Computing Extremal Teichmüller Map of Multiply-Connected Domains Via Beltrami Holomorphic Flow

A numerical method for computing the extremal Teichmüller map between multiply-connected domains is presented. Given two multiply-connected domains, there exists a unique Teichmüller map (T-Map) between them minimizing the conformality distortion. The extremal T-Map can be considered as the ‘most conformal’ map between multiply-connected domains. In this paper, we propose an iterative algorithm to compute the extremal T-Map using the Beltrami holomorphic flow (BHF). The BHF procedure iteratively adjusts the initial map based on a sequence of Beltrami coefficients, which are complex-valued functions defined on the source domain. It produces a sequence of quasi-conformal maps, which converges to the T-Map minimizing the conformality distortion. We test our method on synthetic data together with real human face data. Results show that our algorithm computes the extremal T-Map between two multiply-connected domains of the same topology accurately and efficiently.     

On the Discrete Maximum Principle for the Beltrami Color Flow

We analyze the discrete maximum principle for the Beltrami color flow. The Beltrami flow can display linear as well as nonlinear behavior according to the values of a parameter β, which represents the ratio between spatial and color distances. In general, the standard schemes fail to satisfy the discrete maximum principle. In this work we show that a nonnegative second order difference scheme can be built for this flow only for small β, i.e. linear-like diffusion. Since this limitation is too severe, we construct a novel finite difference scheme, which is not nonnegative and satisfies the discrete maximum principle for all values of β. Numerical results support the analysis.

无对应点三维表面重建的全局优化算法

一、三维平面重建问题陈述图1是成象系统,包括一对焦距f=1的照相机。两坐标系间的关系是 (X_R,Y_R,Z_R)=(X_L-b,Y_L,Z_L)。三维点(X_L,Y_L,Z_L)在左、右图象平面的投影分别是 (x_L,y_L)=(X_L/Z_L,Y_L/Z_L) (x_R,y_R)=(X_R/Z_R,Y_R/Z_R) =((Z_L-b)/Z_L,Y_L/Z_L) (1)则水平和垂直方向的差异场分别是δ_x=x_L-x_R=b/Z_L; δ_y=y_L-y_R=0 (2) 图1 平行轴立体成象系统假设三维点位于平面Z=Z_0+PX+QY上,则对应点匹配约束条件是     

Hypersonic Waverider Surface Development Using Aerodynamic Flow Around Conical Bodies

1 Introduction The future high speed aircrafts flying with hypersonic speeds are in search of configurations giving a better lift to drag ratio. With advent of scramjets, it is also required to provide an adequate inlet pressure and mass flow rate for its operation. The Waverider based forebodies have been considered as one option. They are developed from a known aerodynamic flow field and get their name due to the reason that they develop their lift force form the pressure difference between…     

A Surface Reconstruction Method Using Global Graph Cut Optimization

Surface reconstruction from multiple calibrated images has been mainly approached using local methods, either as a continuous optimization problem driven by level sets, or by discrete volumetric methods such as space carving. We propose a direct surface reconstruction approach which starts from a continuous geometric functional that is minimized up to a discretization by a global graph-cut algorithm operating on a 3D embedded graph. The method is related to the stereo disparity computation based on graph-cut formulation, but fundamentally different in two aspects. First, existing stereo disparity methods are only interested in obtaining layers of constant disparity, while we focus on high resolution surface geometry. Second, most of the existing graph-cut algorithms only reach approximate solutions, while we guarantee a global minimum. The whole procedure is consistently incorporated into a voxel representation that handles both occlusions and discontinuities. We demonstrate our algorithm on real sequences, yielding remarkably detailed surface geometry up to 1/10th of a pixel. Author has worked on this project during his Ph. D. at ARTIS     

贴片机喂料器分配的优化及其遗传算法求解

针对贴片机喂料器的分配问题,给出一个新的模型,在贴装顺序已知的前提下,以贴装整块电路板所花费的总时间作为优化目标.基于该模型给出一种遗传算法,以目标函数作为其评价函数.与贪婪分配算法相比较,所花费的代价平均减少了6.2%,从而验证了该方法的有效性.     

基于响应面和空间映射技术的模面设计优化

阐述了响应面近似模型和空间映射技术用于快速模面设计优化的基本原理．为避免数值噪声干扰和求解隐函数敏度,提出通过多项式响应面方法构造真实目标和约束的逼近曲面,以光滑响应进行全局最优;并利用空间映射技术的代理模型确定新的响应面及其梯度,经精细模型修正优化方向和设计子域,使计算成本降低．算法结合有限元模拟实施,通过对金钣拉延成形和回弹补偿的分析证明,该算法具有很高的效率和鲁棒性,适用于模面设计优化．     

开孔圆柱壳屈曲优化的均匀设计序列响应面方法

为了减少优化中原模型的分析次数,提高优化效率,提出一种序列二次响应面近似优化方法.该方法基于均匀设计建立一个由低精度的全局响应面和精度逐渐提高的局部响应面组成的近似模型,其中,全局响应面用于确定初始子区域,而局部响应面获得问题在子区域内的优化解;采用基于归一化优化解相对位置的运动极限新准则更新子区域,通过子区域内样本点的继承和增补构造响应面并求解,重复迭代过程,实现问题的优化求解.最后通过5组典型测试函数和一个工程设计问题的优化求解验证了文中方法的有效性——可以高效率地完成开孔圆柱壳最大屈曲载荷的优化设计,展现出求解高计算成本工程优化问题的良好应用前景.     

Direct Estimation of Nonrigid Registrations with Image-Based Self-Occlusion Reasoning

The registration problem for images of a deforming surface has been well studied. External occlusions are usually well handled. In 2D image-based registration, self-occlusions are more challenging. Consequently, the surface is usually assumed to be only slightly self-occluding. This paper is about image-based nonrigid registration with self-occlusion reasoning. A specific framework explicitly modeling self-occlusions is proposed. It is combined with an intensity-based, “direct” data term for registration. Self-occlusions are detected as shrinkage areas in the 2D warp. Experimental results on several challenging data sets show that our approach successfully registers images with self-occlusions while effectively detecting the self-occluded regions.     

Two-Dimensional Analysis of Electrokinetically Driven Out-of-Plane Vortices in a Microchannel Liquid Flow Using Patterned Surface Charge

The technology developed for photolithographically patterning the electric surface charge to be negative, positive, or neutral enables the realization of complex liquid flows even in straight and uniform microchannels with extremely small Reynolds number. A theoretical model to analyze a steady incompressible electrokinetically driven two-dimensional liquid flow in a microchannel with an inhomogeneous surface charge under externally applied electric field is derived. The flow field is obtained analytically by solving the biharmonic equation with the Helmholtz-Smoluchowski slip boundary condition using the Fourier series expansion method. The model has been applied to study three basic out-of-plane vortical flow fields: single vortex and a train of corotating and a series of counterrotating vortex pairs. For model verification, the solution for the single vortex has been tested against numerical computations based on the full Navier-Stokes equations revealing the dominant control parameters. Two interesting phenomena have been observed in out-of-plane multivortex dynamics: merging of corotating vortices and splitting of counterrotating vortices. The criteria for the onset of both phenomena are discussed     

一种改进的最优化流控模型

在前人提出的最优化流控模型的基础上,采用非线性优化理论中的DFP算法计算链路价格,提出了一种改进的最优化流控模型。     

基于纹理的高质量的曲面流场可视化

提出一种流线增强的纹理算法,可实时生成高质量的纹理表征曲面矢量场.通过对卷积纹理在垂直矢量方向上进行一维高通滤波,增加流线间的强度对比,提高了图像质量,使得曲面矢量场易于观察.该算法基于图像空间,并且具有很好的时间空间相关性,利用当前图形卡的可编程性和并行运算能力,可以在微机上达到实时绘制的性能.     

Survey on Discrete Surface Ricci Flow

Ricci flow deforms the Riemannian metric proportionally to the curvature, such that the curvature evolves according to a nonlinear heat diffusion process, and becomes constant eventually. Ricci flow is...     

程序控制流检测算法优化

暴露在太空辐射环境下的星载计算机,其电子元器件可能因受到高能带电粒子的轰击而造成硬件系统的瞬时故障,所以,需要使用容错技术来提高其可靠性。对一种面向硬件瞬时故障的纯软件控制流检测算法RSCFC(Relationship Signatures for Control Flow Checking)进行了有效的改进,通过对标签S进行分段编码,克服了原算法中存在的待加固程序的基本块总数受机器字长限制的问题,并给出了具体的计算证明。计算结果表明,如果机器字长为64位,那么改进后的算法在设定前提下能单层加固程序的最大基本块数可以超过218。与RSCFC相比,改进后的算法在加固基本块总数比较大的程序时,性能开销明显降低而且检错能力保持不变。     

Fast Approximation of Laplace‐Beltrami Eigenproblems

The spectrum and eigenfunctions of the Laplace‐Beltrami operator are at the heart of effective schemes for a variety of problems in geometry processing. A burden attached to these spectral methods is that they need to numerically solve a large‐scale eigenvalue problem, which results in costly precomputation. In this paper, we address this problem by proposing a fast approximation algorithm for the lowest part of the spectrum of the Laplace‐Beltrami operator. Our experiments indicate that the resulting spectra well‐approximate reference spectra, which are computed with state‐of‐the‐art eigensolvers. Moreover, we demonstrate that for different applications that comparable results are produced with the approximate and the reference spectra and eigenfunctions. The benefits of the proposed algorithm are that the cost for computing the approximate spectra is just a fraction of the cost required for numerically solving the eigenvalue problems, the storage requirements are reduced and evaluation times are lower. Our approach can help to substantially reduce the computational burden attached to spectral methods for geometry processing.     

Topology-Preserving Image Segmentation by Beltrami Representation of Shapes

A new approach using the Beltrami representation of a shape for topology-preserving image segmentation is proposed in this paper. Using the proposed model, the target object can be segmented from the input image by a region of user-prescribed topology. Given a target image I, a template image J is constructed and then deformed with respect to the Beltrami representation. The deformation on J is designed such that the topology of the segmented region is preserved as which the object is interior in J. The topology-preserving property of the deformation is guaranteed by imposing only one constraint on the Beltrami representation, which is easy to be handled. Introducing the Beltrami representation also allows large deformations on the topological prior J, so that it can be a very simple image, such as an image of disks, torus, disjoint disks. Hence, prior shape information of I is unnecessary for the proposed model. Additionally, the proposed model can be easily incorporated with selective segmentation, in which landmark constraints can be imposed interactively to meet any practical need (e.g., medical imaging). High accuracy and stability of the proposed model to deal with different segmentation tasks are validated by numerical experiments on both artificial and real images.     

用粒子群优化算法计算点到复杂曲面最短距离

点到复杂曲面的最短距离是一个复杂非线性寻优问题.阐述了粒子群优化算法基本原理及在处理复杂的非线性优化问题的独到之处,介绍了复杂曲面的NURBS描述方法,建立了点到复杂曲而最短距离的数学模型,提出了基于粒子群优化算法计算测点到复杂曲面的最小距离的方法,并通过大量算例验证了其可行性和有效性.算法易于计算机实现,且计算精确度高,可以达到任意给定的精度,非常适用于CAD/CAM和虚拟现实中点到复杂曲面最短距离求解.     

Stereo Matching Using Optic Flow

A method for the determination of pixel correspondence in stereo image pairs is presented. The optic flow vectors that result from the displacement of the point of projection are obtained and the correspondence between pixels of the various objects in the scene is derived from the optic flow vectors. The proposed algorithm is implemented and the correspondence vectors are obtained. Various specialized improvements of the method are implemented and thoroughly tested on sequences of image pairs giving rise to interesting conclusions. The algorithm is highly-parallelizable and therefore suitable for real-time applications.