Most image encodings achieve orientation invariance by aligning the patches to their dominant orientations and translation invariance by completely ignoring patch position or by max-pooling. Albeit successful, such choices introduce too much invariance because they do not guarantee that the patches are rotated or translated consistently. In this paper, we propose a geometric-aware aggregation strategy, which jointly encodes the local descriptors together with their patch dominant angle or location. The geometric attributes are encoded in a continuous manner by leveraging explicit feature maps. Our technique is compatible with generic match kernel formulation and can be employed along with several popular encoding methods, in particular Bag-of-Words, VLAD and the Fisher vector. The method is further combined with an efficient monomial embedding to provide a codebook-free method aggregating local descriptors into a single vector representation. Invariance is achieved by efficient similarity estimation of multiple rotations or translations, offered by a simple trigonometric polynomial. This 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. 
Rotation and translation covariant match kernels for image retrieval