry, and computer graphics to model such things as diffusion of chemicals on biological cells or membranes, pattern formations in biology, nonlinear chemical oscillators in excitable media, and texture mappings. Our kernel method is based on radial basis functions and uses a semi-discrete approach (or the method-of-lines) in which the surface derivative operators that appear in the PDEs are approximated using collocation. The method only requires nodes at “scattered” locations on the surface and the corresponding normal vectors to the surface. Additionally, it does not rely on any surface-based metrics and avoids any intrinsic coordinate systems, and thus does not suffer from any coordinate distortions or singularities. We provide error estimates for the kernel-based approximate surface derivative operators and numerically study the accuracy and stability of the method. Applications to different non-linear systems of PDEs that arise in biology and chemistry are also presented.     

基于遗传迭代最近点算法的激光数据配准

扫描匹配算法被广泛应用于基于视觉、声纳、激光等传感器数据的特征匹配中,其中迭代最近点扫描匹配算法(ICP)是最常见的扫描匹配算法,但该算法存在匹配误差较大、对角度误差修正较差等缺点;针对基于ICP的激光传感器数据配准中存在的问题,提出了一种遗传迭代最近点扫描匹配算法(GICP);通过遗传算法搜索当前扫描数据和参考扫描数据的最优匹配,修正初始里程计读数的误差以及机器人的位姿;实验结果表明,提出的算法能够有效地解决扫描匹配算法中任意的配准问题,提高了机器人的定位精度。     

基于水平集的三维脑部肿瘤分割

脑部肿瘤的分割在临床的诊断、治疗以及研究方面都有很重要的作用,但是由于脑肿瘤的大小、类型、位置等的多变性,脑部肿瘤分割一直是一个难点问题.根据脑肿瘤在核磁共振图像上的梯度以及图像中点的强度分布提出了一种新的基于水平集的分割方法.算法定义了一个新的能量函数,更好地匹配图像中肿瘤区域的强度分布.在实际的脑部核磁共振图像上进行实验,文中算法可以准确地分割出脑部肿瘤.与传统的水平集方法比较,该算法分割结果更加准确.     

导弹非零给定点LQR自动驾驶仪设计

静不稳定控制技术是提高空空导弹机动性能的有效手段.针对静不稳定导弹的控制问题,基于非零给定点线性二次型调节器(LQR)理论设计了纵向两回路自动驾驶仪.首先给出一种基于英美弹体坐标系的静不稳定导弹状态空间模型,引入加速度计到质心的距离参量;然后使用非零给定点输出调节器理论,推导了针对一般状态空间表达式描述的系统的最优控制问题,求得了通用解和自动驾驶仪的结构和参数表达式;最后根据经典控制理论对权重系数的选择进行理论研究和仿真分析,并对所设计自动驾驶仪的鲁棒性能以及引入加速度计到质心的距离变量对控制效果的影响进行仿真分析.结果表明所设计的自动驾驶仪有较强的鲁棒性,对静不稳定导弹起到了较好的控制作用.     

基于水平集方法的航拍图像运动分割

针对航拍图像由于受噪声和光照影响导致分割精度差问题,将一种改进的C-V水平集方法引入到航拍图像运动分割中.首先对C-V模型作了改进,通过引入新的能量项使改进方法无需重新初始化符号距离函数,在保证分割精度的同时提高了分割速度;其次对水平集函数的偏微分方程进行改进,消除了原始C-V方法对远离实际边缘的轮廓曲线进化的抑制作用.实验结果显示,改进方法能有效地分割出航拍图像中的运动目标,在初始轮廓线远离目标实际轮廓时也能够正确分割,并能更好地满足实时性的要求.改进方法具有分割精度高,耗时少的优点,可用于航拍图像运动目标检测跟踪系统.     

基于一个水平集函数的多相图像分割方法

利用多个特征函数标记不同区域的方法进行图像分割时,需要对多个函数求极值,导致计算量增大。针对该问题,设计一个函数在多层水平集标记的方法,通过求解一个标记函数的极值问题实现对图像不同区域的分割。总结区域标记函数规律,得到多项图像分割模型表达式,将其与变分水平集方法相结合,运用交替方向乘子法加速求解能量泛函极值问题。实验结果表明,该方法能够实现图像多个区域的分割,并且保证分割结果的鲁棒性和计算高效性。     

一种基于水平集的图像分割新方法

首先从理论上分析了无需重新初始化的水平集方法的主动轮廓图像分割模型,该模型对一些具有不光滑的尖角的图像分割时,捕捉这些尖角往往不精确甚至失败。然后通过修正边缘检测函数,则能准确地捕捉到物体的尖角,保证了分割的准确性。实验证明了该方法的可行性。     

基于遗传算法的水平集超声图像分割

鉴于医学超声图像的信噪比较低,用经典的边缘提取算法无法得到较好的结果,因此,提出超声图像自动分割的一种新方法.其基本思想是在水平集分割方法的基础上,以能量函数作为评价函数,把图像分割问题变成一个优化问题,利用遗传算法的寻优高效性,搜索到能使分割质量到达最优的轮廓曲线.应用此方法对肝脏超声图像进行肿瘤的边缘提取,得到比较好的结果,从而完成图像的自动分割.