3D Reconstruction with Fast Dipole Sums (2405.16788v4)

Abstract: We introduce a method for high-quality 3D reconstruction from multi-view images. Our method uses a new point-based representation, the regularized dipole sum, which generalizes the winding number to allow for interpolation of per-point attributes in point clouds with noisy or outlier points. Using regularized dipole sums, we represent implicit geometry and radiance fields as per-point attributes of a dense point cloud, which we initialize from structure from motion. We additionally derive Barnes-Hut fast summation schemes for accelerated forward and adjoint dipole sum queries. These queries facilitate the use of ray tracing to efficiently and differentiably render images with our point-based representations, and thus update their point attributes to optimize scene geometry and appearance. We evaluate our method in inverse rendering applications against state-of-the-art alternatives, based on ray tracing of neural representations or rasterization of Gaussian point-based representations. Our method significantly improves 3D reconstruction quality and robustness at equal runtimes, while also supporting more general rendering methods such as shadow rays for direct illumination.

• The paper presents a novel dipole sum representation that generalizes the winding number for handling noisy point clouds, resulting in robust geometry reconstruction.
• It introduces Barnes-Hut fast summation to accelerate dipole sum queries and enables efficient, differentiable inverse rendering via ray tracing.
• Evaluation on datasets like DTU and BlendedMVS demonstrates superior reconstruction quality and comparable runtimes to state-of-the-art techniques.

3D Reconstruction with Fast Dipole Sums

The paper "3D Reconstruction with Fast Dipole Sums" introduces a novel technique for reconstructing high-fidelity surfaces from multi-view images. Authored by Hanyu Chen, Bailey Miller, and Ioannis Gkioulekas from Carnegie Mellon University, this research leverages a newly proposed point-based representation called the dipole sum. This representation extends the concept of the winding number, allowing for the interpolation of arbitrary per-point attributes even in the presence of noisy or outlier points within point clouds.

Overview

The proposed technique is particularly effective for inverse rendering applications where scene geometry and radiance fields are represented as per-point attributes within a point cloud. The process begins with initializing these attributes via structure from motion (SfM). The authors further enhance the computational efficiency by deriving Barnes-Hut fast summation schemes for accelerated dipole sum queries, facilitating efficient and differentiable rendering using ray tracing. This accelerated querying system enables fast optimization of scene geometry and appearance, resulting in significant improvements in reconstruction quality while maintaining equal runtimes compared to state-of-the-art alternatives.

Contributions and Results

Geometry and Radiance Field Representation

1. Geometry Field: The dipole sum representation generalizes the winding number by introducing regularized kernels and general per-point attributes, enabling it to handle noisy or outlier point clouds from SfM. The geometry field $\sigma$ is represented as a regularized dipole sum:

$$\sigma(\mathbf{x}) = \sum_{m} \frac{\alpha_m}{4\pi} \frac{\mathbf{n}_m \cdot (\mathbf{x} - \mathbf{x}_m)}{|\mathbf{x} - \mathbf{x}_m|^3},$$

where $\alpha_m$ are learned scalar weights, $\mathbf{n}_m$ are normals, and $\mathbf{x}_m$ are point positions in the point cloud.

1. Radiance Field: The radiance field representation interpolates appearance attributes through the same dipole sum mechanism, feeding these attributes into a shallow MLP to predict colors. Efficient computation and backpropagation are ensured using fast summation techniques.

Performance and Evaluation

The authors validate the efficacy of their approach through extensive empirical evaluation against several state-of-the-art techniques, including ray tracing of neural representations and rasterization of Gaussian point-based representations. Key results include:

• Efficiency: The technique achieves notable computational efficiency due to the Barnes-Hut fast summation scheme, enabling inverse rendering at speeds competitive with rasterization.
• Quality: The proposed method surpasses others in reconstructing detailed and high-quality surfaces, particularly when evaluated on datasets such as DTU and BlendedMVS.
• Compatibility: The technique maintains compatibility with advanced rendering techniques, including shadow rays, essential for rendering direct illumination.

Implications and Future Directions

The implications of this work are far-reaching both in practical applications and theoretical developments:

• Practical Applications: By significantly improving the reconstruction quality and efficiency of 3D surfaces from multi-view images, this technique can greatly benefit various fields such as virtual reality, augmented reality, and film production.
• Theoretical Advances: This research contributes to the understanding of point-based representations and interpolation schemes in computer graphics and vision. It bridges the gap between traditional geometry-based techniques and modern neural rendering methods.
• Future Research: Future work could explore further enhancements in query efficiency, perhaps by leveraging packet queries for multiple points. Additionally, extending the method to handle dynamic scenes or integrating it with real-time applications could provide substantial advancements.

In conclusion, the introduction of fast dipole sums for 3D reconstruction represents a significant advance in point-based modeling and inverse rendering. By combining robust geometric regularity with computational efficiency, this research opens new avenues for high-quality, scalable 3D reconstruction from multi-view images.