As an alternative to vector representations, a recent trend in image classification suggests to integrate additional structural information in the description of images in order to enhance classification accuracy. Rather than being represented in a p-dimensional space, images can typically be encoded in the form of strings, trees or graphs and are usually compared either by computing suited metrics such as the (string or tree)-edit distance, or by testing subgraph isomorphism. In this paper, we propose a new way for representing images in the form of strings whose symbols are weighted according to a TF-IDF-based weighting scheme, inspired from information retrieval. To be able to handle such real-valued weights, we first introduce a new weighted string edit distance that keeps the properties of a distance. In particular, we prove that the triangle inequality is preserved which allows the computation of the edit distance in quadratic time by dynamic programming. We show on an image clas...