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Has files: true × Subject: Computing methodologies → Shape modeling ×

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    Symmetrized Poisson Reconstruction
    (The Eurographics Association and John Wiley & Sons Ltd., 2025) Kohlbrenner, Maximilian; Liu, Hongyi; Alexa, Marc; Kazhdan, Misha; Attene, Marco; Sellán, Silvia
    Many common approaches for reconstructing surfaces from point clouds leverage normal information to fit an implicit function to the points. Normals typically play two roles: the direction provides a planar approximation to the surface and the sign distinguishes inside from outside. When the sign is missing, reconstructing a surface with globally consistent sidedness is challenging. In this work, we investigate the idea of squaring the Poisson Surface Reconstruction, replacing the normals with their outer products, making the approach agnostic to the signs of the input/estimated normals. Squaring results in a quartic optimization problem, for which we develop an iterative and hierarchical solver, based on setting the cubic partial derivatives to zero. We show that this technique significantly outperforms standard L-BFGS solver and demonstrate reconstruction of surfaces from unoriented noisy input in linear time.
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    OctFusion: Octree-based Diffusion Models for 3D Shape Generation
    (The Eurographics Association and John Wiley & Sons Ltd., 2025) Xiong, Bojun; Wei, Si-Tong; Zheng, Xin-Yang; Cao, Yan-Pei; Lian, Zhouhui; Wang, Peng-Shuai; Attene, Marco; Sellán, Silvia
    Diffusion models have emerged as a popular method for 3D generation. However, it is still challenging for diffusion models to efficiently generate diverse and high-quality 3D shapes. In this paper, we introduce OctFusion, which can generate 3D shapes with arbitrary resolutions in 2.5 seconds on a single Nvidia 4090 GPU, and the extracted meshes are guaranteed to be continuous and manifold. The key components of OctFusion are the octree-based latent representation and the accompanying diffusion models. The representation combines the benefits of both implicit neural representations and explicit spatial octrees and is learned with an octree-based variational autoencoder. The proposed diffusion model is a unified multi-scale U-Net that enables weights and computation sharing across different octree levels and avoids the complexity of widely used cascaded diffusion schemes. We verify the effectiveness of OctFusion on the ShapeNet and Objaverse datasets and achieve state-of-the-art performances on shape generation tasks. We demonstrate that OctFusion is extendable and flexible by generating high-quality color fields for textured mesh generation and high-quality 3D shapes conditioned on text prompts, sketches, or category labels. Our code and pre-trained models are available at https://github.com/octree-nn/octfusion.
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    GreenCloud: Volumetric Gradient Filtering via Regularized Green's Functions
    (The Eurographics Association and John Wiley & Sons Ltd., 2025) Tojo, Kenji; Umetani, Nobuyuki; Attene, Marco; Sellán, Silvia
    Gradient-based optimization is a fundamental tool in geometry processing, but it is often hampered by geometric distortion arising from noisy or sparse gradients. Existing methods mitigate these issues by filtering (i.e., diffusing) gradients over a surface mesh, but they require explicit mesh connectivity and solving large linear systems, making them unsuitable for point-based representation. In this work, we introduce a gradient filtering method tailored for point-based geometry. Our method bypasses explicit connectivity by leveraging regularized Green's functions to directly compute the filtered gradient field from discrete spatial points. Additionally, our approach incorporates elastic deformation based on Green's function of linear elasticity (known as Kelvinlets), reproducing various elastic behaviors such as smoothness and volume preservation while improving robustness in affine transformations. We further accelerate computation using a hierarchical Barnes-Hut style approximation, enabling scalable optimization of one million points. Our method significantly improves convergence across a wide range of applications, including reconstruction, editing, stylization, and simplified optimization experiments with Gaussian splatting.