中文摘要：

为了通过几何变形和颜色混合插值来实现2幅图像之间的过渡，采用自定义的三角形坐标系，提出一种图像变形计算方法．首先给出了三角形坐标系的定义，阐述并证明了其关于几何变换的一些定理，使得拓扑变形易于实现，可应用在图像变形技术中；然后描述了基于三角形坐标系的图像变形算法．通过一组人脸表情的合成与移植和另一组变脸技术应用的例子，证明了文中方法的有效性．

英文摘要：

To transform one image into another fluidly by geometric deformation and color blending, the paper proposes a calculation method of image morphing based on a self-defined coordinate system called triangle coordinate system. First, the definition of the triangle coordinate system is given, and some theorems that make topological deformation easy and can be applied in image morphing are discussed. Then the details of image morphing algorithm are presented. As the applications, two experiments are given. One is facial expression synthesis and transplantation, the other is facechanging. And the results are satisfying.