Stochastic Attraction-Repulsion Embedding for Large Scale Image Localization

This paper tackles the problem of large-scale image-based localization (IBL) where the spatial location of a query image is determined by finding out the most similar reference images in a large database. For solving this problem, a critical task is to learn discriminative image representation that captures informative information relevant for localization. We propose a novel representation learning method having higher location-discriminating power. It provides the following contributions: 1) we represent a place (location) as a set of exemplar images depicting the same landmarks and aim to maximize similarities among intra-place images while minimizing similarities among inter-place images; 2) we model a similarity measure as a probability distribution on L_2-metric distances between intra-place and inter-place image representations; 3) we propose a new Stochastic Attraction and Repulsion Embedding (SARE) loss function minimizing the KL divergence between the learned and the actual probability distributions; 4) we give theoretical comparisons between SARE, triplet ranking and contrastive losses. It provides insights into why SARE is better by analyzing gradients. Our SARE loss is easy to implement and pluggable to any CNN. Experiments show that our proposed method improves the localization performance on standard benchmarks by a large margin. Demonstrating the broad applicability of our method, we obtained the third place out of 209 teams in the 2018 Google Landmark Retrieval Challenge. Our code and model are available at https://github.com/Liumouliu/deepIBL.Comment: ICC

Multi-body Non-rigid Structure-from-Motion

Conventional structure-from-motion (SFM) research is primarily concerned with the 3D reconstruction of a single, rigidly moving object seen by a static camera, or a static and rigid scene observed by a moving camera --in both cases there are only one relative rigid motion involved. Recent progress have extended SFM to the areas of {multi-body SFM} (where there are {multiple rigid} relative motions in the scene), as well as {non-rigid SFM} (where there is a single non-rigid, deformable object or scene). Along this line of thinking, there is apparently a missing gap of "multi-body non-rigid SFM", in which the task would be to jointly reconstruct and segment multiple 3D structures of the multiple, non-rigid objects or deformable scenes from images. Such a multi-body non-rigid scenario is common in reality (e.g. two persons shaking hands, multi-person social event), and how to solve it represents a natural {next-step} in SFM research. By leveraging recent results of subspace clustering, this paper proposes, for the first time, an effective framework for multi-body NRSFM, which simultaneously reconstructs and segments each 3D trajectory into their respective low-dimensional subspace. Under our formulation, 3D trajectories for each non-rigid structure can be well approximated with a sparse affine combination of other 3D trajectories from the same structure (self-expressiveness). We solve the resultant optimization with the alternating direction method of multipliers (ADMM). We demonstrate the efficacy of the proposed framework through extensive experiments on both synthetic and real data sequences. Our method clearly outperforms other alternative methods, such as first clustering the 2D feature tracks to groups and then doing non-rigid reconstruction in each group or first conducting 3D reconstruction by using single subspace assumption and then clustering the 3D trajectories into groups.Comment: 21 pages, 16 figure

Dynamic Programming for Positive Linear Systems with Linear Costs

Recent work by Rantzer [Ran22] formulated a class of optimal control problems involving positive linear systems, linear stage costs, and linear constraints. It was shown that the associated Bellman's equation can be characterized by a finite-dimensional nonlinear equation, which is solved by linear programming. In this work, we report complementary theories for the same class of problems. In particular, we provide conditions under which the solution is unique, investigate properties of the optimal policy, study the convergence of value iteration, policy iteration, and optimistic policy iteration applied to such problems, and analyze the boundedness of the solution to the associated linear program. Apart from a form of the Frobenius-Perron theorem, the majority of our results are built upon generic dynamic programming theory applicable to problems involving nonnegative stage costs