| 1. | Projective transformation of rational quadratic bzier curves
曲线的射影变换 |
| 2. | Regular projective transformation
正则射影变换 |
| 3. | Necessary and sufficient condition of 2 - dimension projective transformation being involution
二维射影变换是对合的充要条件 |
| 4. | Some properties of projective transformation on projection plane producing by polar transformation
配极变换诱导的直射变换的若干性质 |
| 5. | First , we compute the larger spatial transformation . then , we refine the parameters using projective transformation . it is proved that this method can produce good result and fast speed
我们采用的是基于频域仿射模型的光流方程，即首先计算比较大的空间变换，然后再对其进行透视变换求精，实验证明这样既可以获得较好的效果，也提高了计算速度。 |
| 6. | In two - view case , a method is presented for calculation 2d projective transformation and construction the virtual elements by combination of spatial points and lines . so more 3d invariants of object ' s spatial structures can be extracted from real elements and virtual eleme nts . ( 3 ) the geometric characteristics of 2d symmetric objects " in perspective images are lucubrated
( 2 )扩展了2d射影变换矩阵的求解方法，将单纯利用点集对应的计算模式扩展到利用直线集、点线组合等多种类型来建立两个射影平面的对应关系；总结了平面上基于点、直线元素可求解的多种3d不变量；提出了双视图下由点、直线元素的多种对应关系求解2d射影变换来构造“虚元素”的方法，结合“实元素”和“虚元素”可以提取更多的空间3d不变量。 |
| 7. | Finally , a method is put forward to construct the nurbs curves on sphere , which extends the de boor recursive algorithm in r3 to one on the sphere by replacing the geodesic distances for the lines and studies their many geometric properties analogous to those in euclidean spaces , such as the differential property , the local property , the parameter invariance under a projective transformation , and so on
两种方法均给出误差估计，使逼近螺线可达到任何预先给定的精确阶。最后，给出球面nurbs曲线生成算法：用球面上测地线? ?劣大圆弧代替直线段，将欧氏空间r ~ 3中的deboor递推算法推广到球面上构造曲线。 |
| 8. | Second , more feature points are extracted for advanced registration based on projective transformation . compared with the ordinary method , our method has a better robust feature with higher accuracy , it also has a fully automatic feature so it need little human intervention in the whole process . the image segmentation , feature extraction , feature correspondency , and transformation model of multi - modality medical image registration are also studied in this paper
本研究的创新之处:针对rf和fa视网膜图像的特点，提出了新的血管细化的新方案;在特征点提取方面，提出了“三轮定心”这种新的特征点提取方法;提出了由“粗配”到“细配”的混合配准方法;力矩主轴法用于图像配准参数的估计及对应性尺度参数范围的定值。 |
| 9. | We introduce five topological characteristics and geometry characteristics that are invariant under projective transformation specially perspective projection . the definition of homograph is given by means of these characteristics , and then the recognizing method of the homograph is proposed according to the definition of homograph
接着，根据透视投影不变性提出了5个用来描述多边形形状的拓扑特征和几何特征，这些特征在透视投影下是不变的，以这些特征给出了在透视投影下平面多边形为类似形的定义。 |
