中文摘要：

针对基于三角形坐标系的非线性拓扑变形过程中会产生像素点缺失的问题，提出一种定位插值算法．首先判断发生三角变形前的各像素点在图像中是否为有效点，并赋予其相应的参数，再在图像变形过程中对关联参数进行更新；其次针对新产生的空点位置，对其小邻域内的点集参数进行统计，并利用积分图像快速计算插值权重，权重大于设定阈值者即判定为待插值空点；最后进行三次卷积插值．通过在多三角形网格下进行表情设计、人脸过渡等实验的结果表明，该算法能够有效地解决三角形坐标系下拓扑变形的插值问题，明显地改善了图像的视觉效果．

英文摘要：

This paper proposes an algorithm based on triangle coordinate system to solve the interpolation problem occurred in image nonlinear topological deformation process. First, mark original pixels according to their positional properties in an image, and then update those marks during the deformation process. Once the blank points generate, calculate the interpolation weights in a small neighborhood using integral image. If the weight is larger than the threshold, the corresponding point was needed and the cubic convolution interpolation was applied to it eventually. Experiments on expressional design and facial transition using multi-triangle grid demonstrate that this algorithm can solve the interpolation problem of topological deformation in the frame of triangle coordinate system effectively and improve the visual looks obviously.