Since tensor usage has become more and more popular in image processing, the assessment of the quality between tensor images is necessary for the evaluation of the advanced processing algorithms that deal with this kind of data. In this paper, we expose the methodology that should be followed to extend well-known image quality measures to tensor data. Two of these measures based on structural comparison are adapted to tensor images and their performance is shown by a set of examples. By means of these experiments the advantages of structural based measures will be highlighted, as well as the need for considering all the tensor components in the quality assessment.