CEDRIC Research Report n 1049 Back to the curse of dimensionality with local image descriptors

In this report, we are interested in the fast retrieval, in a large collection of points in highdimensional space, of points close to a query point: we want to efficiently find the set of points within a sphere of center query point pi and radius ǫ (a sphere query). It has been argued that beyond a rather small dimension (d ≥ 10) for such sphere queries as well as for other similarity queries, sequentially scanning the collection of points is faster than crossing a tree structure indexing the collection (the so-called curse of dimensionality phenomenon). The contribution of this report is to experimentally show that in the presence of redundancy in data, the curse of dimensionality is delayed to higher dimensions, rendering the use of tree-structured index still effective for a large number of applications dealing with points of moderate dimensions. We compare the performance of a single sphere query when the collection is indexed by a tree structure (an SR-tree in our experiments) to that of a sequential scan and to that of the VA-File which is an amelioration of the sequential scan. This study is applied to content-based image retrieval where images are described by local descriptors based on points of interest. Such descriptors involve a relatively small dimension (in general up to 30) and several sphere queries that are usually time consuming, justifying that the collection of points be indexed by a tree structure. The experiments were performed over 30 databases involving different synthetic and real distributions.