在图像处理和计算机视觉的许多任务中,经常需要对图像进行插值从而得到像素点之间的信息。标量值图像的插值方法已经得到充分的发展,但张量值图像的插值方法还没有深刻的发展和认识。通过对比较零散的张量值图像插值方法的研究现状进行了系统综述,从数学理论框架的角度出发,将现有的张量值图像插值方法进行全面分析和分类,指出欧氏理论框架计算张量会带来的问题,梳理从欧氏框架到黎曼度量框架的研究脉络,并比较了张量值图像插值方法的评价指标。最后,给出了张量值图像插值方法未来研究方向的建议。

Many tasks in image processing,computer vision and computer graphics require image interpolation or resampling in order to obtain data at locations that do not coincide with the grid points where the digital image values are known. While image interpolation is fairly well understood for scalar images,not much research has been done so far with respect to the interpolation of tensor fields. In this paper,we present a systematic review of the current research status regarding tensor valued image interpolation. Existing approaches of tensor valued image interpolation are fully analyzed and categorized according to their mathematical framework. First,the drawbacks of tensor calculation under the Euclidean framework are pointed out. Then,the transition of research efforts from under Euclidean framework towards under the Riemannian framework are sorted out. After that,different evaluation metrics of tensor field interpolation methods are compared. Finally,future research directions are discussed.