Revised definition of optical flow: integration of radiometric andgeometric cues for dynamic scene analysis

Optical flow has been commonly defined as the apparent motion of image brightness patterns in an image sequence. In this paper, we propose a revised definition to overcome shortcomings in interpreting optical flow merely as a geometric transformation field. The new definition is a complete representation of geometric and radiometric variations in dynamic imagery. We argue that this is more consistent with the common interpretation of optical flow induced by various scene events. This leads to a general framework for the investigation of problems in dynamic scene analysis, based on the integration and unified treatment of both geometric and radiometric cues in time-varying imagery. We discuss selected models, including the generalized dynamic image model, for the estimation of optical flow. We show how various 3D scene information are encoded in, and thus may be extracted from, the geometric and radiometric components of optical flow. We provide selected examples based on experiments with real images     

Area and length preserving geometric invariant scale-spaces

In this paper, area preserving multi-scale representations of planar curves are described. This allows smoothing without shrinkage at the same time preserving all the scale-space properties. The representations are obtained deforming the curve via geometric heat flows while simultaneously magnifying the plane by a homethety which keeps the enclosed area constant. When the Euclidean geometric heat flow is used, the resulting representation is Euclidean invariant, and similarly it is affine invariant when the affine one is used. The flows are geometrically intrinsic to the curve, and exactly satisfy all the basic requirements of scale-space representations. In the case of the Euclidean heat flow, it is completely local as well. The same approach is used to define length preserving geometric flows. A similarity (scale) invariant geometric heat flow is studied as well in this work     

Images as Embedded Maps and Minimal Surfaces: Movies,Color, Texture,and Volumetric Medical Images

We extend the geometric framework introduced in Sochen et al. (IEEE Trans. on Image Processing, 7(3):310–318, 1998) for image enhancement. We analyze and propose enhancement techniques that selectively smooth images while preserving either the multi-channel edges or the orientation-dependent texture features in them. Images are treated as manifolds in a feature-space. This geometrical interpretation lead to a general way for grey level, color, movies, volumetric medical data, and color-texture image enhancement.We first review our framework in which the Polyakov action from high-energy physics is used to develop a minimization procedure through a geometric flow for images. Here we show that the geometric flow, based on manifold volume minimization, yields a novel enhancement procedure for color images. We apply the geometric framework and the general Beltrami flow to feature-preserving denoising of images in various spaces.Next, we introduce a new method for color and texture enhancement. Motivated by Gabor's geometric image sharpening method (Gabor, Laboratory Investigation, 14(6):801–807, 1965), we present a geometric sharpening procedure for color images with texture. It is based on inverse diffusion across the multi-channel edge, and diffusion along the edge.     

基于几何流多级树Bandelet分割编码的医学图像压缩方法

本文提出了一种新的医学图像压缩方法,利用稀疏表示方法结合图像结构的几何规律,构建图像的灰度级有规则变化的方向的几何流表示方法,获得二元方形图像四叉树表示形式。针对几何正则化数据的小波分解结果存在较少的显着系数问题,使用二维向量场表示正则性的方向,并用样条表示法得到了这些方向的逼近。最后,在几何流图像的方向分解的基础上,利用M-band离散小波变换构建多级树Bandelet分割编码方式,实现了Bandelet系数计算改进。实验结果表明,该方法可有效提高医学图像压缩方法的计算效率。     

基于几何着色器的流场动态可视化研究与实现

为有效解决复杂流场可视化效率低下问题，加快可视化速度，提出了一种基于几何着色器的快速流场可视化算法。在流场可视化的过程当中引入几何着色器，利用GPU的并行处理能力和强大的图像处理能力对流场实时地进行箭头和流线的绘制，然后采用积分颜色映射方法，与常规的线性颜色映射法相比较，改善了颜色的均匀分布，增强流场强度层次感。实验表明，该算法可以有效地反映流场特征分布，减少可视化过程中的数据传输量，降低资源浪费，提高可视化渲染效率。     

Computing general geometric structures on surfaces using Ricci flow

Systematically generalizing planar geometric algorithms to manifold domains is of fundamental importance in computer aided design field. This paper proposes a novel theoretic framework, geometric structure, to conquer this problem. In order to discover the intrinsic geometric structures of general surfaces, we developed a theoretic rigorous and practical efficient method, Discrete Variational Ricci flow.Different geometries study the invariants under the corresponding transformation groups. The same geometry can be defined on various manifolds, whereas the same manifold allows different geometries. Geometric structures allow different geometries to be defined on various manifolds, therefore algorithms based on the corresponding geometric invariants can be applied on the manifold domains directly.Surfaces have natural geometric structures, such as spherical structure, affine structure, projective structure, hyperbolic structure and conformal structure. Therefore planar algorithms based on these geometries can be defined on surfaces straightforwardly.Computing the general geometric structures on surfaces has been a long lasting open problem. We solve the problem by introducing a novel method based on discrete variational Ricci flow.We thoroughly explain both theoretical and practical aspects of the computational methodology for geometric structures based on Ricci flow, and demonstrate several important applications of geometric structures: generalizing Voronoi diagram algorithms to surfaces via Euclidean structure, cross global parametrization between high genus surfaces via hyperbolic structure, generalizing planar splines to manifolds via affine structure. The experimental results show that our method is rigorous and efficient and the framework of geometric structures is general and powerful.     

Applying multiquadric quasi-interpolation for boundary detection

In this paper, we propose a novel scheme for simulating geometric active contours (geometric flow) of one kind, applying multiquadric (MQ) quasi-interpolation. We first represent the geometric flow in its parametric form. Then we obtain the numerical scheme by using the derivatives of the quasi-interpolation to approximate the spatial derivative of each dependent variable and a forward difference to approximate the temporal derivative of each dependent variable. The resulting scheme is simple, efficient and easy to implement. Also images with complex boundaries can be more easily proposed on the basis of the good properties of the MQ quasi-interpolation. Several biomedical and astronomical examples of applications are shown in the paper. Comparisons with other methods are included to illustrate the validity of the method.     

静压止推气体轴承性能仿真

运用计算流体力学软件FLUENT仿真静压止推气体轴承性能,分析轴承的几何参数对系统性能的影响。采用不同几何参数的静压止推气体轴承的气膜建模并划分网格;运用FLUENT软件对轴承的气膜流场进行数值仿真,计算轴承在不同几何参数下的承载能力和气体流量。仿真结果表明静压止推气体轴承的节流孔直径和气膜厚度越小,气腔直径越大,轴承的承载能力和气膜刚度越好,同时气腔深度对轴承性能影响较小。FLUENT软件可以有效的应用于静压止推气体轴承的性能分析,而优化了静压止推气体轴承的设计,达到优化效果。     

几何偏微分方程和离散曲面设计

使用若干个几何本质的曲率驱动的偏微分方程来构造符合指定C0或C1边界条件的三边曲面片和四边曲面片,这些方程的数值解由所涉及的微分几何算子的离散化来得到,微分几何算子的离散化则源于参数逼近.所构造的曲面片满足某些特定的几何偏微分方程,故具有理想的形状,将这些曲面片组装起来便构造出复杂的几何模型.通过反复的子分和演化,得到几何模型的多尺度表示.     

Image Labeling by Assignment

We introduce a novel geometric approach to the image labeling problem. Abstracting from specific labeling applications, a general objective function is defined on a manifold of stochastic matrices, whose elements assign prior data that are given in any metric space, to observed image measurements. The corresponding Riemannian gradient flow entails a set of replicator equations, one for each data point, that are spatially coupled by geometric averaging on the manifold. Starting from uniform assignments at the barycenter as natural initialization, the flow terminates at some global maximum, each of which corresponds to an image labeling that uniquely assigns the prior data. Our geometric variational approach constitutes a smooth non-convex inner approximation of the general image labeling problem, implemented with sparse interior-point numerics in terms of parallel multiplicative updates that converge efficiently.     

A CFD parametric study of geometrical variations on the pressure pulsations and performance characteristics of a centrifugal pump

Pressure pulsations may be troublesome during the operation and performance of centrifugal pumps. Such pressure pulsations have traditionally been investigated experimentally but numerical analysis techniques allow these effects to be explored. The multi-block, structured grid CFD code TASCflow has been used to investigate the time variation of pressure within a complete double entry, double volute centrifugal pump. This investigation has taken the form of a parametric study covering four geometric parameters, namely the cutwater gap, vane arrangement, snubber gap and the sidewall clearance. Taguchi methods allowed the number of transient analyses to be limited to a total of 27. Three flow rates were investigated and the pulsations were extracted at 15 different locations covering important pump regions. Taguchi post-processing analysis tools were used to rank the relative importance of the four geometric parameters at each location for each flow rate. The cutwater gap and vane arrangement were found to exert the greatest influence across the various monitored locations and the flow range. A rationalisation process aimed at increased component life and reduced noise/vibration through reductions in pressure pulsations has produced geometric recommendations, which should be useful to designers.     

Microfluidic analysis of CO<Subscript>2</Subscript> bubble dynamics using thermal lattice-Boltzmann method

By means of microfluidic analysis with a thermal lattice-Boltzmann method, we investigated the hydrophilic, thermal and geometric effects on the dynamics of CO₂ bubbles at anode microchannels (e.g., porous layers and flow channels) of a micro-direct methanol fuel cell. The simulation results show that a more hydrophilic wall provides an additional attractive force to the aqueous methanol in the flow direction and that moves the CO₂ bubble more easily. The bubble propagates quicker in the microchannel with a positive temperature gradient imposed from the inlet to the exit, mainly due to the Marangoni effect. Regarding the geometric effect of the microchannel, the bubble moves more rapidly in a divergent microchannel than in a straight or convergent channel. On the basis of the quantitative evaluation of hydrophilic, thermal and geometric effects, we are able to design the bubble-removal technique in micro fuel cells.     

一种基于局部特征的鲁棒的盲数字水印算法

提出了一种基于图像局部特征与图像几何正则性的鲁棒数字水印算法.采取的主要方法有:1)利用图像中的局部最稳定特征点生成具有几何不变性的局部特征区域;2)在局部特征分块中快速寻找最佳几何流方向,近似最佳逼近效果;3)设计了一种正交向量盲提取水印.实验结果表明该算法能获得很高的图像质量,且具有较强的抗攻击能力.     

拟极小平均曲率变差流及其在G~2曲面构造中的应用

曲面的变分设计方法在构造高质量的曲面方面显示出了明显的优越性.通过对Greiner所提出的三阶能量泛函进行变分,得到相应的Euler-Lagrange方程,并构造了一个新的六阶梯度流.采用类差分法对所构造的几何流进行数值求解,并用其解决几何设计中的各种问题,包括曲面处理、 N-边洞填补方面以及曲面恢复等.实验结果表明,文中所构造的几何流确能产生高质量的曲面.     

基于全变差的Bandelet变换域SAR图像相干斑抑制方法

根据SAR图像的特性,提出了一种基于全变差最小化的Bandelet变换域SAR图像相干斑抑制方法。该方法首先对SAR图像进行Bandelet变换,得到图像的Bandelet系数和几何流,然后采用主成分分析法提取图像的Bandelet系数和几何流的主成分,利用全变差最小化的方法确定阈值,并通过循环递归运算处理重构后的图像。实验表明:该方法在抑制图像相干斑的同时较好地保留了几何结构信息,并去除了伪吉布斯现象。     

三维渗流有限元软件GWSS开发与应用

针对复杂地质条件的三维地质建模、复杂建筑物的几何建模和复杂防渗排水系统作用下渗流场精细模拟等三维渗流场有限元分析的难点问题,采用IDL开发面向水工结构和岩土工程的渗流有限元分析软件GWSS（Ground Water Simulation System）.该软件包括系统控制模块、数据管理模块、前处理模块、计算模块、后处理模块和制图输出模块等六大模块.前处理模块具有基于钻孔和钻孔剖面的三维地质建模、几何建模与有限元网格生成等功能;计算模块主要用于各种闸坝、堤防、隧道和地下洞室等渗流问题的计算分析等;后处理模块可显示各渗流要素的三维云图和任意截面的二维云图等.GWSS已经在国内四十多个工程的渗流计算中得到应用和检验.     

Gradient vector flow fast geometric active contours

In this paper, we propose an edge-driven bidirectional geometric flow for boundary extraction. To this end, we combine the geodesic active contour flow and the gradient vector flow external force for snakes. The resulting motion equation is considered within a level set formulation, can deal with topological changes and important shape deformations. An efficient numerical schema is used for the flow implementation that exhibits robust behavior and has fast convergence rate. Promising results on real and synthetic images demonstrate the potentials of the flow.     

二元超声速进气道数值仿真建模过程自动化

研究高速巡航导弹动力装置优化问题,针对进气道结构严重影响速度的提高,为减少人工建模的工作量,以提高数值仿真分析工作效率和满足二元超声速进气道设计方案的快速评比和选型的需要,提出建立流场计算域通用的结构化分区几何模型,统一基于所构造的基准进气道模型,一次性人工划分进气道结构化计算网格,根据边界几何控制,运用网格映射和比例变换方法,编程自动化实现由基准进气道计算网格映射生成实际结构不同的系列化二元进气道计算网格。用建立的模型进行仿真。结果证明,减少了建模工作量和提高了工作效率。     

Controllable Image‐Based Transfer of Flow Phenomena

Modelling flow phenomena and their related weathering effects is often cumbersome due their dependence on the environment, materials and geometric properties of objects in the scene. Example‐based modelling provides many advantages for reproducing real textures, but little effort has been devoted to reproducing and transferring complex phenomena. In order to produce realistic flow effects, it is possible to take advantage of the widespread availability of flow images on the Internet, which can be used to gather key information about the flow. In this paper, we present a technique that allows the transfer of flow phenomena between photographs, adapting the flow to the target image and giving the user flexibility and control through specifically tailored parameters. This is done through two types of control curves: a fitted theoretical curve to control the mass of deposited material, and an extended colour map for properly adapting to the target appearance. In addition, our method filters and warps the input flow in order to account for the geometric details of the target surface. This leads to a fast and intuitive approach to easily transfer phenomena between images, providing a set of simple and intuitive parameters to control the process.