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3D object detection is an important capability needed in various practical applications such as driver assistance systems. Monocular 3D detection, as a representative general setting among image-based approaches, provides a more economical…

Collision detection plays an important role in simulation, control, and learning for robotic systems. However, no existing method is differentiable with respect to the configurations of the objects, greatly limiting the sort of algorithms…

Spatial join processing techniques that identify intersections between complex geometries (e.g., polygons) commonly follow a two-step filter-and-refine pipeline. The filter step evaluates the query predicate on the minimum bounding…

This report presents a new, algorithmic approach to the distributions of the distance between two points distributed uniformly at random in various polygons, based on the extended Kinematic Measure (KM) from integral geometry. We first…

Collision detection is one of the most time-consuming operations during motion planning. Thus, there is an increasing interest in exploring machine learning techniques to speed up collision detection and sampling-based motion planning. A…

This study presents a novel algorithm for identifying the set of extreme points that constitute the exact convex hull of a point set in high-dimensional Euclidean space. The proposed method iteratively solves a sequence of dynamically…

Exploiting internal spatial geometric constraints of sparse LiDARs is beneficial to depth completion, however, has been not explored well. This paper proposes an efficient method to learn geometry-aware embedding, which encodes the local…

For multi-vehicle complex traffic scenarios in shared spaces such as intelligent intersections, safe coordination and trajectory planning is challenging due to computational complexity. To meet this challenge, we introduce a computationally…

State-of-the-art object pose estimation handles multiple instances in a test image by using multi-model formulations: detection as a first stage and then separately trained networks per object for 2D-3D geometric correspondence prediction…

Regular object detection methods output rectangle bounding boxes, which are unable to accurately describe the actual object shapes. Instance segmentation methods output pixel-level labels, which are computationally expensive for real-time…

Under conditions that prevent tangential intersection, we prove quadratic convergence of a projection algorithm for the feasibility problem of finding a point in the intersection of a smooth curve and line in $\mathbb{R}^2$. This nonconvex…

We address the task of 6D multi-object pose: given a set of known 3D objects and an RGB or RGB-D input image, we detect and estimate the 6D pose of each object. We propose a new approach to 6D object pose estimation which consists of an…

DeepAngle is a machine learning-based method to determine the contact angles of different phases in the tomography images of porous materials. Measurement of angles in 3--D needs to be done within the surface perpendicular to the angle…

Understanding the geometry of collision-free configuration space (C-free) in the presence of task-space obstacles is an essential ingredient for collision-free motion planning. While it is possible to check for collisions at a point using…

Combining LiDAR and Camera-view data has become a common approach for 3D Object Detection. However, previous approaches combine the two input streams at a point-level, throwing away semantic information derived from camera features. In this…

Collision detection is a critical functionality for robotics. The degree to which objects collide cannot be represented as a continuously differentiable function for any shapes other than spheres. This paper proposes a framework for…

This paper proposes vehicle motion planning methods with obstacle avoidance in tight spaces by incorporating polygonal approximations of both the vehicle and obstacles into a model predictive control (MPC) framework. Representing these…

Computing the diameter of the intersection graphs of objects is a basic problem in computational geometry. Previous works showed that the complexity of computing the diameter mainly depends on the object types: for unit disks and squares in…

Computing optimal, collision-free trajectories for high-dimensional systems is a challenging problem. Sampling-based planners struggle with the dimensionality, whereas trajectory optimizers may get stuck in local minima due to inherent…

The detection and classification of intersections between triangles are crucial tasks in a wide range of applications within Computer Graphics and Geometry Processing, including mesh Arrangements, mesh Booleans, and generic mesh processing…