  Image search systems based on local descriptors typically achieve orientation
invariance by aligning the patches on their dominant orientations. Albeit
successful, this choice introduces too much invariance because it does not
guarantee that the patches are rotated consistently. This paper introduces an
aggregation strategy of local descriptors that achieves this covariance
property by jointly encoding the angle in the aggregation stage in a continuous
manner. It is combined with an efficient monomial embedding to provide a
codebook-free method to aggregate local descriptors into a single vector
representation. Our strategy is also compatible and employed with several
popular encoding methods, in particular bag-of-words, VLAD and the Fisher
vector. Our geometric-aware aggregation strategy is effective for image search,
as shown by experiments performed on standard benchmarks for image and
particular object retrieval, namely Holidays and Oxford buildings.
