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Open-vocabulary panoptic reconstruction is essential for advanced robotics perception and simulation. However, existing methods based on 3D Gaussian Splatting (3DGS) often struggle to simultaneously achieve geometric accuracy, coherent…
In this paper, we propose a new covering technique localized for the trajectories of SGD. This localization provides an algorithm-specific complexity measured by the covering number, which can have dimension-independent cardinality in…
A simple and efficient algorithm to numerically compute the genus of surfaces of three-dimensional objects using the Euler characteristic formula is presented. The algorithm applies to objects obtained by thresholding a scalar field in a…
Polygonal mesh reconstruction of a raw point cloud is a valuable topic in the field of computer graphics and 3D vision. Especially to 3D architectural models, polygonal mesh provides concise expressions for fundamental geometric structures…
Towards identifying the number of minimal surfaces sharing the same boundary from the geometry of the boundary, we propose a numerical scheme with high speed and high accuracy. Our numerical scheme is based on the method of fundamental…
3D printing of surfaces has become an established method for prototyping and visualisation. However, surfaces often contain certain degenerations, such as self-intersecting faces or non-manifold parts, which pose problems in obtaining a 3D…
How does one generalize differential geometric constructs such as curvature of a manifold to the discrete world of graphs and other combinatorial structures? This problem carries significant importance for analyzing models of discrete…
Representing large-scale motions and topological changes in the finite volume (FV) framework, while at the same time preserving the accuracy of the numerical solution, is difficult. In this paper, we present a robust, highly efficient…
Defined mathematically as critical points of surface area subject to a volume constraint, constant mean curvatures (CMC) surfaces are idealizations of interfaces occurring between two immiscible fluids. Their behavior elucidates phenomena…
Surface normal integration is a fundamental problem in computer vision, dealing with the objective of reconstructing a surface from its corresponding normal map. Existing approaches require an iterative global optimization to jointly…
3D Gaussian Splatting (3DGS) achieves remarkable results in the field of surface reconstruction. However, when Gaussian normal vectors are aligned within the single-view projection plane, while the geometry appears reasonable in the current…
Modeling the effect of complex terrain on high Reynolds number flows is important to improve our understanding of flow dynamics in wind farms and the dispersion of pollen and pollutants in hilly or mountainous terrain as well as the flow in…
Conformal and quasi-conformal mappings have widespread applications in imaging science, computer vision and computer graphics, such as surface registration, segmentation, remeshing, and texture map compression. While various conformal and…
Ruled surface is widely used in engineering design such as parting surface design of injection mold and checking surface design of checking fixture, which are usually generated by offsetting 3D curves. However, in 3D curve offset, there…
We develop and analyze the Generalized Multiplicative Gradient (GMG) method for solving a class of convex optimization problems over symmetric cones, where the objective function does not have Lipschitz gradient over the feasible region.…
Gaussian curvature is an important geometric property of surfaces, which has been used broadly in mathematical modeling. Due to the full nonlinearity of the Gaussian curvature, efficient numerical methods for models based on it are uncommon…
With advances in technology, there has been growing interest in developing effective mapping methods for 3-dimensional objects in recent years. Volumetric parameterization for 3D solid manifolds plays an important role in processing 3D…
Globally localizing in a given map is a crucial ability for robots to perform a wide range of autonomous navigation tasks. This paper presents OneShot - a global localization algorithm that uses only a single 3D LiDAR scan at a time, while…
We present a method for fabricating general models with multi-directional 3D printing systems by printing different model regions along with different directions. The core of our method is a support-effective volume decomposition algorithm…
In this paper, we study the computation of curvatures at the singular points of algebraic curves and surfaces. The idea is to convert the problem to compute the curvatures of the corresponding regular parametric curves and surfaces, which…