Real‐Time Fluid Effects on Surfaces using the Closest Point Method

The Closest Point Method (CPM) is a method for numerically solving partial differential equations (PDEs) on arbitrary surfaces, independent of the existence of a surface parametrization. The CPM uses a closest point representation of the surface, to solve the unmodified Cartesian version of a surface PDE in a 3D volume embedding, using simple and well‐understood techniques. In this paper, we present the numerical solution of the wave equation and the incompressible Navier‐Stokes equations on surfaces via the CPM, and we demonstrate surface appearance and shape variations in real‐time using this method. To fully exploit the potential of the CPM, we present a novel GPU realization of the entire CPM pipeline. We propose a surface‐embedding adaptive 3D spatial grid for efficient representation of the surface, and present a high‐performance approach using CUDA for converting surfaces given by triangulations into this representation. For real‐time performance, CUDA is also used for the numerical procedures of the CPM. For rendering the surface (and the PDE solution) directly from the closest point representation without the need to reconstruct a triangulated surface, we present a GPU ray‐casting method that works on the adaptive 3D grid.     

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.     

Anisotropic Point Set Surfaces

Point Set Surfaces define smooth surfaces from regular samples based on weighted averaging of the points. Because weighting is done based on a spatial scale parameter, point set surfaces apply basically only to regular samples. We suggest to attach individual weight functions to each sample rather than to the location in space. This extends Point Set Surfaces to irregular settings, including anisotropic sampling adjusting to the principal curvatures of the surface. In particular, we describe how to represent surfaces with ellipsoidal weight functions per sample. Details of deriving such a representation from typical inputs and computing points on the surface are discussed.     

A Correntropy-based Affine Iterative Closest Point Algorithm for Robust Point Set Registration

The iterative closest point (ICP) algorithm has the advantages of high accuracy and fast speed for point set registration, but it performs poorly when the point set has a large number of noisy outliers. To solve this problem, we propose a new affine registration algorithm based on correntropy which works well in the affine registration of point sets with outliers. Firstly, we substitute the traditional measure of least squares with a maximum correntropy criterion to build a new registration model, which can avoid the influence of outliers. To maximize the objective function, we then propose a robust affine ICP algorithm. At each iteration of this new algorithm, we set up the index mapping of two point sets according to the known transformation, and then compute the closed-form solution of the new transformation according to the known index mapping. Similar to the traditional ICP algorithm, our algorithm converges to a local maximum monotonously for any given initial value. Finally, the robustness and high efficiency of affine ICP algorithm based on correntropy are demonstrated by 2D and 3D point set registration experiments.      

隐式曲面上两相图像分割的变分水平集方法

在平面图像分割的Chan-Vese模型基础上,提出隐式曲面上两相图像分割模型。用静态水平集函数的零水平集表达图像所在的闭合曲面,用另一动态水平集函数的零水平集与静态水平集函数零水平集的交线表达静态曲面上图像分割的动态轮廓线。所研究模型的能量泛函的数据项即为曲面上两分割区域的图像强度与对应区域平均图像强度的差的平方,其轮廓线长度项为两水平集函数的零水平集交线的长度。为避免动态水平集函数的重新初始化,在能量泛函中引入水平集函数为符号距离函数的约束惩罚项。通过变分方法得到图像分割空间轮廓线演化的梯度降方程。通过显式差分格式对演化方程进行离散。实验结果表明,该模型能有效实现复杂封闭曲面上图像的两相分割。     

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.     

基于聚类的迭代双向最近点机器人位姿估计

针对迭代最近点（ICP）算法在存在严重遮挡的情况下容易陷入局部最小值的问题,对最近点规则（CP） 进行了修改,提出双向最近点规则（DCP）．DCP 规则包含两次CP 规则对应,使计算量增加了一倍．为了降低算法 的复杂度,继而提出基于聚类的迭代双向最近点（IDCP BoC）算法．IDCP BoC 对扫描数据进行聚类,在聚类的基础 上进行数据精简．在相邻两次迭代的残差之差小于某个阈值之前,用精简数据进行迭代以提高计算速度,之后再改 用非精简数据以保证精度．实验结果表明,IDCP BoC 算法能够有效避免陷入局部最小值的问题且其实时性也是可 接受的．     

变分水平集分割方法

针对三维图像多相分割问题,提出一种变分水平集分割方法。由变分方法和梯度坡降方法得到能量泛函取极小值的水平集函数演化方程,与基于区域模型的参数估计构成一个交替迭代过程。仿真结果表明,该方法简单高效,能快速实现三维图像的轮廓分割与重建,真实反映采集序列断层图像的信息,具有较好的应用价值。     

基于Level Set方法的曲线演化

Level Set方法是一种描述曲线以曲率相关的速度演化的有力工具,最近几年在医学图像处理、自然现象的模拟以及计算机视觉等领域得到了广泛的应用.其中,曲线演化后的平滑算法和轮廓跟踪方法是Level Set方法实际应用中的两个关键算法.给出了一种平滑Level Set距离函数的简单方法.该方法只采用内插值的方式,消除平面上的全部孤立点以及部分可能产生歧义的点,在允许存在部分冗余点的情况下,利用曲线轮廓跟踪算法,得到平面上所有曲线的轮廓.经过实验验证,该方法简单、高效,适应范围广.     

变分水平集分割方法

针对三维图像多相分割问题,提出一种变分水平集分割方法。由变分方法和梯度坡降方法得到能量泛函取极小值的水平集函数演化方程,与基于区域模型的参数估计构成一个交替迭代过程。仿真结果表明,该方法简单高效,能快速实现三维图像的轮廓分割与重建,真实反映采集序列断层图像的信息,具有较好的应用价值。     

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.     

基于先验知识水平集方法的草莓图像分割

在实际应用中,当目标本身含有一些固有的颜色纹理特征时,可将这些特征作为一种先验信息,这样可以大大提高分割的准确性.为此,本文提出了一种基于先验信息的改进水平集图像分割方法.首先,利用传统的C-V模型能量项的构造思想构建了基于颜色信息的局部能量项,该项是用于处理彩色图像;然后将颜色分量引入到传统的结构张量中构建出新的扩展型结构张量,该项是用于处理纹理信息;最后,将上述新构造的能量项以及Li模型约束项引入到传统C-V模型中得到新的水平集模型.鉴于草莓果实所具有的颜色信息和纹理信息,本文将上述改进水平集方法应用到农业自动化应用中草莓果实分割中.对实验室环境与草莓生长环境下的草莓图像进行分别实验,结果显示该方法能够不仅能够分割出草莓果实且能够很好地处理草莓表面的纹理信息.另还与OTSU算法、传统C-V模型、改进C-V模型对草莓图像作对比实验,结果表明本文算法均比上述三种算法具有更好的分割效果.     

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。     

基于Level Set方法的医学图像分割

对图像分割进行了研究,这是医学图像处理中的关键问题之一。提出了一种结合Fast Marching算法和Watershed 变换的医学图像分割方法。首先用非线扩散滤波对原始图像进行平滑，然后利用Watershed算法对图像进行过度分割，最后用改进的Fast Marching方法对图像进行分割。除此之外，根据区域之间的统计特性的相似度重新定义了Fast Marching 方法的速度函数。实验结果表明，该方法能够快速、准确地得到医学图像的分割结果。