Orientation covariant aggregation of local descriptors with embeddings

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.Comment: European Conference on Computer Vision (2014

Learning Equivariant Representations

State-of-the-art deep learning systems often require large amounts of data and computation. For this reason, leveraging known or unknown structure of the data is paramount. Convolutional neural networks (CNNs) are successful examples of this principle, their defining characteristic being the shift-equivariance. By sliding a filter over the input, when the input shifts, the response shifts by the same amount, exploiting the structure of natural images where semantic content is independent of absolute pixel positions. This property is essential to the success of CNNs in audio, image and video recognition tasks. In this thesis, we extend equivariance to other kinds of transformations, such as rotation and scaling. We propose equivariant models for different transformations defined by groups of symmetries. The main contributions are (i) polar transformer networks, achieving equivariance to the group of similarities on the plane, (ii) equivariant multi-view networks, achieving equivariance to the group of symmetries of the icosahedron, (iii) spherical CNNs, achieving equivariance to the continuous 3D rotation group, (iv) cross-domain image embeddings, achieving equivariance to 3D rotations for 2D inputs, and (v) spin-weighted spherical CNNs, generalizing the spherical CNNs and achieving equivariance to 3D rotations for spherical vector fields. Applications include image classification, 3D shape classification and retrieval, panoramic image classification and segmentation, shape alignment and pose estimation. What these models have in common is that they leverage symmetries in the data to reduce sample and model complexity and improve generalization performance. The advantages are more significant on (but not limited to) challenging tasks where data is limited or input perturbations such as arbitrary rotations are present

Early burst detection for memory-efficient image retrieval

International audienceRecent works show that image comparison based on local descriptors is corrupted by visual bursts, which tend to dominate the image similarity. The existing strategies, like power-law normalization, improve the results by discounting the contribution of visual bursts to the image similarity. In this paper, we propose to explicitly detect the visual bursts in an image at an early stage. We compare several detection strategies jointly taking into account feature similarity and geometrical quantities. The bursty groups are merged into meta-features, which are used as input to state-of-the-art image search systems such as VLAD or the selective match kernel. Then, we show the interest of using this strategy in an asymmetrical manner, with only the database features being aggregated but not those of the query. Extensive experiments performed on public benchmarks for visual retrieval show the benefits of our method, which achieves performance on par with the state of the art but with a significantly reduced complexity, thanks to the lower number of features fed to the indexing system

On the Expressive Power of Geometric Graph Neural Networks

The expressive power of Graph Neural Networks (GNNs) has been studied extensively through the Weisfeiler-Leman (WL) graph isomorphism test. However, standard GNNs and the WL framework are inapplicable for geometric graphs embedded in Euclidean space, such as biomolecules, materials, and other physical systems. In this work, we propose a geometric version of the WL test (GWL) for discriminating geometric graphs while respecting the underlying physical symmetries: permutations, rotation, reflection, and translation. We use GWL to characterise the expressive power of geometric GNNs that are invariant or equivariant to physical symmetries in terms of distinguishing geometric graphs. GWL unpacks how key design choices influence geometric GNN expressivity: (1) Invariant layers have limited expressivity as they cannot distinguish one-hop identical geometric graphs; (2) Equivariant layers distinguish a larger class of graphs by propagating geometric information beyond local neighbourhoods; (3) Higher order tensors and scalarisation enable maximally powerful geometric GNNs; and (4) GWL's discrimination-based perspective is equivalent to universal approximation. Synthetic experiments supplementing our results are available at https://github.com/chaitjo/geometric-gnn-dojoComment: NeurIPS 2022 Workshop on Symmetry and Geometry in Neural Representation