In this paper, we present a set of texture features that are locally invariant to similarity or affinity. The proposed indexing scheme relies on the topographic map, a shape-based representation of images. Thanks to the hierarchical organization of the topographic map, the approach gives a grip on the multi-scale structure of textures. Using simple one dimensional histograms, the method is shown to achieve state-of-the-art performances among locally invariant methods, both on the whole Brodatz and UIUC databases.