Amir Vaxman

Thomas Walker, Octave Mariotti, Amir Vaxman et al.

We introduce Explicit Neural Surfaces (ENS), an efficient smooth surface representation that directly encodes topology with a deformation field from a known base domain. We apply this representation to reconstruct explicit surfaces from multiple views, where we use a series of neural deformation fields to progressively transform the base domain into a target shape. By using meshes as discrete surface proxies, we train the deformation fields through efficient differentiable rasterization. Using a fixed base domain allows us to have Laplace-Beltrami eigenfunctions as an intrinsic positional encoding alongside standard extrinsic Fourier features, with which our approach can capture fine surface details. Compared to implicit surfaces, ENS trains faster and has several orders of magnitude faster inference times. The explicit nature of our approach also allows higher-quality mesh extraction whilst maintaining competitive surface reconstruction performance and real-time capabilities.

Haim Sawdayee, Amir Vaxman, Amit H. Bermano

Reconstructing 3D shapes from planar cross-sections is a challenge inspired by downstream applications like medical imaging and geographic informatics. The input is an in/out indicator function fully defined on a sparse collection of planes in space, and the output is an interpolation of the indicator function to the entire volume. Previous works addressing this sparse and ill-posed problem either produce low quality results, or rely on additional priors such as target topology, appearance information, or input normal directions. In this paper, we present OReX, a method for 3D shape reconstruction from slices alone, featuring a Neural Field as the interpolation prior. A modest neural network is trained on the input planes to return an inside/outside estimate for a given 3D coordinate, yielding a powerful prior that induces smoothness and self-similarities. The main challenge for this approach is high-frequency details, as the neural prior is overly smoothing. To alleviate this, we offer an iterative estimation architecture and a hierarchical input sampling scheme that encourage coarse-to-fine training, allowing the training process to focus on high frequencies at later stages. In addition, we identify and analyze a ripple-like effect stemming from the mesh extraction step. We mitigate it by regularizing the spatial gradients of the indicator function around input in/out boundaries during network training, tackling the problem at the root. Through extensive qualitative and quantitative experimentation, we demonstrate our method is robust, accurate, and scales well with the size of the input. We report state-of-the-art results compared to previous approaches and recent potential solutions, and demonstrate the benefit of our individual contributions through analysis and ablation studies.

Hongyi Liu, Oded Stein, Amir Vaxman et al.

We introduce a new extrinsic discretization of tangent vector fields on triangle meshes that is continuous, with bounded derivatives that are continuous almost everywhere, supporting pointwise evaluation and integration of differential operators. We achieve this by building a continuous normal field over the mesh via Phong interpolation and using minimal Rodrigues rotations to transport vertex-based tangent vectors into triangle interiors. Unlike most existing discretizations, which typically sacrifice either continuity or the ability to evaluate derivatives pointwise, our approach supports both. Because it is pointwise evaluatable, and using the fact that the covariant derivative can be decomposed into its symmetric, antisymmetric, and scalar components, our discretization supports the construction of standard vector-field processing operators including the connection and Hodge Laplacians, Killing energy, divergence, curl, and the Lie bracket. This framework provides a simple and practical finite-element formulation for vector-field processing on meshes, supporting both integration-based operators and pointwise queries. To our knowledge, ours is the first discretization that jointly enables extrinsic continuous vector fields, bounded derivatives, and pointwise evaluation of this collection of operators.

Miaowei Wang, Jakub Zadrożny, Oisin Mac Aodha et al.

Accurately simulating existing 3D objects and a wide variety of materials often demands expert knowledge and time-consuming physical parameter tuning to achieve the desired dynamic behavior. We introduce MotionPhysics, an end-to-end differentiable framework that infers plausible physical parameters from a user-provided natural language prompt for a chosen 3D scene of interest, removing the need for guidance from ground-truth trajectories or annotated videos. Our approach first utilizes a multimodal large language model to estimate material parameter values, which are constrained to lie within plausible ranges. We further propose a learnable motion distillation loss that extracts robust motion priors from pretrained video diffusion models while minimizing appearance and geometry inductive biases to guide the simulation. We evaluate MotionPhysics across more than thirty scenarios, including real-world, human-designed, and AI-generated 3D objects, spanning a wide range of materials such as elastic solids, metals, foams, sand, and both Newtonian and non-Newtonian fluids. We demonstrate that MotionPhysics produces visually realistic dynamic simulations guided by natural language, surpassing the state of the art while automatically determining physically plausible parameters. The code and project page are available at: https://wangmiaowei.github.io/MotionPhysics.github.io/.

Thomas Walker, Octave Mariotti, Amir Vaxman et al.

Positional encodings are a common component of neural scene reconstruction methods, and provide a way to bias the learning of neural fields towards coarser or finer representations. Current neural surface reconstruction methods use a "one-size-fits-all" approach to encoding, choosing a fixed set of encoding functions, and therefore bias, across all scenes. Current state-of-the-art surface reconstruction approaches leverage grid-based multi-resolution hash encoding in order to recover high-detail geometry. We propose a learned approach which allows the network to choose its encoding basis as a function of space, by masking the contribution of features stored at separate grid resolutions. The resulting spatially adaptive approach allows the network to fit a wider range of frequencies without introducing noise. We test our approach on standard benchmark surface reconstruction datasets and achieve state-of-the-art performance on two benchmark datasets.

Thomas Walker, Salvatore Esposito, Daniel Rebain et al.

Reconstructing complex structures from planar cross-sections is a challenging problem, with wide-reaching applications in medical imaging, manufacturing, and topography. Out-of-the-box point cloud reconstruction methods can often fail due to the data sparsity between slicing planes, while current bespoke methods struggle to reconstruct thin geometric structures and preserve topological continuity. This is important for medical applications where thin vessel structures are present in CT and MRI scans. This paper introduces CrossSDF, a novel approach for extracting a 3D signed distance field from 2D signed distances generated from planar contours. Our approach makes the training of neural SDFs contour-aware by using losses designed for the case where geometry is known within 2D slices. Our results demonstrate a significant improvement over existing methods, effectively reconstructing thin structures and producing accurate 3D models without the interpolation artifacts or over-smoothing of prior approaches.

Miaowei Wang, Changjian Li, Amir Vaxman

We introduce Canonical Consolidation Fields (CanFields). This novel method interpolates arbitrary-length sequences of independently sampled 3D point clouds into a unified, continuous, and coherent deforming shape. Unlike prior methods that oversmooth geometry or produce topological and geometric artifacts, CanFields optimizes fine-detailed geometry and deformation jointly in an unsupervised fitting with two novel bespoke modules. First, we introduce a dynamic consolidator module that adjusts the input and assigns confidence scores, balancing the optimization of the canonical shape and its motion. Second, we represent the motion as a diffeomorphic flow parameterized by a smooth velocity field. We have validated our robustness and accuracy on more than 50 diverse sequences, demonstrating its superior performance even with missing regions, noisy raw scans, and sparse data. Our project page is at: https://wangmiaowei.github.io/CanFields.github.io/.