相关论文: Measuring shape relations using r-parallel sets

Dimension theory lies at the heart of fractal geometry and concerns the rigorous quantification of how large a subset of a metric space is. There are many notions of dimension to consider, and part of the richness of the subject is in…

Correspondence identifies relationships among objects via similarities among their components; it is ubiquitous in the analysis of spatial datasets, including images, weather maps, and computational simulations. This paper develops a novel…

Interactions among individuals from the same-species of wild animals are an important component of population dynamics. An interaction can be either static (based on overlap of space use) or dynamic (based on movement). The goal of this…

We present results of a long-term team collaboration of mathematicians and biologists. We focus on building a mathematical framework for the shape space constituted by a collection of homologous bones or teeth from many species. The…

We present a method for learning 3D spatial relationships between object pairs, referred to as object-object spatial relationships (OOR), by leveraging synthetically generated 3D samples from pre-trained 2D diffusion models. We hypothesize…

3D shape creation and modeling remains a challenging task especially for novice users. Many methods in the field of computer graphics have been proposed to automate the often repetitive and precise operations needed during the modeling of…

A fundamental challenge to sensory processing tasks in perception and robotics is the problem of obtaining data associations across views. We present a robust solution for ascertaining potentially dense surface patch (superpixel)…

In this study, we investigate the problem of tracking objects with unknown shapes using three-dimensional (3D) point cloud data. We propose a Gaussian process-based model to jointly estimate object kinematics, including position,…

It is argued that spectral features of quantal systems with random interactions can be given a geometric interpretation. This conjecture is investigated in the context of two simple models: a system of randomly interacting d bosons and one…

This paper introduces geometry and object shape and pose costs for multi-object tracking in urban driving scenarios. Using images from a monocular camera alone, we devise pairwise costs for object tracks, based on several 3D cues such as…

Measurements play a crucial role in doing physics: Their results provide the basis on which we adopt or reject physical theories. In this note, we examine the effect of subjecting measurements themselves to our experience. We require that…

We study a particular model of a random medium, called the orthant model, in general dimensions $d\ge 2$. Each site $x\in \Z^d$ independently has arrows pointing to its positive neighbours $x+e_i$, $i=1,\dots, d$ with probability $p$ and…

A method is developed to calculate collision probability in this paper. Based on the encounter geometric features of space objects, it is reasonable to separate the radial orbital motions from that in the cross section for most encounter…

This paper proposes a novel method for understanding daily hand-object manipulation by developing computer vision-based techniques. Specifically, we focus on recognizing hand grasp types, object attributes and manipulation actions within an…

In this article, we study several aspects of the intersections of algorithmically random closed sets. First, we answer a question of Cenzer and Weber, showing that the operation of intersecting relatively random closed sets (with respect to…

Spatial relationships between objects provide important information for text-based image retrieval. As users are more likely to describe a scene from a real world perspective, using 3D spatial relationships rather than 2D relationships that…

Research on group activity recognition mostly leans on the standard two-stream approach (RGB and Optical Flow) as their input features. Few have explored explicit pose information, with none using it directly to reason about the persons…

We analyze geometrical structures necessary to represent bulk and surface interactions of standard and substructural nature in complex bodies. Our attention is mainly focused on the influence of diffuse interfaces on sharp discontinuity…

In this paper, we establish the Hausdorff dimensions of inverse images and collision time sets for a large class of symmetric Markov processes on metric measure spaces. We apply the approach in the works by Hawkes and Jain--Pruitt, and make…

Objects are made of parts, each with distinct geometry, physics, functionality, and affordances. Developing such a distributed, physical, interpretable representation of objects will facilitate intelligent agents to better explore and…