Hierarchical Encoding of Sequential Data With Compact and Sub-Linear Storage Cost

Snapshot-based visual localization is an important problem in several computer vision and robotics applications such as Simultaneous Localization And Mapping (SLAM). To achieve real-time performance in very large-scale environments with massive amounts of training and map data, techniques such as approximate nearest neighbor search (ANN) algorithms are used. While several state-of-the-art variants of quantization and indexing techniques have demonstrated to be efficient in practice, their theoretical memory cost still scales at least linearly with the training data (i.e., O(n) where n is the number of instances in the database), since each data point must be associated with at least one code vector. To address these limitations, in this paper we present a totally new hierarchical encoding approach that enables a sub-linear storage scale. The algorithm exploits the widespread sequential nature of sensor information streams in robotics and autonomous vehicle applications and achieves, both theoretically and experimentally, sub-linear scalability in storage required for a given environment size. Furthermore, the associated query time of our algorithm is also of sub-linear complexity. We benchmark the performance of the proposed algorithm on several real-world benchmark datasets and experimentally validate the theoretical sub-linearity of our approach, while also showing that our approach yields competitive absolute storage performance as well.