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Articulated objects and their representations pose a difficult problem for robots. These objects require not only representations of geometry and texture, but also of the various connections and joint parameters that make up each…
This paper concentrates on the homogeneous (conformal) model of Euclidean space (Horosphere) with subspaces that intuitively correspond to Euclidean geometric objects in three dimensions. Mathematical details of the construction and…
The heterogeneous multi-scale method (HMM) is a general strategy for dealing with problems involving multi-scales, with multi-physics, using multi-grids. It not only unifies several existing multi-scale methods, but also provide a…
Multi-view learning has progressed rapidly in recent years. Although many previous studies assume that each instance appears in all views, it is common in real-world applications for instances to be missing from some views, resulting in…
Spatial networks are networks whose graph topology is constrained by their embedded spatial space. Understanding the coupled spatial-graph properties is crucial for extracting powerful representations from spatial networks. Therefore,…
Past approaches for statistical shape analysis of objects have focused mainly on objects within the same topological classes, e.g., scalar functions, Euclidean curves, or surfaces, etc. For objects that differ in more complex ways, the…
The previously described methodology for hierarchical grouping of objects through iterative averaging has been used for simulation of cooperative interactions between objects of a system with the purpose of investigation of the…
Boundary Representation (B-Rep) is the widely adopted standard in Computer-Aided Design (CAD) and manufacturing. However, generative modeling of B-Reps remains a formidable challenge due to their inherent heterogeneity as geometric cell…
In this paper, we propose a novel hypergraph based method (called HF) to fit and segment multi-structural data. The proposed HF formulates the geometric model fitting problem as a hypergraph partition problem based on a novel hypergraph…
Integral transforms are invaluable mathematical tools to map functions into spaces where they are easier to characterize. We introduce the hyperdimensional transform as a new kind of integral transform. It converts square-integrable…
Constructing a high-quality dense map in real-time is essential for robotics, AR/VR, and digital twins applications. As Neural Radiance Field (NeRF) greatly improves the mapping performance, in this paper, we propose a NeRF-based mapping…
Scene-level 3D generation represents a critical frontier in multimedia and computer graphics, yet existing approaches either suffer from limited object categories or lack editing flexibility for interactive applications. In this paper, we…
We develop a method for solving elliptic partial differential equations on surfaces described by CAD patches that may have gaps/overlaps. The method is based on hybridization using a three-dimensional mesh that covers the gap/overlap…
We consider numerical solution of elliptic problems with heterogeneous diffusion coefficients containing thin highly conductive structures. Such problems arise e.g. in fractured porous media, reinforced materials, and electric circuits. The…
Deep learning inference that needs to largely take place on the 'edge' is a highly computational and memory intensive workload, making it intractable for low-power, embedded platforms such as mobile nodes and remote security applications.…
Recommendation system has been a widely studied task both in academia and industry. Previous works mainly focus on homogeneous recommendation and little progress has been made for heterogeneous recommender systems. However, heterogeneous…
Articulated objects (e.g., doors and drawers) exist everywhere in our life. Different from rigid objects, articulated objects have higher degrees of freedom and are rich in geometries, semantics, and part functions. Modeling different kinds…
In recent years, substantial progress has been achieved in learning-based reconstruction of 3D objects. At the same time, generative models were proposed that can generate highly realistic images. However, despite this success in these…
Generating high-quality novel view renderings of 3D Gaussian Splatting (3DGS) in scenes featuring transient objects is challenging. We propose a novel hybrid representation, termed as HybridGS, using 2D Gaussians for transient objects per…
Heterogeneous graphs are ubiquitous in real-world applications because they can represent various relationships between different types of entities. Therefore, learning embeddings in such graphs is a critical problem in graph machine…