Geometry Field Splatting with Gaussian Surfels (2411.17067v2)

Abstract: Geometric reconstruction of opaque surfaces from images is a longstanding challenge in computer vision, with renewed interest from volumetric view synthesis algorithms using radiance fields. We leverage the geometry field proposed in recent work for stochastic opaque surfaces, which can then be converted to volume densities. We adapt Gaussian kernels or surfels to splat the geometry field rather than the volume, enabling precise reconstruction of opaque solids. Our first contribution is to derive an efficient and almost exact differentiable rendering algorithm for geometry fields parameterized by Gaussian surfels, while removing current approximations involving Taylor series and no self-attenuation. Next, we address the discontinuous loss landscape when surfels cluster near geometry, showing how to guarantee that the rendered color is a continuous function of the colors of the kernels, irrespective of ordering. Finally, we use latent representations with spherical harmonics encoded reflection vectors rather than spherical harmonics encoded colors to better address specular surfaces. We demonstrate significant improvement in the quality of reconstructed 3D surfaces on widely-used datasets.

• The paper introduces an efficient differentiable rendering algorithm using Gaussian surfels for precise geometric reconstruction.
• It stabilizes optimization by ensuring continuous loss landscapes and mitigating surfel clustering issues.
• The method employs spherical harmonic encodings to enhance specular surface representation, leading to high-quality 3D reconstructions.

Geometry Field Splatting with Gaussian Surfels

The paper at hand, "Geometry Field Splatting with Gaussian Surfels," presents an advanced method for geometric reconstruction of opaque surfaces using a combination of geometry fields and Gaussian surfels. This approach is positioned within the broader context of recent advances in computer vision, particularly those leveraging volumetric view synthesis algorithms like Neural Radiance Fields (NeRF). The authors focus on addressing the challenges associated with reconstructing precise geometry from radiance-based models, which often struggle due to their volumetric rather than surface-specific nature.

Contributions and Methodology

The authors propose a novel approach that adapts Gaussian kernels or surfels to splat geometry fields instead of conventional volume splatting techniques. This adaptation allows for more precise geometric reconstructions. The main contributions and methodological advancements introduced are as follows:

1. Differentiable Rendering Algorithm: The researchers have derived an efficient and nearly exact differentiable rendering algorithm which is parameterized by Gaussian surfels. This method improves upon existing approximations by eliminating reliance on Taylor series expansions and addressing self-attenuation issues present in conventional methods.
2. Loss Landscape Continuity: The paper identifies a critical issue related to discontinuity in the loss landscape, which occurs when surfels cluster near the geometry. This can lead to discontinuous rendered color outputs due to unstable ordering of surfels. To counteract this, the method ensures rendered color is a continuous function of kernel properties, thus stabilizing the optimization process.
3. Specular Surface Representation: The authors utilize latent representations with spherical harmonics to encode reflection vectors instead of colors. This significantly enhances the model's ability to handle specular surfaces, a traditional challenge for similar models.
4. Performance and Results: Empirical results demonstrate substantial improvement in the quality of reconstructed 3D surfaces when tested on widely-acknowledged datasets. These improvements reflect the proposed method's capability to achieve smooth and highly detailed reconstructions without the typical artifacts such as cracks or holes.

Implications and Speculations

The research offers both theoretical and practical implications. Theoretically, it bridges a gap between surface representations and volumetric rendering by creating a geometry field model with enforced smoothness and determinism. Practically, the method provides a robust tool for applications requiring precise geometric reconstructions from image data, such as virtual reality, photorealistic rendering, and 3D modeling in industrial design.

Looking forward, this work could inspire further exploration into integrating geometry fields with other neural rendering techniques, possibly extending to dynamic scenes or objects with complex transparency and refraction properties. Additionally, this approach sets the stage for enhanced real-time applications due to its computational efficiency, which is a pivotal concern in immersive technologies.

In conclusion, this paper pushes the boundaries of how geometric information is processed within volumetric rendering frameworks, providing insights that could be foundational for future developments in AI-driven geometric reconstructions. The proposed Gaussian surfel-based method represents a significant stride towards achieving seamless integration of geometric detail and computational efficiency in computer vision systems.