相关论文: Shape Representation using Gaussian Process mixtur…

We observe that Gaussians exhibit distinct roles and characteristics analogous to traditional artistic techniques -- like how artists first sketch outlines before filling in broader areas with color, some Gaussians capture high-frequency…

In this paper, we introduce a novel method for comparing 3D point clouds, a critical task in various machine learning applications. By interpreting point clouds as samples from underlying probability density functions, the statistical…

Statistical shape models (SSMs) represent a class of shapes as a normal distribution of point variations, whose parameters are estimated from example shapes. Principal component analysis (PCA) is applied to obtain a low-dimensional…

We propose a shape fitting/registration method based on a Gaussian Processes formulation, suitable for shapes with extensive regions of missing data. Gaussian Processes are a proven powerful tool, as they provide a unified setting for shape…

Dimensionality reduction algorithms map high-dimensional data into visualizable 2D or 3D spaces, but traditionally rely on a discrete point-cloud paradigm. This discrete abstraction is susceptible to visual occlusion and artificial…

We propose a method to generate 3D shapes using point clouds. Given a point-cloud representation of a 3D shape, our method builds a kd-tree to spatially partition the points. This orders them consistently across all shapes, resulting in…

We introduce 3DShape2VecSet, a novel shape representation for neural fields designed for generative diffusion models. Our shape representation can encode 3D shapes given as surface models or point clouds, and represents them as neural…

This paper introduces and demonstrates a computational pipeline for the statistical analysis of shape graph datasets, namely geometric networks embedded in 2D or 3D spaces. Unlike traditional abstract graphs, our purpose is not only to…

In this paper, we focus on the task of 3D shape completion from partial point clouds using deep implicit functions. Existing methods seek to use voxelized basis functions or the ones from a certain family of functions (e.g., Gaussians),…

Computational models of complex physical systems often rely on simplifying assumptions which inevitably introduce model error, with consequent predictive errors. Given data on model observables, the estimation of parameterized model-error…

Rendering high-fidelity images from sparse point clouds is still challenging. Existing learning-based approaches suffer from either hole artifacts, missing details, or expensive computations. In this paper, we propose a novel framework to…

Physics simulation is paramount for modeling and utilizing 3D scenes in various real-world applications. However, integrating with state-of-the-art 3D scene rendering techniques such as Gaussian Splatting (GS) remains challenging. Existing…

Gaussian Processes (GPs) are powerful non-parametric Bayesian regression models that allow exact posterior inference, but exhibit high computational and memory costs. In order to improve scalability of GPs, approximate posterior inference…

We introduce a novel neural representation for maps between 3D shapes based on flow-matching models, which is computationally efficient and supports cross-representation shape matching without large-scale training or data-driven procedures.…

3D Gaussian Splatting is a recognized method for 3D scene representation, known for its high rendering quality and speed. However, its substantial data requirements present challenges for practical applications. In this paper, we introduce…

Learning 3D representations that generalize well to arbitrarily oriented inputs is a challenge of practical importance in applications varying from computer vision to physics and chemistry. We propose a novel multi-resolution convolutional…

Most point cloud compression methods operate in the voxel or octree domain which is not the original representation of point clouds. Those representations either remove the geometric information or require high computational power for…

This paper introduces a generative model for 3D surfaces based on a representation of shapes with mean curvature and metric, which are invariant under rigid transformation. Hence, compared with existing 3D machine learning frameworks, our…

This paper introduces a 3D shape generative model based on deep neural networks. A new image-like (i.e., tensor) data representation for genus-zero 3D shapes is devised. It is based on the observation that complicated shapes can be well…

We propose principled Gaussian processes (GPs) for modeling functions defined over the edge set of a simplicial 2-complex, a structure similar to a graph in which edges may form triangular faces. This approach is intended for learning…