Source-linked AI summary
Learning to Infer Implicit Surfaces without 3D Supervision
Shichen Liu, Shunsuke Saito, Weikai Chen, Hao Li
TL;DR
Learning implicit surfaces from 2D images is challenging because implicit fields are difficult to connect differentiably to image renderings and to constrain geometrically. The paper introduces ray-based field probing and finite-difference geometric regularization, achieving high-fidelity single-view shape modeling that outperforms explicit alternatives qualitatively and quantitatively.
Problem
Learning implicit surfaces without 3D supervision requires connecting implicit fields to 2D image supervision while controlling their geometric properties.
Method
The framework predicts occupancy fields from images using sparse anchor-and-ray field probing and constrains geometry with finite-difference regularization and importance weighting.
Results
The method achieves high-fidelity single-view implicit-surface modeling from 2D images and outperforms state-of-the-art methods using alternative representations in quantitative and qualitative measures.
Takeaways & Limitations
2D images alone can support high-fidelity implicit-surface modeling for complex shapes, including arbitrary topologies and unconstrained regions.
Abstract
from arXiv · showhide
Recent advances in 3D deep learning have shown that it is possible to train highly effective deep models for 3D shape generation, directly from 2D images. This is particularly interesting since the availability of 3D models is still limited compared to the massive amount of accessible 2D images, which is invaluable for training. The representation of 3D surfaces itself is a key factor for the quality and resolution of the 3D output. While explicit representations, such as point clouds and voxels, can span a wide range of shape variations, their resolutions are often limited. Mesh-based representations are more efficient but are limited by their ability to handle varying topologies. Implicit surfaces, however, can robustly handle complex shapes, topologies, and also provide flexible resolution control. We address the fundamental problem of learning implicit surfaces for shape inference without the need of 3D supervision. Despite their advantages, it remains nontrivial to (1) formulate a differentiable connection between implicit surfaces and their 2D renderings, which is needed for image-based supervision; and (2) ensure precise geometric properties and control, such as local smoothness. In particular, sampling implicit surfaces densely is also known to be a computationally demanding and very slow operation. To this end, we propose a novel ray-based field probing technique for efficient image-to-field supervision, as well as a general geometric regularizer for implicit surfaces, which provides natural shape priors in unconstrained regions. We demonstrate the effectiveness of our framework on the task of single-view image-based 3D shape digitization and show how we outperform state-of-the-art techniques both quantitatively and qualitatively.
1 Introduction
The paper motivates implicit surfaces for their topology flexibility, resolution control, and memory efficiency, then introduces a framework for learning them from 2D supervision. Its key components are efficient ray-based field probing and geometric regularization for precise, locally controlled surfaces.
- 3D learning from 2D images is motivated by the limited quantity and variation of available 3D datasets compared with abundant photographs.
- Implicit surfaces handle arbitrary topologies while supporting high-fidelity, multi-resolution modeling with a small memory footprint.
- Learning implicit surfaces from 2D images is difficult because image supervision does not directly project implicit fields and dense ray sampling is computationally expensive.
- The proposed framework treats occupancy prediction as classification and uses sparse 3D anchors, spherical support regions, and probing rays to connect fields with image supervision.
- A finite-difference geometric regularizer with importance weighting constrains implicit-surface properties near the decision boundary.
- The contributions include the first 2D-supervised implicit-surface framework, efficient anchor-and-ray sampling, and a general geometric-regularization formulation.
2 Related Work
Related work contrasts explicit and implicit 3D representations and reviews learning shapes from abundant 2D supervision. The paper’s ray-based probing approach addresses the need to supervise implicit fields from images.
- Geometric Representation for 3D Deep Learning: Voxel, point-cloud, and mesh representations are common explicit alternatives, but their spatial structure, resolution, or topology handling can limit shape modeling.
- Geometric Representation for 3D Deep Learning: Implicit surfaces extract shapes from continuous fields, providing flexibility for complex topologies, fine details at arbitrary resolution, and reduced training memory.
- Learning Shapes from 2D Supervision: Shape-learning methods increasingly exploit massive 2D photo collections because clean, high-fidelity 3D model databases remain limited and costly to acquire.
- Learning Shapes from 2D Supervision: Ray-based field probing samples occupancy at sparse 3D anchors, intersects them with rays, aggregates values, and compares predictions with image silhouettes.
3 Unsupervised Learning of Implicit Surfaces
The framework learns an implicit occupancy field from 2D images by probing sampled 3D points along rays and regularizing geometric properties near the surface. Its pipeline combines image encoding, implicit decoding, silhouette-based supervision, and importance-weighted finite-difference regularization.
- Overview: 2D supervision is formulated as occupancy classification because images provide binary field occupancy rather than a continuous signed distance field.The model predicts a continuous occupancy probability field from single images, with the 0.5 iso-surface depicting the shape.
- Network Architecture: The network maps an input image to a latent code, then predicts occupancy probabilities for queried 3D points whose 0.5 iso-surface represents the inferred shape.The encoder produces z, while the implicit decoder consumes z and a query point to predict φ(pj).
- Sampling-Based 2D Supervision: Ray probing aggregates sampled occupancy values along each ray, using max pooling because ray-object intersection is determined by the maximum detected occupancy.The resulting ray prediction is compared with ground-truth silhouettes using an l2 silhouette loss.
- Sampling-Based 2D Supervision: Anchor points are represented by finite-radius spheres for efficient ray-point intersection, while boundary-aware assignment reduces erroneous labels near the decision boundary.Supporting regions can cause non-intersecting rays to be mislabeled when an anchor center lies inside the object.
- Sampling-Based 2D Supervision: Importance sampling concentrates rays and anchor points near estimated surface boundaries using image contours and 3D visual-hull cues rather than uniform random sampling.Pixel and 3D-point sampling densities are smoothed with Gaussian-kernel weighting functions.
- Geometric Regularization on Implicit Surfaces: Geometric regularization estimates field derivatives with finite differences and weights samples near occupancy 0.5, encouraging neighboring surface normals to remain similar.The regularizer samples neighboring points along the coordinate axes and combines with silhouette loss through a trade-off factor λ.
4 Experiments
Experiments evaluate single-view reconstruction on ShapeNet across surface representations and ablate geometric regularization, importance sampling, and boundary-aware assignment. The approach produces detailed reconstructions while supporting arbitrary topologies, and each component improves specific geometric properties or sampling accuracy.
- Experimental Setup: Evaluations use six ShapeNet categories with 64 × 64 rendered images and 24 views per object.
- Comparisons: Our approach produces visually appealing, higher-resolution reconstructions with sharper local details than voxel, point-cloud, and mesh-based alternatives.Examples include the plane engine and vehicle wheels.
- Comparisons: Implicit surfaces faithfully capture complex shapes and arbitrary topologies that mesh-based methods struggle to represent from limited visual cues.The comparison highlights chairs and tables with varying topologies.
- Geometric Regularization: Geometric regularization improves reconstructed-object regularity and allows control through the norm p.p = 2.0 encourages smooth surfaces, while p approaching 0 encourages piece-wise linear surfaces.
- Importance Sampling: Importance sampling yields more detailed reconstructions and substantially outperforms normal sampling quantitatively.The ablation compares normal sampling against importance sampling for anchors and rays.
- Boundary-Aware Assignment: Disabling boundary-aware assignment reduces accuracy around thin regions and can prevent recovery of holes and thin structures.
5 Discussion
The framework learns high-fidelity implicit surfaces from 2D images alone, combining occupancy-field learning with efficient field probing and geometric regularization. It supports higher-resolution modeling and arbitrary topologies, while future work targets textured geometry and reduced reliance on silhouette segmentation.
- The framework learns an occupancy field from 2D silhouettes using efficient field probing and finite-difference geometric regularization.
- Experiments show high-fidelity implicit surface modeling from 2D images alone, including unconstrained regions.
- Compared with voxels and point clouds, the approach produces more visually pleasant and higher-resolution results, while implicit surfaces handle arbitrary topologies.
- Future work includes unsupervised textured geometries and eliminating silhouette segmentations to improve scalability.