SUPRA: Subspace Parameterized Attention for Neural Operator on General Domains

Neural operators are efficient surrogate models for solving partial differential equations (PDEs), but their key components face challenges: (1) in order to improve accuracy, attention mechanisms suffer from computational inefficiency on large-scale meshes, and (2) spectral convolutions rely on the Fast Fourier Transform (FFT) on regular grids and assume a flat geometry, which causes accuracy degradation on irregular domains. To tackle these problems, we regard the matrix-vector operations in the standard attention mechanism on vectors in Euclidean space as bilinear forms and linear operators in vector spaces and generalize the attention mechanism to function spaces. This new attention mechanism is fully equivalent to the standard attention but impossible to compute due to the infinite dimensionality of function spaces. To address this, inspired by model reduction techniques, we propose a Subspace Parameterized Attention (SUPRA) neural operator, which approximates the attention mechanism within a finite-dimensional subspace. To construct a subspace on irregular domains for SUPRA, we propose using the Laplacian eigenfunctions, which naturally adapt to domains' geometry and guarantee the optimal approximation for smooth functions. Experiments show that the SUPRA neural operator reduces error rates by up to 33% on various PDE datasets while maintaining state-of-the-art computational efficiency.

MASH: Masked Anchored SpHerical Distances for 3D Shape Representation and Generation

We introduce Masked Anchored SpHerical Distances (MASH), a novel multi-view and parametrized representation of 3D shapes. Inspired by multi-view geometry and motivated by the importance of perceptual shape understanding for learning 3D shapes, MASH represents a 3D shape as a collection of observable local surface patches, each defined by a spherical distance function emanating from an anchor point. We further leverage the compactness of spherical harmonics to encode the MASH functions, combined with a generalized view cone with a parameterized base that masks the spatial extent of the spherical function to attain locality. We develop a differentiable optimization algorithm capable of converting any point cloud into a MASH representation accurately approximating ground-truth surfaces with arbitrary geometry and topology. Extensive experiments demonstrate that MASH is versatile for multiple applications including surface reconstruction, shape generation, completion, and blending, achieving superior performance thanks to its unique representation encompassing both implicit and explicit features.

ArticulatedGS: Self-supervised Digital Twin Modeling of Articulated Objects using 3D Gaussian Splatting

We tackle the challenge of concurrent reconstruction at the part level with the RGB appearance and estimation of motion parameters for building digital twins of articulated objects using the 3D Gaussian Splatting (3D-GS) method. With two distinct sets of multi-view imagery, each depicting an object in separate static articulation configurations, we reconstruct the articulated object in 3D Gaussian representations with both appearance and geometry information at the same time. Our approach decoupled multiple highly interdependent parameters through a multi-step optimization process, thereby achieving a stable optimization procedure and high-quality outcomes. We introduce ArticulatedGS, a self-supervised, comprehensive framework that autonomously learns to model shapes and appearances at the part level and synchronizes the optimization of motion parameters, all without reliance on 3D supervision, motion cues, or semantic labels. Our experimental results demonstrate that, among comparable methodologies, our approach has achieved optimal outcomes in terms of part segmentation accuracy, motion estimation accuracy, and visual quality.

No Parameters, No Problem: 3D Gaussian Splatting without Camera Intrinsics and Extrinsics

While 3D Gaussian Splatting (3DGS) has made significant progress in scene reconstruction and novel view synthesis, it still heavily relies on accurately pre-computed camera intrinsics and extrinsics, such as focal length and camera poses. In order to mitigate this dependency, the previous efforts have focused on optimizing 3DGS without the need for camera poses, yet camera intrinsics remain necessary. To further loose the requirement, we propose a joint optimization method to train 3DGS from an image collection without requiring either camera intrinsics or extrinsics. To achieve this goal, we introduce several key improvements during the joint training of 3DGS. We theoretically derive the gradient of the camera intrinsics, allowing the camera intrinsics to be optimized simultaneously during training. Moreover, we integrate global track information and select the Gaussian kernels associated with each track, which will be trained and automatically rescaled to an infinitesimally small size, closely approximating surface points, and focusing on enforcing multi-view consistency and minimizing reprojection errors, while the remaining kernels continue to serve their original roles. This hybrid training strategy nicely unifies the camera parameters estimation and 3DGS training. Extensive evaluations demonstrate that the proposed method achieves state-of-the-art (SOTA) performance on both public and synthetic datasets.

Text2VDM: Text to Vector Displacement Maps for Expressive and Interactive 3D Sculpting

Professional 3D asset creation often requires diverse sculpting brushes to add surface details and geometric structures. Despite recent progress in 3D generation, producing reusable sculpting brushes compatible with artists' workflows remains an open and challenging problem. These sculpting brushes are typically represented as vector displacement maps (VDMs), which existing models cannot easily generate compared to natural images. This paper presents Text2VDM, a novel framework for text-to-VDM brush generation through the deformation of a dense planar mesh guided by score distillation sampling (SDS). The original SDS loss is designed for generating full objects and struggles with generating desirable sub-object structures from scratch in brush generation. We refer to this issue as semantic coupling, which we address by introducing classifier-free guidance (CFG) weighted blending of prompt tokens to SDS, resulting in a more accurate target distribution and semantic guidance. Experiments demonstrate that Text2VDM can generate diverse, high-quality VDM brushes for sculpting surface details and geometric structures. Our generated brushes can be seamlessly integrated into mainstream modeling software, enabling various applications such as mesh stylization and real-time interactive modeling.

HybridGS: Decoupling Transients and Statics with 2D and 3D Gaussian Splatting

Generating high-quality novel view renderings of 3D Gaussian Splatting (3DGS) in scenes featuring transient objects is challenging. We propose a novel hybrid representation, termed as HybridGS, using 2D Gaussians for transient objects per image and maintaining traditional 3D Gaussians for the whole static scenes. Note that, the 3DGS itself is better suited for modeling static scenes that assume multi-view consistency, but the transient objects appear occasionally and do not adhere to the assumption, thus we model them as planar objects from a single view, represented with 2D Gaussians. Our novel representation decomposes the scene from the perspective of fundamental viewpoint consistency, making it more reasonable. Additionally, we present a novel multi-view regulated supervision method for 3DGS that leverages information from co-visible regions, further enhancing the distinctions between the transients and statics. Then, we propose a straightforward yet effective multi-stage training strategy to ensure robust training and high-quality view synthesis across various settings. Experiments on benchmark datasets show our state-of-the-art performance of novel view synthesis in both indoor and outdoor scenes, even in the presence of distracting elements.

Learning Neural Volumetric Pose Features for Camera Localization

We introduce a novel neural volumetric pose feature, termed PoseMap, designed to enhance camera localization by encapsulating the information between images and the associated camera poses. Our framework leverages an Absolute Pose Regression (APR) architecture, together with an augmented NeRF module. This integration not only facilitates the generation of novel views to enrich the training dataset but also enables the learning of effective pose features. Additionally, we extend our architecture for self-supervised online alignment, allowing our method to be used and fine-tuned for unlabelled images within a unified framework. Experiments demonstrate that our method achieves 14.28% and 20.51% performance gain on average in indoor and outdoor benchmark scenes, outperforming existing APR methods with state-of-the-art accuracy.

FrameNeRF: A Simple and Efficient Framework for Few-shot Novel View Synthesis

We present a novel framework, called FrameNeRF, designed to apply off-the-shelf fast high-fidelity NeRF models with fast training speed and high rendering quality for few-shot novel view synthesis tasks. The training stability of fast high-fidelity models is typically constrained to dense views, making them unsuitable for few-shot novel view synthesis tasks. To address this limitation, we utilize a regularization model as a data generator to produce dense views from sparse inputs, facilitating subsequent training of fast high-fidelity models. Since these dense views are pseudo ground truth generated by the regularization model, original sparse images are then used to fine-tune the fast high-fidelity model. This process helps the model learn realistic details and correct artifacts introduced in earlier stages. By leveraging an off-the-shelf regularization model and a fast high-fidelity model, our approach achieves state-of-the-art performance across various benchmark datasets.

Guided Diffusion for Fast Inverse Design of Density-based Mechanical Metamaterials

Mechanical metamaterial is a synthetic material that can possess extraordinary physical characteristics, such as abnormal elasticity, stiffness, and stability, by carefully designing its internal structure. To make metamaterials contain delicate local structures with unique mechanical properties, it is a potential method to represent them through high-resolution voxels. However, it brings a substantial computational burden. To this end, this paper proposes a fast inverse design method, whose core is an advanced deep generative AI algorithm, to generate voxel-based mechanical metamaterials. Specifically, we use the self-conditioned diffusion model, capable of generating a microstructure with a resolution of $128^3$ to approach the specified homogenized tensor matrix in just 3 seconds. Accordingly, this rapid reverse design tool facilitates the exploration of extreme metamaterials, the sequence interpolation in metamaterials, and the generation of diverse microstructures for multi-scale design. This flexible and adaptive generative tool is of great value in structural engineering or other mechanical systems and can stimulate more subsequent research.

NeRF synthesis with shading guidance

The emerging Neural Radiance Field (NeRF) shows great potential in representing 3D scenes, which can render photo-realistic images from novel view with only sparse views given. However, utilizing NeRF to reconstruct real-world scenes requires images from different viewpoints, which limits its practical application. This problem can be even more pronounced for large scenes. In this paper, we introduce a new task called NeRF synthesis that utilizes the structural content of a NeRF patch exemplar to construct a new radiance field of large size. We propose a two-phase method for synthesizing new scenes that are continuous in geometry and appearance. We also propose a boundary constraint method to synthesize scenes of arbitrary size without artifacts. Specifically, we control the lighting effects of synthesized scenes using shading guidance instead of decoupling the scene. We have demonstrated that our method can generate high-quality results with consistent geometry and appearance, even for scenes with complex lighting. We can also synthesize new scenes on curved surface with arbitrary lighting effects, which enhances the practicality of our proposed NeRF synthesis approach.