In the fourth chapter , the vector rational interpolation have been used in cagd . we present two methods for generating a segmant of circular arc by the vector continued frations 第四章向量有理插值在cagd中的应用利用向量连分式给出了两种生成圆弧的方法。
In section two , the algorithms of vector - valued rational interpolants are stated generally . then a new algorithm of brivate vector - valued rational interpolants by means of complexification of the knots and backward three - term recurrence relations is given 然后利用插值型值点复数化的方法及向量值连分式的向后三项递推关系式讨论并给出了二元向量值有理插值的一种新算法。
Though the rational fractions based on one - variable ( vector valued ) continued fractions have been used in other engineering fields , its application in the field of digital image processing has n ' t yet been reported in the literature so far . 2 基于一元(向量)连分式形式的有理分式已应用于其它工程领域，但基于矩形网格和三角网格上的混合有理插值在数字图像处理领域目前还没看到这方面的报道。
In the thesis , the fundamental formula of ffd method derives from the square root that is approximated by a continued fraction expansion in the one - way wave equation . optimizations of the parameters of the finite - difference operator improve the validity of the method 本论文用连分式近似单程波波动方程中的平方根导出ffd算法的基本公式，并对ffd算法中的有限差分算子进行了系数优化，进一步提高了计算的有效性。
Our algorithm significantly outperforms the classical bilinear and bicubic interpolation methods in terms of edge sharpness and artifact reduction . 4 . the applications of the continued fractions are extended , which will further push forward the study of the continued fractions 而本文的方法是基于用非线性方法进行边缘处理，该方法将newton线性插值方法和连分式有理插值方法进行有机的结合，提高了图像的插值速度和效果。
In recent years , nonlinear methods have attracted more and more attention and there have been some successful cases , such as median filter , mathematical morphology , etc . as a preferred way to inverstigate nonlinear numerical problems , the continued fractions method can effectively express the gradually changing data or abrupt data , so it is meaningful to study image processing by means of the continued fractions theory and algorithms 近年来在图像处理领域，利用非线性方法进行图像处理取得较好效果的有中值滤波、数学形态学等，非线性方法已引起越来越多研究者的重视。作为研究非线性数值问题的首选方法?连分式方法，不仅能反映数据的渐变性，也能反映数据的突变性。鉴于这些原因，本文将连分式插值和逼近引入到数字图像处理领域，开展了图像插值、图像重建等方面的研究。
And in this part , the algorithm of polygons is emphasized . the second part is focused on image morphing . after expatiating its principal algorithms and mature methods , a method among multiple images is presented and analysed in detail . second , in the second chapter of this thesis , the basic theories and methods are systematically discussed , especially thiele continued fractions , because it is the main interpolation tool in the experiments . and finally , the processes and results of experiments in the application of continued fractions to 2d object metamorphosis are given , and detailed analyzing and discussing are made . the experiments show that the results are good . this demonstrates that it is successful for continued fractions to be applied in the processes of 2d object metamorphosis 其次，在本文的第二章，系统地论述了连分式的基本原理和应用方法，尤其是对thiele型连分式插值函数作了具体的讨论，因为，它是在实验中所用到的主要的插值工具。最后，本文的结尾，给出连分式应用于二维物体渐变的实验过程和结果，并对其进行了仔细的分析和讨论。实验表明，把连分式用在二维物体的渐变过程中，取得了不错的效果，是成功的。
With the review of digital image properties and continued fractions theory , this dissertation focuses on the study of the image interpolation and image reconstruction ; the main contributions are as fallows : first of all , the methods of solving the problem of inverse difference being infinite are successfully found while constructing the thiele - type continued fractions . in this case it is proposed to reorder the set of interpolating points and then construct a thiele - newton blending continued fraction 本文的主要工作可归纳如下：首先，在以图像像素为插值节点集，构造连分式插值函数过程中出现逆差商为无穷大的情况，给出了合理的解决办法，提出了重新调整插值节点集的节点顺序、构造thiele - newton型混合有理的插值方法。
There are a lot of methods of 2d object metamorphosis . the current algorithms have advantages and disadvantages . whether the shape morphing algorithms or image morphing algorithms are concerned , most of them deal with the morphing between two objects . in this thesis , an algorithm of the morphing among multiple 2d objects is presented with the aid of theory of continued fractions 二维物体渐变技术实现方法多种多样，目前提出的算法各有优缺点，无论是形状渐变算法，还是图象渐变算法，它们中的大多数都是处理两个物体之间的渐变。在本文中，利用连分式理论，提出了一种在多个二维物体之间进行渐变的算法。
