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Representation learning on large-scale unstructured volumetric and surface meshes poses significant challenges in neuroimaging, especially when models must incorporate diverse vertex-level morphometric descriptors, such as cortical…
We present a novel coarse-to-fine framework that derives a semi-regular multiscale mesh representation of an original input mesh via remeshing. Our approach differs from the conventional mesh wavelet transform strategy in two ways. First,…
Recovering sewing patterns from draped 3D garments is a challenging problem in human digitization research. In contrast to the well-studied forward process of draping designed sewing patterns using mature physical simulation engines, the…
We explore the three-body problem in two dimensions using the adiabatic hyperspherical representation. We develop the main equations in terms of democratic hyperangular coordinates and determine several symmetry properties and boundary…
The task of reconstructing detailed 3D human body models from images is interesting but challenging in computer vision due to the high freedom of human bodies. In order to tackle the problem, we propose a coarse-to-fine method to…
LiDAR point clouds can effectively depict the motion and posture of objects in three-dimensional space. Many studies accomplish the 3D object detection by voxelizing point clouds. However, in autonomous driving scenarios, the sparsity and…
Semantic understanding of 3D point clouds is important for various robotics applications. Given that point-wise semantic annotation is expensive, in this paper, we address the challenge of learning models with extremely sparse labels. The…
Multi-cellular robot design aims to create robots comprised of numerous cells that can be efficiently controlled to perform diverse tasks. Previous research has demonstrated the ability to generate robots for various tasks, but these…
It is conjectured that every cusped hyperbolic 3-manifold has a decomposition into positive volume ideal hyperbolic tetrahedra (a "geometric" triangulation of the manifold). Under a mild homology assumption on the manifold we construct…
Existing rotation-invariant point cloud masked autoencoders (MAE) rely on random masking strategies that overlook geometric structure and semantic coherence. Random masking treats patches independently, failing to capture spatial…
We study multilevel techniques, commonly used in PDE multigrid literature, to solve structured optimization problems. For a given hierarchy of levels, we formulate a coarse model that approximates the problem at each level and provides a…
Existing state-of-the-art 3D point cloud understanding methods merely perform well in a fully supervised manner. To the best of our knowledge, there exists no unified framework that simultaneously solves the downstream high-level…
Triply periodic minimal surface (TPMS) metamaterials characterized by mathematically-controlled topologies exhibit better mechanical properties compared to uniform structures. The unit cell topology of such metamaterials can be further…
3D visual grounding allows an embodied agent to understand visual information in real-world 3D environments based on human instructions, which is crucial for embodied intelligence. Existing 3D visual grounding methods typically rely on…
Interference detection of arbitrary geometric objects is not a trivial task due to the heavy computational load imposed by implementation issues. The hierarchically structured bounding boxes help us to quickly isolate the contour of…
Volumetric medical image segmentation is a fundamental problem in medical image analysis where the objective is to accurately classify a given 3D volumetric medical image with voxel-level precision. In this work, we propose a novel…
Denoising diffusion models have demonstrated outstanding results in 2D image generation, yet it remains a challenge to replicate its success in 3D shape generation. In this paper, we propose leveraging multi-view depth, which represents…
We introduce a new approach for reconstruction and novel view synthesis of unbounded real-world scenes. In contrast to previous methods using either volumetric fields, grid-based models, or discrete point cloud proxies, we propose a hybrid…
Deformable objects present a formidable challenge for robotic manipulation due to the lack of canonical low-dimensional representations and the difficulty of capturing, predicting, and controlling such objects. We construct compact…
Recent works in 3D multimodal learning have made remarkable progress. However, typically 3D multimodal models are only capable of handling point clouds. Compared to the emerging 3D representation technique, 3D Gaussian Splatting (3DGS), the…