Universal Discrete Filtering with Lookahead or Delay

We consider the universal discrete filtering problem, where an input sequence generated by an unknown source passes through a discrete memoryless channel, and the goal is to estimate its components based on the output sequence with limited lookahead or delay. We propose and establish the universality of a family of schemes for this setting. These schemes are induced by universal Sequential Probability Assignments (SPAs), and inherit their computational properties. We show that the schemes induced by LZ78 are practically implementable and well-suited for scenarios with limited computational resources and latency constraints. In passing, we use some of the intermediate results to obtain upper and lower bounds that appear to be new, in the purely Bayesian setting, on the optimal filtering performance in terms, respectively, of the mutual information between the noise-free and noisy sequence, and the entropy of the noise-free sequence causally conditioned on the noisy one.

Fully Geometric Panoramic Localization

We introduce a lightweight and accurate localization method that only utilizes the geometry of 2D-3D lines. Given a pre-captured 3D map, our approach localizes a panorama image, taking advantage of the holistic 360 view. The system mitigates potential privacy breaches or domain discrepancies by avoiding trained or hand-crafted visual descriptors. However, as lines alone can be ambiguous, we express distinctive yet compact spatial contexts from relationships between lines, namely the dominant directions of parallel lines and the intersection between non-parallel lines. The resulting representations are efficient in processing time and memory compared to conventional visual descriptor-based methods. Given the groups of dominant line directions and their intersections, we accelerate the search process to test thousands of pose candidates in less than a millisecond without sacrificing accuracy. We empirically show that the proposed 2D-3D matching can localize panoramas for challenging scenes with similar structures, dramatic domain shifts or illumination changes. Our fully geometric approach does not involve extensive parameter tuning or neural network training, making it a practical algorithm that can be readily deployed in the real world. Project page including the code is available through this link: https://82magnolia.github.io/fgpl/.