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Given two probability densities on related data spaces, we seek a map pushing one density to the other while satisfying application-dependent constraints. For maps to have utility in a broad application space (including domain translation,…
Mobile robots rely on maps to navigate through an environment. In the absence of any map, the robots must build the map online from partial observations as they move in the environment. Traditional methods build a map using only direct…
As the application scenarios of mobile robots are getting more complex and challenging, scene understanding becomes increasingly crucial. A mobile robot that is supposed to operate autonomously in indoor environments must have precise…
In many applications of autonomous mobile robots the following problem is encountered. Two maps of the same environment are available, one a prior map and the other a sensor map built by the robot. To benefit from all available information…
Robotic surgical subtask automation has the potential to reduce the per-patient workload of human surgeons. There are a variety of surgical subtasks that require geometric information of subsurface anatomy, such as the location of tumors,…
Image-based localization is a core component of many augmented/mixed reality (AR/MR) and autonomous robotic systems. Current localization systems rely on the persistent storage of 3D point clouds of the scene to enable camera pose…
Optimal transport (OT) is a widely used technique for distribution alignment, with applications throughout the machine learning, graphics, and vision communities. Without any additional structural assumptions on trans-port, however, OT can…
We study the use of amortized optimization to predict optimal transport (OT) maps from the input measures, which we call Meta OT. This helps repeatedly solve similar OT problems between different measures by leveraging the knowledge and…
Precise and long-term stable localization is essential in parking lots for tasks like autonomous driving or autonomous valet parking, \textit{etc}. Existing methods rely on a fixed and memory-inefficient map, which lacks robust data…
Optimal Transport (OT) theory investigates the cost-minimizing transport map that moves a source distribution to a target distribution. Recently, several approaches have emerged for learning the optimal transport map for a given cost…
Off-road environments present unique challenges for autonomous navigation due to their complex and unstructured nature. Traditional global path-planning methods, which typically aim to minimize path length and travel time, perform poorly on…
Optimal transport on a graph focuses on finding the most efficient way to transfer resources from one distribution to another while considering the graph's structure. This paper introduces a new distributed algorithm that solves the optimal…
This article introduces a generalization of the discrete optimal transport, with applications to color image manipulations. This new formulation includes a relaxation of the mass conservation constraint and a regularization term. These two…
One of the main difficulties of scaling current localization systems to large environments is the on-board storage required for the maps. In this paper we propose to learn to compress the map representation such that it is optimal for the…
Building on progress in feature representations for image retrieval, image-based localization has seen a surge of research interest. Image-based localization has the advantage of being inexpensive and efficient, often avoiding the use of 3D…
In this paper, we propose a general graph optimization based framework for localization, which can accommodate different types of measurements with varying measurement time intervals. Special emphasis will be on range-based localization.…
Map-to-map matching is a critical task for aligning spatial data across heterogeneous sources, yet it remains challenging due to the lack of ground truth correspondences, sparse node features, and scalability demands. In this paper, we…
This article presents a general approximation-theoretic framework to analyze measure transport algorithms for probabilistic modeling. A primary motivating application for such algorithms is sampling -- a central task in statistical…
Mapping is crucial in robotics for localization and downstream decision-making. As robots are deployed in ever-broader settings, the maps they rely on continue to increase in size. However, storing these maps indefinitely (cold storage),…
This paper presents a unified framework for smooth convex regularization of discrete optimal transport problems. In this context, the regularized optimal transport turns out to be equivalent to a matrix nearness problem with respect to…