Estimation of Camera Locations in Highly Corrupted Scenarios: All About that Base, No Shape Trouble

Robust Group Synchronization via Cycle-Edge Message Passing

“…However, this approach lacks any theoretical guarantees and may fail in various cases. For example, the case where edges are maliciously corrupted and some cycles with corrupted edges satisfy d G (g L , e) < / √ m. An iterative reweighting strategy, referred to as IR-AAB, was proposed in [38] to identify corrupted pairwise directions when estimating camera locations. Experiments on synthetic data showed that IR-AAB was able to detect exactly the set of corrupted pairwise directions that were uniformly distributed on S 2 with low or medium corruption rate.…”

“…The basic idea of this work was first sketched for the different problem of camera location estimation in a conference paper [38] (we explain this problem later in Sect. 2.1).…”

“…2.1). In addition to formulating this idea to the general group synchronization problem as well as carefully explaining it in the context of message passing, we present nontrivial theoretical guarantees, unlike the very basic and limited ones in [38]. Most importantly, we establish exact and fast recovery of the underlying group elements.…”

“…A somewhat similar problem to group synchronization is camera location estimation [20,33,34,38]. It uses the noncompact group R 3 with vector addition, and its input includes possibly corrupted measurements of {T g * i j } i j∈E , where T (g…”

A Computational Theory of Robust Localization Verifiability in the Presence of Pure Outlier Measurements

“…In [22], [23], the authors estimate the location of the nodes (with relative direction measurements) by minimizing a least square objective function with global scale constraints through a semi-definite relaxation (SDR), while [27], [28] solve a similar problem through constrained gradient descent; in both cases, although some theoretical analysis of the robustness of the method to noise is given, the resulting methods are not robust to outliers (due to the use of the least squares cost). To obtain robustness, a possible approach is to use a pre-processing stage (e.g., using Bayesian inference or other mechanisms) to pre-process the measurements and remove outliers, followed by PGO [19], [21], [30], [31], [33]. An alternative or complementary method is to optimize robust (ideally convex) cost functions, such as the Least Unsquared Deviation (LUD) [15], [34] or others [32]; in this case, the optimization can be carried out using re-weighting techniques (such as Iterative Reweighted Least Squares, IRLS [17] or others [1], [25]), or Alternate Direction Method of Multipliers (ADMM, [7], [12]).…”