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The growth of personal image collections has boosted the creation of many applications, many of which depend on the existence of fast schemes to match similar image descriptors. In this paper we present multicurves, a new indexing method for multimedia descriptors, able to handle high dimensionalities (100 dimensions and over) and large databases (millions of descriptors). The technique allows a fast implementation of approximate kNN search, and deals easily with data updating (insertions and deletions). The index is based on the simultaneous use of several moderate-dimensional space-filling curves. The combined effect of having more than one curve, and reducing the dimensionality of each individual curve allows overcoming undesirable boundary effects. In empirical evaluations, the method compares favorably with state-of-the-art methods, especially when the constraints of secondary storage are considered.