Optimal transport (OT) measures distances between distributions in a way that depends on the geometry of the sample space. In light of recent advances in computational OT, OT distances are widely used as loss functions in machine learning. Despite their prevalence and advantages, OT loss functions can be extremely sensitive to outliers. In fact, a single adversarially-picked outlier can increase the standard W2-distance arbitrarily. To address this issue, we propose an outlier-robust formulation of OT. Our formulation is convex but challenging to scale at a first glance. Our main contribution is deriving an \emph{equivalent} formulation based on cost truncation that is easy to incorporate into modern algorithms for computational OT. We demonstrate the benefits of our formulation in mean estimation problems under the Huber contamination model in simulations and outlier detection tasks on real data.
Optimal pose and shape estimation for category-level 3D object perception
We consider a category-level perception problem, where one is given 3D sensor data picturing an object of a given
category (e.g., a car), and has to reconstruct the pose and shape of the object despite intra-class variability (i.e., different car models have different shapes). We consider an active shape model, where —for an object category— we are given a library of potential CAD models describing objects in that category, and we adopt a standard formulation where pose and shape estimation are formulated as a non-convex optimization. Our first contribution is to provide the first certifiably optimal solver for pose and shape estimation. In particular, we show that rotation estimation can be decoupled from the estimation of the object translation and shape, and we demonstrate that (i) the optimal object rotation can be computed via a tight (small-size) semidefinite relaxation, and (ii) the translation and shape parameters can be computed in closed-form given the rotation. Our second contribution is to add an outlier rejection layer to our solver, hence making it robust to a large number of misdetections. Towards this goal, we wrap our optimal solver in a robust estimation scheme based on graduated non-convexity. To further enhance robustness to outliers, we more »
- Award ID(s):
- 2044973
- Publication Date:
- NSF-PAR ID:
- 10317130
- Journal Name:
- Robotics science and systems
- ISSN:
- 2330-765X
- Sponsoring Org:
- National Science Foundation
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Accepted Manuscript1.0
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