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We discuss convergence and coupling of Markov chains, and present general relations between the transfer matrices describing these two processes. We then analyze a recently developed local-patch algorithm, which computes rigorous upper…

We study high-dimensional sparse estimation tasks in a robust setting where a constant fraction of the dataset is adversarially corrupted. Specifically, we focus on the fundamental problems of robust sparse mean estimation and robust sparse…

In this paper, we propose a new primal-dual algorithmic framework for a class of convex-concave saddle point problems frequently arising from image processing and machine learning. Our algorithmic framework updates the primal variable…

Establishing character shape correspondence is a critical and fundamental task in computer vision and graphics, with diverse applications including re-topology, attribute transfer, and shape interpolation. Current dominant functional map…

Estimating position and orientation change of a mobile platform from two consecutive point clouds provided by a high-resolution sensor is a key problem in autonomous navigation. In particular, scan matching algorithms aim to find the…

How to extract significant point cloud features and estimate the pose between them remains a challenging question, due to the inherent lack of structure and ambiguous order permutation of point clouds. Despite significant improvements in…

We introduce a planner designed to guide robot manipulators in stably placing objects within intricate scenes. Our proposed method reverses the traditional approach to object placement: our planner selects contact points first and then…

A novel numerical approach to solving the shallow-water equations on the sphere using high-order numerical discretizations in both space and time is proposed. A space-time tensor formalism is used to express the equations of motion…

Global registration using 3D point clouds is a crucial technology for mobile platforms to achieve localization or manage loop-closing situations. In recent years, numerous researchers have proposed global registration methods to address a…

A fast and exact algorithm is developed for the spin +-2 spherical harmonics transforms on equi-angular pixelizations on the sphere. It is based on the Driscoll and Healy fast scalar spherical harmonics transform. The theoretical exactness…

Image-to-point cloud registration aims to determine the relative camera pose between an RGB image and a reference point cloud, serving as a general solution for locating 3D objects from 2D observations. Matching individual points with…

Registration of pre-operative 3-D volumes to intra-operative 2-D X-ray images is important in minimally invasive medical procedures. Rigid registration can be performed by estimating a global rigid motion that optimizes the alignment of…

Probabilistic collision detection (PCD) is essential in motion planning for robots operating in unstructured environments, where considering sensing uncertainty helps prevent damage. Existing PCD methods mainly used simplified geometric…

In many applications data are measured or defined on a spherical manifold; spherical harmonic transforms are then required to access the frequency content of the data. We derive algorithms to perform forward and inverse spin spherical…

Over the past two decades, we have seen an exponentially increased amount of point clouds collected with irregular shapes in various areas. Motivated by the importance of solid modeling for point clouds, we develop a novel and efficient…

In this paper, we develop a modified differential Structure from Motion (SfM) algorithm that can estimate relative pose from two consecutive frames despite of Rolling Shutter (RS) artifacts. In particular, we show that under constant…

Point cloud segmentation (PCS) is to classify each point in point clouds. The task enables robots to parse their 3D surroundings and run autonomously. According to different point cloud representations, existing PCS models can be roughly…

With the objective of improving the registration of LiDAR point clouds produced by kinematic scanning systems, we propose a novel trajectory adjustment procedure that leverages on the automated extraction of selected reliable 3D…

This work introduces a new cubic regularization method for nonconvex unconstrained multiobjective optimization problems. At each iteration of the method, a model associated with the cubic regularization of each component of the objective…

Point patterns are characterized by their density and correlation. While spatial variation of density is well-understood, analysis and synthesis of spatially-varying correlation is an open challenge. No tools are available to intuitively…