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.