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This paper is about the old Wahba problem in its more general form, which we call "simultaneous rotation and correspondence search". In this generalization we need to find a rotation that best aligns two partially overlapping $3$D point…

Tracking the pose of instruments is a central problem in image-guided surgery. For microscopic scenarios, optical coherence tomography (OCT) is increasingly used as an imaging modality. OCT is suitable for accurate pose estimation due to…

We propose a general framework for end-to-end learning of data structures. Our framework adapts to the underlying data distribution and provides fine-grained control over query and space complexity. Crucially, the data structure is learned…

We study the point location problem on dynamic planar subdivisions that allows insertions and deletions of edges. In our problem, the underlying graph of a subdivision is not necessarily connected. We present a data structure of linear size…

The Bin Packing Problem (BPP) has attracted enthusiastic research interest recently, owing to widespread applications in logistics and warehousing environments. It is truly essential to optimize the bin packing to enable more objects to be…

We consider the classical problem of representing a collection of priority queues under the operations \Findmin{}, \Insert{}, \Decrease{}, \Meld{}, \Delete{}, and \Deletemin{}. In the comparison-based model, if the first four operations are…

Distribution Regression on path-space refers to the task of learning functions mapping the law of a stochastic process to a scalar target. The learning procedure based on the notion of path-signature, i.e. a classical transform from rough…

Deep learning algorithms have achieved excellent performance lately in a wide range of fields (e.g., computer version). However, a severe challenge faced by deep learning is the high dependency on hyper-parameters. The algorithm results may…

Symmetric orthogonalization via SVD, and closely related procedures, are well-known techniques for projecting matrices onto $O(n)$ or $SO(n)$. These tools have long been used for applications in computer vision, for example optimal 3D…

The resource recharging station location routing problem is a generalization of the location routing problem with sophisticated and critical resource consumption and recharging constraints. Based on a representation of discretized acyclic…

A 1-bend boundary labelling problem consists of an axis-aligned rectangle $B$, $n$ points (called sites) in the interior, and $n$ points (called ports) on the labels along the boundary of $B$. The goal is to find a set of $n$ axis-aligned…

A longest repeat query on a string, motivated by its applications in many subfields including computational biology, asks for the longest repetitive substring(s) covering a particular string position (point query). In this paper, we extend…

Chan [JACM, 2010] gave a data structure for maintaining the convex hull of a dynamic set of 3D points under insertions and deletions, supporting extreme-point queries. Subsequent refinements by Kaplan, Mulzer, Roditty, Seiferth, and Sharir…

The most commonly used method for addressing 3D geometric registration is the iterative closet-point algorithm, this approach is incremental and prone to drift over multiple consecutive frames. The Common strategy to address the drift is…

Currently, visual odometry and LIDAR odometry are performing well in pose estimation in some typical environments, but they still cannot recover the localization state at high speed or reduce accumulated drifts. In order to solve these…

Orthogonal matrix has shown advantages in training Recurrent Neural Networks (RNNs), but such matrix is limited to be square for the hidden-to-hidden transformation in RNNs. In this paper, we generalize such square orthogonal matrix to…

Spatial perception is the backbone of many robotics applications, and spans a broad range of research problems, including localization and mapping, point cloud alignment, and relative pose estimation from camera images. Robust spatial…

We consider the problem of maximizing the $\ell_1$ norm of a linear map over the sphere, which arises in various machine learning applications such as orthogonal dictionary learning (ODL) and robust subspace recovery (RSR). The problem is…

Let $G$ be a planar $3$-graph (i.e., a planar graph with vertex degree at most three) with $n$ vertices. We present the first $O(n^2)$-time algorithm that computes a planar orthogonal drawing of $G$ with the minimum number of bends in the…

Point location problems for $n$ points in $d$-dimensional Euclidean space (and $\ell_p$ spaces more generally) have typically had two kinds of running-time solutions: * (Nearly-Linear) less than $d^{poly(d)} \cdot n \log^{O(d)} n$ time, or…