用子午投影法建立回转曲面轮廓线的方程式

强调了子午投影法的两个特点,即几何元素至回转轴和至水平投影面的距离都不改变。提出以这两个不变量建立直线的子午投影的方程式,也就是确定回转曲面轮廓线的方程式。以二维的平面曲线的方程式代替了三维空间曲面的方程式。文中通过方程式的推导,论证了上述观点,并以此为基础,进一步论述了各种特殊位置直线的子午投影的方程式,以及这些子午投影旋转后所形成的曲面。     

用于在流体曲面设计中构造样条的流线的射影等价性与几何构造分析

在流体曲面设计中,从样条必须适应理论流场的一般流体光顺性条件出发,对几种典型的构造样的流线进行了射影与几何综合分析,为构造用于流体曲面设计的样条函数或曲线和选择现有数学样条函数或曲线进行流体曲面设计提供了依据。     

印刷体中文文档中数学公式字符的定位

数学公式字符的定位对整个印刷体中文文档识别系统而言是提高其识别率的重要内容之一。在介绍典型的数学公式字符定位技术的基础上,提出了一种新的两级公式字符定位方法。该方法是采用了印刷体中文文档中不同字符之间的投影分布特征的不同与汉字识别拒识公式字符的思想结合起来对公式字符进行定位。从实验结果可以看出该定位方法能够在公式字符定位的准确率和时间上有了较大的改进,为提高印刷体中文文档识别系统的识别率奠定了基础。     

The Problem of Degeneracy in Structure and Motion Recovery from Uncalibrated Image Sequences

The aim of this work is the recovery of 3D structure and camera projection matrices for each frame of an uncalibrated image sequence. In order to achieve this, correspondences are required throughout the sequence. A significant and successful mechanism for automatically establishing these correspondences is by the use of geometric constraints arising from scene rigidity. However, problems arise with such geometry guided matching if general viewpoint and general structure are assumed whilst frames in the sequence and/or scene structure do not conform to these assumptions. Such cases are termed degenerate.In this paper we describe two important cases of degeneracy and their effects on geometry guided matching. The cases are a motion degeneracy where the camera does not translate between frames, and a structure degeneracy where the viewed scene structure is planar. The effects include the loss of correspondences due to under or over fitting of geometric models estimated from image data, leading to the failure of the tracking method. These degeneracies are not a theoretical curiosity, but commonly occur in real sequences where models are statistically estimated from image points with measurement error.We investigate two strategies for tackling such degeneracies: the first uses a statistical model selection test to identify when degeneracies occur: the second uses multiple motion models to overcome the degeneracies. The strategies are evaluated on real sequences varying in motion, scene type, and length from 13 to 120 frames.     

Minimal Decomposition of Model-Based Invariants

Model-based invariants are relations between model parameters and image measurements, which are independent of the imaging parameters. Such relations are true for all images of the model. Here we describe an algorithm which, given L independent model-based polynomial invariants describing some shape, will provide a linear re-parameterization of the invariants. This re-parameterization has the properties that: (i) it includes the minimal number of terms, and (ii) the shape terms are the same in all the model-based invariants. This final representation has 2 main applications: (1) it gives new representations of shape in terms of hyperplanes, which are convenient for object recognition; (2) it allows the design of new linear shape from motion algorithms. In addition, we use this representation to identify object classes that have universal invariants.     

光正交码的有限射影几何设计方法

光正交码是适用于光纤CDMA系统的扩频序列。但在定义中并未给出构造、生成方法,本文研究的有限几何法是一种有效的光正交码设计方法,它可以设计出最优码。本文对此法原理、设计方法进行了研究,提出了一种计算机辅助设计方法,并给出了实际设计过程及结果。     

Fiducial Marker Based on Projective Invariant for Augmented Reality

Fiducial marker based Augmented Reality has many applications.So far the inner pattern of the fiducial marker is always used to encode the markers.Thus a large portion of the fiducial marker image is used for encoding instead of providing corresponding feature points for pose accuracy.This paper presents a novel method which utilizes directly the projective invariant contained in the positional relation of the corresponding feature points to encode the marker.The proposed method does not require the region of pattern image for encoding any more and can provide more corresponding feature points so that higher pose accuracy can be achieved easily.Many related approaches such as cmnulative distribution function,reprojection verification and robust process are proposed to overcome the problem of sensibility of the projective invariant.Experimental results show that the proposed fiducial marker system is reliable and robust,and can provide higher pose accuracy than that achieved by existing fiducial marker systems.     

具有传输干扰的混沌全状态射影同步

针对具有传输干扰的混沌系统的同步问题,提出一种新的全状态射影同步方案.利用Lyapunov稳定性理论,设计了混沌系统的非线性观测器,得到了具有传输干扰的混沌系统射影同步的充分条件.该方案不仅能够得到以特定缩放因子的射影同步,并且可以在不降低可控性的条件下,根据控制的情况,任意调整缩放因子.利用鲁棒稳定性理论进一步证明了所提方案可大大减小传输干扰对混沌射影同步的影响,从而得到了满意的混沌全状态射影同步.最后,以陈氏系统为例,进行数值仿真,验证了所提方案能够有效地抑制混沌同步系统的信道干扰,得到混沌系统的全状态射影同步.     

采用模糊控制实现混沌系统的广义投影同步

研究了离散混沌系统的广义投影同步问题.基于Takagi-Sugeno(TS)模糊动态模型和Lyapunov稳定性理论,导出了离散混沌系统广义投影同步的一个充分条件.通过一些矩阵操作技巧,这个准则被转化为一组线性矩阵不等式形式.然后,这些线性矩阵不等式的求解可以用Matlab工具箱方便地解决.对Henon映射的数值模拟,仿真结果表明该方法的有效性.     

线性多视图重构的新算法

研究了由多幅图像恢复摄像机矩阵和空间物体三维几何形状这一多视图三维重构问题,改进了由Hartley和Rother等人分别给出的基于由无穷远平面诱导的单应进行射影重构的算法,提出了一种新的线性算法,它仅需要空间中3个点在每幅图像上均可见。因为空间中不在同一直线上的3个点恰好确定一个平面,所以它避免了Hartley和Rother等方法中需要确定空间4个点是否共面这一比较棘手的问题。大量实验结果表明,这种方法快速、准确且受噪声影响小。