neural deformation model

To address the lack of native geometric processing capabilities in neural surface representations, this paper introduces spherical neural surface representation—a framework enabling seamless, mesh-free estimation of normals, first and second fundamental forms, gradients, divergence, and the Laplace–Beltrami operator on genus-0 neural surfaces. Our method leverages spherical parameterization with implicit neural representation, employs automatic differentiation to derive differential geometric operators, and establishes a numerical verification framework alongside neural spectral analysis tools. Key contributions include: (1) breaking the conventional “mesh-then-process” paradigm by establishing a systematic theoretical bridge between neural representations and classical differential geometry; (2) enabling geometric processing tasks—including neural heat flow and mean curvature flow—with robustness under isometric deformations; and (3) achieving numerical accuracy comparable to analytical solutions and mesh-based baselines, significantly outperforming existing neural surrogates.

This study addresses the generalization bottleneck in point cloud geometric representation by proposing transferable Geometric Neural Operators (GNOs) as foundational models. Methodologically, it introduces the first pretraining framework for unordered, unstructured point clouds: leveraging mesh-free, coordinate-agnostic functional mappings; embedding differential-geometric priors—such as covariant derivatives and curvature constraints; and employing self-supervised geometric losses to enable robust representation learning across shapes, topologies, and noise levels. Contributions include: (1) unified support for curvature estimation, geometric PDE solving on manifolds, and curvature-driven deformation modeling; (2) state-of-the-art performance across multiple benchmarks, significantly outperforming existing methods; and (3) open-sourced code and pretrained weights enabling plug-and-play integration.

Spatiotemporal registration and statistical modeling of zero-genus 4D surfaces—i.e., time-varying 3D surfaces—are challenged by arbitrary parameterizations and non-uniform deformation velocities. Method: We propose Dynamic Spherical Neural Surfaces (D-SNS), a continuous spatiotemporal functional representation that unifies parameterization alignment, geodesic computation, and Riemannian mean estimation directly in the continuous domain. D-SNS integrates implicit neural representations, spherical parameterization, Riemannian manifold optimization, and functional-statistical shape analysis—bypassing reliance on discrete meshes. Results: Evaluated on 4D human and facial datasets, D-SNS achieves significantly improved registration accuracy and computational efficiency, while enhancing fidelity, generalizability, and cross-sequence transferability of deformation modeling.

High-fidelity, joint-articulable 3D foot modeling under no/weak supervision remains challenging. Method: We propose Foot Implicit Neural Deformation (FIND), an end-to-end framework integrating implicit neural representations (INRs) and neural deformation fields, enabling disentangled reconstruction of shape, texture, and joint pose from a single monocular 2D image. We introduce a novel unsupervised part-level loss and establish a progressive learning paradigm—from zero-label initialization to weakly supervised refinement—to enforce anatomical consistency and articulation awareness. Additionally, we release Foot3D, the first high-accuracy 3D foot dataset. Results: On Foot3D, FIND significantly outperforms PCA-based baselines in shape fidelity and part correspondence accuracy. The unsupervised loss improves robustness of 2D inference under occlusion and viewpoint variation. Furthermore, FIND supports arbitrary-resolution mesh extraction, demonstrating strong potential for multi-platform deployment.

Existing neural field deformation methods struggle to simultaneously achieve high surface quality, robustness, and efficiency under spatial constraints. This paper proposes an efficient handle-constrained neural field deformation framework. First, it constructs a discrete signed distance function (SDF) representation based on local patch-based meshes, achieving higher geometric fidelity than Marching Cubes. Second, it introduces two As-Rigid-As-Possible (ARAP) deformation pipelines—the first to unify ARAP optimization across both high-resolution explicit meshes and neural implicit fields. The method integrates SDF-gradient-driven patch projection, implicit field modeling, and constraint-aware geometric solving, ensuring scalability and numerical stability. Experiments demonstrate significant improvements over state-of-the-art baselines in deformation fidelity, computational efficiency, and robustness—enabling real-time interactive editing of million-patch meshes and complex neural fields.

This work addresses the challenge of achieving cross-shape consistency in spherical parameterizations for genus-zero 3D shape collections. The authors propose a continuous parameterization method based on neural generative modeling, which learns a continuous mapping from the unit sphere to each target shape and leverages its inverse to obtain consistent spherical parameterizations. To mitigate discretization artifacts, an intermediate shape is introduced to bridge the sphere and target geometry, while a generative tree in latent space propagates initial correspondences across the collection. By integrating neural generative modeling, continuous deformation representations, and latent structural analysis, the method significantly reduces geometric distortion and achieves markedly superior cross-shape parameterization consistency compared to existing approaches on the ShapeNet dataset.

This work addresses the challenge of accurately and efficiently modeling continuous deformations of deformable objects, a task where existing methods often sacrifice either precision or real-time performance due to reliance on discrete time steps or high computational costs. The authors propose a novel 4D continuous deformation modeling framework based on Neural Ordinary Differential Equations (Neural ODEs), which maps 3D point clouds and physical conditions into a unified latent space to enable efficient and temporally continuous dynamics simulation. This approach represents the first extension of Neural ODEs to 4D motion modeling of deformable objects, demonstrating strong generalization to unseen shapes and physical parameters, as well as superior interpolation and extrapolation capabilities. Experiments show significant improvements in prediction accuracy under unseen physical configurations, successful transfer to real-world 3D capture data, and the release of code and datasets to support further research.

Existing 3D generation methods struggle to directly produce animatable assets with valid skeletons and skinning weights, often resulting in topological errors or invalid rigs during post-hoc rigging. This work proposes AniGen, the first unified framework that generates animatable 3D assets directly from a single image by jointly modeling shape, skeleton, and skinning as mutually consistent $S^3$ fields over a shared spatial domain. AniGen employs a two-stage flow-matching strategy: first generating a sparse skeletal structure, then synthesizing dense geometry and binding information. To address geometric ambiguity in bone prediction, it introduces a confidence-decayed skeleton field, and designs dual skinning feature fields to decouple skinning weights from joint count, enabling generation of skeletons with arbitrary complexity. Experiments demonstrate that AniGen significantly outperforms existing methods in rig validity and animation quality, and generalizes robustly across diverse in-the-wild images of humans, animals, and mechanical objects.

This work addresses the approximation errors inherent in conventional approaches to minimal surface representation and generation—errors arising either from discretization or from the use of physics-informed neural networks (PINNs). To overcome these limitations, the paper proposes a neural representation grounded in the Weierstrass–Enneper parameterization, which leverages an analytic formulation of minimal surfaces. By training the model with a variational objective derived from the Plateau problem, the method eliminates reliance on mesh-based representations or numerical solutions of differential equations. This framework constitutes the first neural approach to achieve nearly integration-error-free representation of minimal surfaces, simultaneously enforcing exact boundary conditions and preserving high geometric fidelity. Empirical results demonstrate its significant superiority over existing PINN-based and discrete mesh methods.