DiffCD: A Symmetric Differentiable Chamfer Distance for Neural Implicit Surface Fitting (2407.17058v1)

Abstract: Neural implicit surfaces can be used to recover accurate 3D geometry from imperfect point clouds. In this work, we show that state-of-the-art techniques work by minimizing an approximation of a one-sided Chamfer distance. This shape metric is not symmetric, as it only ensures that the point cloud is near the surface but not vice versa. As a consequence, existing methods can produce inaccurate reconstructions with spurious surfaces. Although one approach against spurious surfaces has been widely used in the literature, we theoretically and experimentally show that it is equivalent to regularizing the surface area, resulting in over-smoothing. As a more appealing alternative, we propose DiffCD, a novel loss function corresponding to the symmetric Chamfer distance. In contrast to previous work, DiffCD also assures that the surface is near the point cloud, which eliminates spurious surfaces without the need for additional regularization. We experimentally show that DiffCD reliably recovers a high degree of shape detail, substantially outperforming existing work across varying surface complexity and noise levels. Project code is available at https://github.com/linusnie/diffcd.

• The paper introduces DiffCD, a symmetric differentiable Chamfer loss that minimizes both point-to-surface and surface-to-point distances to reduce spurious surfaces.
• The paper leverages a minimum-norm gradient computation with refined surface sampling to enhance reconstruction accuracy and mitigate over-smoothing.
• The paper demonstrates robust empirical results on datasets like FAMOUS and Thingi10k, significantly outperforming traditional surface fitting techniques.

DiffCD: A Symmetric Differentiable Chamfer Distance for Neural Implicit Surface Fitting

The paper entitled "DiffCD: A Symmetric Differentiable Chamfer Distance for Neural Implicit Surface Fitting" by Härenstam-Nielsen et al. presents an innovative approach to surface reconstruction from point clouds using neural implicit surfaces. This paper addresses the intrinsic limitations of existing surface fitting techniques that often struggle with spurious surfaces and over-smoothing. The authors introduce a novel loss function, DiffCD, which provides a more accurate and efficient mechanism for minimizing surface-fitting errors.

Neural implicit surfaces are an advantageous representation for surface reconstruction due to their continuous nature and ability to represent shapes with arbitrary topology. However, state-of-the-art methods like IGR and SIREN tend to optimize only a one-sided Chamfer distance, leading to notable issues with spurious surfaces and undesired over-smoothing. Recognizing this, the authors propose the Differentiable Chamfer Distance (DiffCD), a symmetric loss function that ensures more reliable surface reconstruction by considering both the point cloud to surface and surface to point cloud Chamfer distances.

Key Contributions

1. Symmetric Chamfer Distance: The authors argue that current methods effectively reduce to minimizing a one-sided Chamfer distance, neglecting the inverse distance (surface to point cloud). This negligence leads to erroneous spurious surfaces, which are large artifacts unrelated to the true surface. DiffCD includes both distances, providing a balanced approach that mitigates spurious surfaces without over-smoothing the surface.
2. Theoretical Insights: The paper provides an analytical exploration of existing regularization methods such as the SIREN loss term. The authors theoretically demonstrate that the SIREN loss term acts as a surface area regularizer, which, while effective at reducing spurious surfaces, often leads to an overall reduction in surface detail or even the total disappearance of the surface in some scenarios.
3. Gradient Computation and Surface Sampling: To efficiently compute gradients given their novel loss formulation, the authors extend the level set method proposed by Atzmon et al. They advocate for a minimum-norm solution for computing the distance, which ensures stability in the optimization process and a propensity towards smooth interpolating surfaces. Additionally, they refine the surface sampling process by leveraging SDF-descent to ensure surface points are accurately targeted, minimizing sampling inefficiencies.
4. Empirical Validation: The authors provide extensive empirical validation on datasets like FAMOUS and Thingi10k, demonstrating that DiffCD significantly outperforms traditional methods. In the presence of various noise levels, DiffCD consistently recovered superior surface details and demonstrated robustness by effectively handling noise without prior knowledge of its level.

Implications and Future Directions

Practical Implications

• Improved Surface Reconstruction: By providing a method that mitigates spurious surfaces and avoids over-smoothing, DiffCD can significantly benefit practical applications in industries where accurate 3D reconstruction is vital, such as in autonomous driving, medical imaging, and robotic navigation.
• Adapting to Noisy Data: The robustness of DiffCD to varying noise levels is particularly advantageous for real-world applications where input data often contains imperfections due to sensor limitations.
• Reduction in Hyperparameter Tuning: The symmetric Chamfer distance approach mitigates the need for extensive hyperparameter tuning to balance between accuracy and regularization, simplifying the deployment of neural implicit surfaces.

Theoretical Implications

• Surface Area Regularization Analysis: The theoretical insights provided into the effects of the SIREN loss term offer a deeper understanding of surface area regularization in neural implicit surfaces. This insight may inspire the development of new regularization techniques that do not overly compromise surface details.
• Gradient Norm and Stability: The minimum-norm gradient approach highlights the importance of appropriate gradient computation methods in ensuring the stability and accuracy of surface fitting methods. Researchers may build upon this to develop more efficient and accurate gradient computation strategies for implicit surfaces.

Future Directions

• Adaptive Regularization Techniques: Building upon the insights into surface regularization, future work could explore adaptive methods that adjust regularization strength based on the local characteristics of the surface, further improving the balance between detail preservation and noise mitigation.
• Integration with Supervised Learning: Combining the strengths of DiffCD with supervised learning techniques to incorporate learned priors could further enhance the robustness and accuracy of surface reconstructions in complex real-world scenarios.
• Efficiency Improvements: While effective, the computational cost associated with DiffCD's surface sampling is high. Future research could focus on optimizing this process, perhaps through more efficient sampling techniques or leveraging hardware accelerations.

In summary, the DiffCD method introduced by Härenstam-Nielsen et al. marks a significant improvement in the domain of neural implicit surface fitting. By addressing the critical issues of spurious surfaces and over-smoothing through a symmetric Chamfer distance, the authors provide both theoretical and practical contributions that enhance the accuracy, robustness, and efficiency of 3D surface reconstruction.