从阴影恢复形状的径向基函数反射模型研究

目的 为解决传统阴影恢复形状（SFS）算法由于光源方向初始信息估计不准确,恢复的物体表面过于光滑,3维表面形状误差较大等问题,建立了基于径向基函数神经网络的反射模型,并对传统的神经网络进行了改进。方法 建立的基于径向基函数（SFS）神经网络的从阴影恢复形状反射模型代替了传统方法中采用的理想朗伯体表面反射模型。该模型利用径向基函数优秀的局部映射和函数逼近能力来处理SFS问题,通过网络训练过程中的权值代替物体所受到的初始光源信息,解决了传统算法在进行计算时,必须已知光源参数的限制。在该网络模型中添加自适应学习率算法,加速网络的收敛和训练速度。结果 针对SFS问题处理的两幅经典合成图像以及两幅实际图像进行了实验,实验结果表明,改进后的算法在3维视觉效果和3维形状信息的恢复方面都明显优于传统算法。归一化后的3维高度误差结果相比传统算法缩小了60%以上,而且同时适用合成图像和实际图像;自适应学习率的加入,使得网络的训练速度大大加快,对一幅128×128像素的图像,运算速度提升了50%。结论 本文针对SFS问题建立了基于RBF神经网络的从阴影恢复形状反射模型,利用网络模型中的参数代替SFS问题中的初始光源信息,通过最优化方法求解SFS问题。并针对传统的神经网络固定学习率造成网络收敛速度慢,容易陷入局部极小值的问题,加入了自适应学习率算法。实验结果表明,改进后的算法在处理该SFS问题时表现了优秀的性能,适用范围更广,收敛速度更快。     

基于径向基函数网络的SFS算法研究

分析了现有从明暗恢复形状(SFS)的几种方法普遍存在对恢复的形状的连续性和光滑性的缺点，提出了一种基于径向基函数网络模型进行从明暗恢复形状的新算法。该算法先采用网络构造一个曲面方程，再利用反射函数作为约束条件，通过调整权因子和径向基函数中心和宽度对网络进行自学习，得到一个满意的曲面方程。理论和实验证明，该算法在恢复形状的准确性和曲面的光滑性，连续性上有较大改进。     

基于混合基稀疏图像表示的压缩传感图像重构

单一基函数不能对同时包含边缘和纹理信息的自然图像进行最优压缩传感图像重构. 本文根据Meyer的卡通--纹理图像模型和生物视觉原理, 用拉普拉斯塔式分解和圆对称轮廓波分别表示图像的光滑成分和边缘成分, 并构造了窄带轮廓波变换实现纹理成分的稀疏表示. 三种稀疏变换的基函数分别与视觉皮层中的侧膝体、简单细胞及栅格细胞的感受野类似. 结合三种图像稀疏表示方法和凸集交替投影算法提出了基于混合基稀疏表示的压缩传感图像重构算法. 实验结果表明,与基于块匹配三维变换迭代收缩的图像重构算法比较, 本文算法能获得更高的图像重构质量.     

基于Phong模型的明暗恢复形状的新算法

针对传统的混合表面形状恢复算法存在较大误差的问题,提出一种透视投影下从单幅图像混合表面明暗信息恢复形状的新算法。采用Phong反射模型来描述物体表面反射特性,假设光源处于相机的光心处,建立透视投影下的图像辐照度方程。然后由辐照度方程构造包含物体深度信息的Hamilton Jacobi偏微分方程,引入局部高阶LLF通量分裂格式和五阶WENO格式逼近微分方程的粘性解,最终得到物体表面三维形状。实验结果表明,与传统算法相比,新算法的恢复高度的最大误差和平均误差均显著降低。     

基于单张人脸图像三维形状模型重建

在人脸图像识别优化的研究中,针对由单张人脸图像重建三维模型时对人脸图像姿态存在要求的问题,为了提高识别精度,提出基于单张人脸图像姿态预估计和主成分分析(PCA)的形状模型重建算法.首先由三维姿态估计方法得到人脸姿态,并建立人脸形状模型样本库,然后通过选取的特征点,利用主成分分析进行三维人脸形状模型的重构,最后利用径向基函数(RBF)变换和特征点坐标精确调整三维人脸形状模型,并进行仿真.仿真结果表明,重构的三维人脸形状模型效果良好,提高了精度,对有旋转姿态的人脸图像和特征点定位误差也有很好的鲁棒性.     

结合深度图像和强度图像的人脸浅浮雕生成算法

针对单纯基于深度图像压缩方法生成的三维浮雕模型容易存在大量噪声,并且易丢失细节的问题,为了生成特征表达准确且具有艺术美感的人脸浅浮雕,提出一种基于三维深度图像和与之对应的二维强度图像的混合人脸浅浮雕的生成算法.首先对三维深度图像的高度场进行压缩生成浮雕基网格;然后提取二维强度图像的灰度信息、梯度信息和显著度信息,并基于显著度信息对基网格的高度场相应地叠加灰度和梯度信息,以保持脸部五官的细节;最后根据显著度信息使用Laplace算子对网格进行光顺处理,使脸部光滑.实验结果表明,与单纯使用基于深度图像压缩方法相比,文中算法生成的浅浮雕模型可以更好地保持五官的细节特征;与基于图像的浮雕生成方法相比,该算法避免了复杂交互操作,可以更好地保持人脸的整体轮廓和形状.     

GPU加速的多分辨率几何图像快速绘制方法

为实现多分辨率几何图像的高效逼真绘制,将满足饱和性质的层次包围球概念与基于屏幕空间的误差判据思想引入到节点误差测度函数的设计中,提出一种适用于视点相关几何图像的节点误差测度函数.针对传统多分辨率几何图像裂缝消除算法复杂、难以用GPU加速的问题,使用正切函数控制顶点偏移;在GPU上快速消除几何图像四叉树结构的不同分辨率节点绘制时出现的裂缝,实现了节点间网格的快速平滑过渡.实验结果证明,该节点误差测度函数能实现几何图像四叉树节点的精确选择,三维模型特征保持明显;裂缝处理算法易于GPU实现,能获得较高的帧率.     

基于多分辨统计模型和曲面恢复的腹部图像分割算法

针对腹部器官边缘模糊、形状差异大、小样本集合难建立统计模型等问题,提出了基于多分辨率统计集成模型和曲面缺失数据恢复的混合图像分割算法。该算法根据器官模型的纹理特征,建立外观轮廓模型;并定义标志点自信度。对于自信度较高的点,使用基于主动图像搜索和模型变形的方法进行分割;将自信度较低的点视为未知点,利用统计模型和自信度高的已知点进行数据恢复。实验结果表明,该混合算法可成功地降低器官分割的平均误差。     

基于区域分割的三维自由曲面相似性评价算法

为了在工程应用中检索已有的三维CAD模型,以便重用相应零件的设计信息,节省设计和加工成本,提出一种基于曲面分割技术的CAD自由曲面相似性评价算法.依据曲面的曲率将自由曲面分割成具有相对固定曲率特征的不同区域;对每个分割得到的区域用一个7维向量表达其形状的几何特征和拓扑特征,一个自由曲面形状特征即可通过各分割区域所对应的7维向量组成的向量组表达;将该向量组作为自由曲面的形状描述子,2个自由曲面的相似性可通过相对应的形状描述子间的相似性表达.在评价2个曲面形状描述子的相似性时,将描述子中的每个向量看成是一个带有属性的节点,2个形状描述子所对应的2组属性节点可看成是一个二分图,2组属性节点间相应节点距离看成是二分图的权值,并利用赋权二分图最优匹配的算法求出2组属性节点的相似性,实现2个自由曲面之间的相似性评价.实验结果表明,该算法是有效、可行的.     

基于SFS方法的三维重构及精度分析

从明暗恢复形状(SFS)是计算机视觉中三维重构问题的研究热点和难点之一,目前已有算法存在两个问题:1)选择的反射模型不符合物体表面的反射特性;2)引入的约束条件和求解过程过于复杂,求解速度慢,效率低。对SFS算法进行了详细分析,引入了朗伯特光照反射模型,对物体表面做球形假设,然后对图像做近似微分运算以求出高度函数,实现了利用单幅灰度图像恢复物体表面三维形状并仿真的数据处理方法,同时对传统线性化SFS算法和所提算法进行了实验验证,对两种模型的重构精度和算法的执行效率进行了比较和分析。实验仿真结果表明,在保证一定精度的前提下,所提算法的执行效率比传统算法高。     

Color constancy from mutual reflection

Mutual reflection occurs when light reflected from one surface illuminates a second surface. In this situation, the color of one or both surfaces can be modified by a color-bleeding effect. In this article we examine how sensor values (e.g., RGB values) are modified in the mutual reflection region and show that a good approximation of the surface spectral reflectance function for each surface can be recovered by using the extra information from mutual reflection. Thus color constancy results from an examination of mutual reflection. Use is made of finite dimensional linear models for ambient illumination and for surface spectral reflectance. If m and n are the number of basis functions required to model illumination and surface spectral reflectance respectively, then we find that the number of different sensor classes p must satisfy the condition p(2 n+m)/3. If we use three basis functions to model illumination and three basis functions to model surface spectral reflectance, then only three classes of sensors are required to carry out the algorithm. Results are presented showing a small increase in error over the error inherent in the underlying finite dimension models.     

Analysis of certain unilateral problems in von karman plate theory by a penalty method-part 1. A variational principle with penalty

A method is presented here for solving the linear hydrodynamic equations for the sea, using an expansion of the horizontal component of current in terms of depth-varying functions (the basis functions) with coefficients that vary with time and horizontal position. The coefficients in this expansion are determined using a finite difference method in the horizontal and the Galerkin technique in the vertical.Initially the method is presented using an expansion of B-splines in the vertical (a finite element representation in the vertical). The ease with which arbitrary surface and bottom boundary conditions can be satisfied with these basis functions is demonstrated.The paper describes in detail the conditions under which a basis set can be used which does not explicitly satisfy bottom or surface boundary conditions. In such circumstances the boundary conditions are of course incorporated into the differential equations of the problem using the Galerkin method.The effect upon accuracy of using a basis set of cosine functions (a spectral representation in the vertical) which do not satisfy a slip bottom boundary condition, compared with using a similar set of functions which do satisfy this condition, is examined.The error in the surface current (which occurs when a basis set which does not satisfy a nonzero stress surface condition is used) is also considered in detail.The paper shows that by using a basis set of cosine functions a computationally economic method can be derived for solving the three-dimensional linear hydrodynamic equations. The method is sufficiently general to allow for an arbitrary vertical eddy viscosity that varies with space and time though a continuous depth variation of current is still retained. In problems involving a wind-induced flow this viscosity can be related to the wind stress acting on the sea surface. An arbitrary depth variation of sea-bed topography is used throughout.     

图形与图象再现的有限元算法

在计算机视觉以及CAD／CAM等领域都涉及到基于离散观测数据的目标图象或三维曲面图形的重建问题，为此，将最佳逼近与数据平滑理论相结合，提出了一种基于有限元技术的图形与图象重建方法，该方法首先采用Lagrange乘子方法建立正定泛函，进而应用有限元技术及Wewton失代方法求得函极值解，然后通过有限元解的插值计算，重新构造出图形或图象，由于结合了数据平滑处理，因此该方法不仅消除了数据上噪声的影响，而且提高了重建的精度，实验结果证明了方法的有效性和实用性。     

Shape from shading with a linear triangular element surface model

The authors propose to combine a triangular element surface model with a linearized reflectance map to formulate the shape-from-shading problem. The main idea is to approximate a smooth surface by the union of triangular surface patches called triangular elements and express the approximating surface as a linear combination of a set of nodal basis functions. Since the surface normal of a triangular element is uniquely determined by the heights of its three vertices (or nodes), image brightness can be directly related to nodal heights using the linearized reflectance map. The surface height can then be determined by minimizing a quadratic cost functional corresponding to the squares of brightness errors and solved effectively with the multigrid computational technique. The proposed method does not require any integrability constraint or artificial assumptions on boundary conditions. Simulation results for synthetic and real images are presented to illustrate the performance and efficiency of the method     

Bifurcation and post-buckling analysis of laminated composite plates via reduced basis technique

A reduced basis technique and a problem-adaptive computational algorithm are presented for the bifurcation and post-buckling analysis of laminated anisotropic plates. The computational algorithm can be conveniently divided into three distinct stages. The first stage is that of determining the bifurcation point. The plate is discretized by using displacement finite element (or finite difference) models. The special symmetries exhibited by the response of the anisotropic plate are used to reduce the size of the analysis region. The vector of unknown nodal parameters is expressed as a linear combination of a small number of basis vectors, and a Rayleigh-Ritz technique is used to approximate the finite element equations by a small system of algebraic equations. The reduced equations are used to determine the bifurcation point and the associated eigen mode of the panel.In the second stage of the bifurcation buckling mode is used to obtain a nonlinear solution in the vicinity of the bifurcation point and new (updated) sets of basis vectors and reduced equations are generated. In the third stage the reduced equations are used to trace the post-buckling paths.The effectiveness of the proposed technique for predicting the bifurcation and post-buckling behavior of plates is demonstrated by means of numerical examples for plates loaded by means of prescribed edge displacements.     

Series expansion approach to the analysis and identification of discrete Hammerstein systems

In this paper, a finite–series expansion method is presented for the analysis and parameter identification of a discrete non-linear system that is described by a Hammerstein model consisting of a memoryless gain of polynomial form followed by a linear discrete system. By expanding the system variables in discrete Legendre orthogonal polynomials (DLOPs) and using the shift and product operational properties of DLOPs, the Hammerstein model is converted into a set of linear equations in the DLOP coefficients of unknown output variables and in the system parameters. This converted set of linear algebraic equations is convenient for finding the DLOP coefficients of unknown variables. Also, it allows one to determine the unknown system parameters using the least-squares method when the system input and output data are available.     

Numerical analysis of some dual-phase-lag models

In this paper we analyse, from the numerical point of view, two dual-phase-lag models appearing in the heat conduction theory. Both models are written as linear partial differential equations of third order in time. The variational formulations, written in terms of the thermal acceleration, lead to linear variational equations, for which existence and uniqueness results, and energy decay properties, are recalled. Then, fully discrete approximations are introduced for both models using the finite element method to approximate the spatial variable and the implicit Euler scheme to discretize the time derivatives. Discrete stability properties are proved, and a priori error estimates are obtained, from which the linear convergence of the approximations is derived. Finally, some numerical simulations are described in one and two dimensions to demonstrate the accuracy of the approximations and the behaviour of the solutions.     

自适应复杂环境的投影图像校正算法

为实现投影仪在任意表面上的自适应投影,提出一种可以在日常环境光照条件下进行自动几何校正和色彩补偿的投影图像校正算法.该算法使用基于二进制编码结构光的离散映射集合方法,通过计算对应像素映射关系消除投影图像的几何畸变;然后应用一种优化的朗伯特反射模型构造投影表面的纹理空间,对原始投影图像进行预处理和全局亮度补偿,最终实现投影图像的颜色补偿.实验结果表明,基于文中算法在复杂环境中进行投影,可以在不规则几何表面上投影出符合视觉期望的无变形图像,并能够有效地消除投影表面固有纹理和环境光照对投影图像的干扰;将自适应复杂环境的投影图像校正算法应用于传统投影机摆脱了投影机对投影幕布的依赖,可以在任意环境中实现近似于白色平板幕布的投影效果.