基于颜色信息和几何不变性的人脸检测定位

由先验知识我们知道,2D人脸正面图像几何对称;然而,当姿态发生变化时,对于人脸这样的不规则3D几何体,不同的视角、不同的摄像机参数使得在透视成像下得到的图像也不同,并且发现正面人脸具有的对称特性也消失了,因此3D人脸的识别是十分困难的;提出一种从人脸特征的结构特殊性出发,利用2D人脸形状、面部特征等内在的几何约束关系构造射影不变的特征参数、特征关系的射影不变性,同时结合颜色物理信息的人脸检测定位方法,有效地避免了构造3D人脸模型的难题,增强了实验结果的效率、可靠性和稳定性.     

2-旋转对称复动力系统的可视化研究

在复解析映射动力系统的计算机可视化研究中,采用Clifford A.Reiter的"共轭函数和"方法,结合本文作者提出的复指数模型分析构造出一个具有2旋转对称特性的复解析映射族.在参数平面上构造出与经典M集的"周期芽苞"的排列方式不同的广义M集,在动力平面上构造了新形式的2旋转对称分形图.发现了M集上的周期芽苞的排列规律,找到了参数与相应充满Julia集图形结构之间的对应关系.利用本文提出的复映射,可以大量生成以原点为充满Julia集各叶片交汇中心的2旋转对称分形图.为复解析映射的计算机可视化研究增添了新的研究对象.     

基于射影几何的CCD相机几何模型研究

为提高由多幅二维图像解算出的空间坐标信息的精度,基于射影几何原理,提出一种像方空间与物方空间的几何形状计算方法。分析电荷耦合器件( CCD)相机成像射影几何原理,根据透视变换和交比不变性质,利用直线之间存在平行、垂直和相交等关系,建立基于直线特征的相机成像几何模型,已知相机参数,证明并推导像方空间二维影像和物方空间形状与坐标信息的几何转换关系。分析结果表明,该方法结合了整幅图像的几何信息,能提高空间点等几何特征的坐标信息计算精度,以及视觉测量和三维重建的精度。     

基于相位信息的对称性检测算法

提出一种基于相位信息的对称性检测新方法,将对称性检测问题转化为频域中的相位分析.文中的可行性分析、PSD的定义及其合理性证明为该算法奠定了理论基础.实验证明：该算法可直接应用于原始图像,不需要图像的任何先验知识,不需分割等任何预处理;具有旋转、亮度和对比度不变性;可以同时检测镜像对称、旋转对称、曲线对称等多种对称性.     

MSC Marc中旋转周期对称分析的tie连接实现

几何形状沿周向周期性变化,在力学上称为旋转周期对称结构或循环对称结构,见图1.如果载荷也沿周向周期性变化,那么只需分析其中一个施加旋转周期性边界条件的子结构,就可直接得到整个结构的计算结果。     

SAR图像数据稀疏性分析及在特征增强中的应用

利用合成孔径雷达(SAR)图像中目标的后向散射特性和目标散射中心的理论,分析了SAR图像数据稀疏性的成因。指出SAR图像的稀疏性与典型散射体的后向散射特性、成像区域目标强散射中心的稀疏性和成像区域的粗糙度等因素有关。根据视觉稀疏表示机制,比较了SAR图像与光学图像稀疏特征在视觉上的差异。然后,分析了稀疏约束在SAR图像分辨率增强中的应用方法。最后,用仿真和实测SAR图像数据验证了稀疏性在特征增强中的作用。     

基于黎曼流形的平面目标识别

平面目标识别中的几何形变可用射影变换群描述. 与紧致李群SO(n, R)不同, 正则化的射影变换群, 即非紧致李群SL(n, R)上由黎曼度量决定的黎曼指数映射不同于由单参数子群决定的李群指数映射. 基于黎曼流形优化算法得到取值于特殊线性群SL(3, R)的样本的内蕴均值和协方差矩阵, 并依此构建李群正态分布. 利用此先验知识, 根据贝叶斯定理进行简单背景下的平面目标的识别实验. 结果表明, 利用射影变换群的统计特性可有效提高平面目标识别的成功率.     

旋转对称三角传感器激光散斑的仿真研究

散斑是激光三角传感器测量不确定度极限的根本影响因素。提出了一种用于旋转对称激光三角传感器的激光散斑的仿真方法,获得了仿真散斑图像。在旋转对称的三角传感器中,投射的激光点在检测器上被成像为一个环,从而散斑也相应是圆弧形。研究了散斑的特性,该散斑在环的半径方向上服从主观散斑的特性,其尺寸由光学系统的数值孔径决定。而在环的切线方向上,其本质上是客观散斑,由于光学系统存在折返光路,其尺寸由物体到检测器的光程、投射的激光光斑尺寸和成像圆环的半径决定。实验结果表明,仿真结果与散斑理论一致。基于仿真给出了对旋转对称三角传感器位移测量不确定度极限的分析,结果表明,使用旋转对称形式的传感器光学布局,在相同的光学系统数值孔径和使用同样的灰度质心算法的情况下,可达到传统激光三角测量不确定度的1/5。     

采用改进的几何算法快速估计图像旋转角度

不规则的旋转运动会明显的降低图像序列的质量,旋转运动估计是实现电子图像稳定的关键技术.采用仿射变换模型可以有效地估计图像二维运动参数,但是求解最小二乘解的计算量太大.提出了一种简单的估计图像旋转角度的方法.利用匹配块相对于旋转中心位移矢量对称的特性,消除平移运动引起的运动矢量,通过简单的几何计算即町获得旋转参数,进一步,通过合理设置阈值,降低局部运动估计误差对全局结果的影响.理论分析和仿真结果表明,在帧间图像旋转角度小于10°的条件下,应用方法能够简单有效的估计出旋转角度.     

蜂窝结构等效电磁模型的比较与改进

蜂窝结构是吸波材料中广泛使用的一种结构,但其复杂的几何结构给其电磁特性分析与设计带来了一定的困难.采用强扰动理论和变分法的两种等效模型与实验结果进行对比,分析了两种模型中横向等效电磁参数的对称性与实验结果中的非对称性方面存在的显著差异,并通过引入代表蜂窝结构横向非对称性参数的方法对等效电磁模型进行了改进.数值仿真表明,在使用等效电磁模型来描述蜂窝结构时,变分模型要优于强扰动模型,而改进模型不仅使得两种等效电磁模型都能够反映出蜂窝结构横向电磁参数的非对称性,而且能够在一定程度上提高等效电磁模型的准确性.     

Finding the M-best consistent correspondences between 3D symmetric objects

This paper proposes a novel algorithm that resolves the underlying ambiguity in shape correspondences between symmetric objects. Due to the equivocal nature of symmetry, each part of a symmetric object may have two or more correspondence candidates in another symmetric object, which may induce local inconsistencies in the correspondence of parts or global ambiguities in shape matching. As an effective approach for resolving these symmetric ambiguities, we find multiple probable solutions for consistent shape correspondences between two 3D symmetric objects and let the user select one of them for an application-specific purpose. We formulate the problem of 3D symmetric object correspondences with a Markov Random Field (MRF) and iteratively search multiple solutions by excluding previously found solutions using Linear Programming (LP). The consistency of each solution is provided by four-point correspondences as high-order measurements in our MRF network, with each node corresponding to a point pair and each edge corresponding to a pair of point pairs. By leveraging the properties of the symmetry structure of the 3D object, we further reduce the complexity of our MRF network while efficiently handling high-order measurements. Finally, we evaluate the proposed algorithm using real-world symmetric object datasets.     

Automatic rotational symmetry determination for shape analysis

The determination of the rotational symmetry of a shape is useful for object recognition and shape analysis in computer vision applications. In this paper, a simple, but effective, algorithm to analyse the rotational symmetry of a given closed-curve shape S is proposed. A circle C with the centroid of S as the circle center and the average radius of S as the circle radius is superimposed on S, resulting in the intersection of C and S at a set of points. By theoretical analysis, the relationship between the order N_s of the rotational symmetry of S and the number of intersection points between C and S is established. All the possible values for N_s are determined. And finally N_s is determined by evaluating the similarity between S and its rotated versions. In the proposed algorithm, only simple pixel operations and second-order moment function computation are involved. Several problems caused by the use of discrete image coordinates are analysed and solved for correct decision-making in the algorithm. Good experimental results are also included.     

Generalized multidimensional orthogonal polynomials withapplications to shape analysis

A technique using the generalized multidimensional orthogonal polynomials (GMDOP) for 2-D shape analysis is proposed. In shape analysis, spatial invariances (i.e. translational invariance, scaling invariance, rotational invariance, etc.) are important requirements for a shape analysis algorithm. The described technique provides not only the three invariant properties but also mirror-image rotational invariance and permutational invariance. Experimental results supporting the theory are presented     

Skewed rotational symmetry detection from a 2D line drawing of a 3D polyhedral object

This paper introduces a new algorithm for detecting skewed rotational symmetry in a 2D line drawing of a 3D polyhedral object by locating the possibly-multiple symmetry axes. The drawing is converted into an edge–vertex graph from which the algorithm finds the faces of the object and the sets of topologically symmetric edges and vertices. It then checks that each set of vertices is rotationally symmetric geometrically by analyzing the distribution of the vertices around the circumference of the best-fit ellipse. The object is rotationally skewed symmetric if the best fit ellipses of all the vertex sets have parallel axes, equal ratio of major radius to minor radius and centers on the axis of rotation. A tolerance is used in the calculation to allow for inaccuracies in the line drawings. A set of experimental results is presented showing that the algorithm works well.     

基于谱对称的形状配准方法

针对现有三维形状配准方法中存在左右翻转的错误匹配问题,提出了基于内蕴对称特征检测的高效形状配准算法。首先,通过热核与几何约束构建模型的内蕴自对称点对;其次,基于谱嵌入特征空间分析提取模型的内蕴对称平面,并依据模型表面法向量有效识别模型的左右结构属性;然后,根据内蕴对称点对获得模型的一致性谱对称结构描述;最后,引入一致性点漂移算法(CPD),实现基于谱对称的非刚性模型的形状配准,有效避免了模型配准中的左右结构翻转问题。实验进一步论证了这种方法不仅有效提高了模型匹配的效率,而且能有效识别同类模型的结构特征,对于非刚性模型的配准具有较强的鲁棒性。     

Rotation Invariant Kernels and Their Application to Shape Analysis

Shape analysis requires invariance under translation, scale, and rotation. Translation and scale invariance can be realized by normalizing shape vectors with respect to their mean and norm. This maps the shape feature vectors onto the surface of a hypersphere. After normalization, the shape vectors can be made rotational invariant by modeling the resulting data using complex scalar-rotation invariant distributions defined on the complex hypersphere, e.g., using the complex Bingham distribution. However, the use of these distributions is hampered by the difficulty in estimating their parameters and the nonlinear nature of their formulation. In the present paper, we show how a set of kernel functions that we refer to as rotation invariant kernels can be used to convert the original nonlinear problem into a linear one. As their name implies, these kernels are defined to provide the much needed rotation invariance property allowing one to bypass the difficulty of working with complex spherical distributions. The resulting approach provides an easy, fast mechanism for 2D & 3D shape analysis. Extensive validation using a variety of shape modeling and classification problems demonstrates the accuracy of this proposed approach.     

几何不变性及其在3D物体识别中的应用

三维物体识别是计算机视觉研究的重要内容之一，它要求从3D物体的2D图象中识别和定位物体．由于物体成像时会受到观察视角、摄像机参数的影响，因此使得同一物体在不同观察视角、不同摄像机参数等条件下所得到的图象存在差异．但由于几何不变性方法可以有效地消除这种差异带给3D物体识别的不利影响，所以，近20年来这种方法受到了广泛的关注和研究．为使人们了解该领域的研究现状，以对该领域的研究有所启发，首先讨论了基于几何不变性的3D物体识别方法的研究内容，包括研究的几何框架和其不变性以及几何不变性在3D物体识别中的主要应用；其次，总结性地评述了该领域的研究现状；最后，提出了研究的发展方向．