Related papers: GAPS: Geometry-Aware Problem Solver
Neural representations of 3D data have been widely adopted across various applications, particularly in recent work leveraging coordinate-based networks to model scalar or vector fields. However, these approaches face inherent challenges,…
We present a framework for learning to guide geometric task and motion planning (GTAMP). GTAMP is a subclass of task and motion planning in which the goal is to move multiple objects to target regions among movable obstacles. A standard…
In this chapter, we identify fundamental geometric structures that underlie the problems of sampling, optimisation, inference and adaptive decision-making. Based on this identification, we derive algorithms that exploit these geometric…
In this paper, we are concerned with geometric constraint solvers, i.e., with programs that find one or more solutions of a geometric constraint problem. If no solution exists, the solver is expected to announce that no solution has been…
3D Gaussian Splatting (3DGS) has been widely adopted for scene reconstruction, where training inherently constitutes a highly coupled and non-convex optimization problem. Recent works commonly incorporate geometric priors, such as LiDAR…
AI has made significant progress in solving math problems, but geometry problems remain challenging due to their reliance on both text and diagrams. In the text description, symbolic characters such as "$\triangle$ABC" often serve as a…
From the beginning of David Hestenes rediscovery of geometric algebra in the 1960s, outermorphisms have been a cornerstone in the mathematical development of GA. Many important mathematical formulations in GA can be expressed as…
An approximate formulation of a robust geometric program (RGP) as a convex program is proposed. Interest in using geometric programs (GPs) to model complex engineering systems has been growing, and this has motivated explicitly modeling the…
This paper proposes a new approach to detecting grasp points on novel objects presented in clutter. The input to our algorithm is a point cloud and the geometric parameters of the robot hand. The output is a set of hand configurations that…
Diagram parsing is an important foundation for geometry problem solving, attracting increasing attention in the field of intelligent education and document image understanding. Due to the complex layout and between-primitive relationship,…
In this paper, we propose a 3D geometry-aware deformable Gaussian Splatting method for dynamic view synthesis. Existing neural radiance fields (NeRF) based solutions learn the deformation in an implicit manner, which cannot incorporate 3D…
Graph partitioning is the problem of dividing the nodes of a graph into balanced partitions while minimizing the edge cut across the partitions. Due to its combinatorial nature, many approximate solutions have been developed, including…
Bayesian learning with Gaussian processes demonstrates encouraging regression and classification performances in solving computer vision tasks. However, Bayesian methods on 3D manifold-valued vision data, such as meshes and point clouds,…
When three-dimensional bodies contain thin features, non-trivial topology, or scan-derived surfaces, volumetric meshing can become the dominant bottleneck in simulation workflows. We replace this step with a learned geometric…
Gaussian Processes (GPs) are expressive models for capturing signal statistics and expressing prediction uncertainty. As a result, the robotics community has gathered interest in leveraging these methods for inference, planning, and…
Geologic map, as a fundamental diagram in geology science, provides critical insights into the structure and composition of Earth's subsurface and surface. These maps are indispensable in various fields, including disaster detection,…
Gaussian processes (GPs) are instrumental in modeling spatial processes, offering precise interpolation and prediction capabilities across fields such as environmental science and biology. Recently, there has been growing interest in…
Our goal is to recognize material categories using images and geometry information. In many applications, such as construction management, coarse geometry information is available. We investigate how 3D geometry (surface normals, camera…
Accurate High-Definition (HD) map construction is critical for autonomous driving, yet existing methods face a fundamental trade-off: vectorization-based approaches preserve topology but struggle with geometric fidelity, while…
Gaussian processes (GPs) are widely used for regression and optimization tasks such as Bayesian optimization (BO) due to their expressiveness and principled uncertainty estimates. However, in settings with large datasets corrupted by…