PET-NeuS: Positional Encoding Tri-Planes for Neural Surfaces (2305.05594v1)

Abstract: A signed distance function (SDF) parametrized by an MLP is a common ingredient of neural surface reconstruction. We build on the successful recent method NeuS to extend it by three new components. The first component is to borrow the tri-plane representation from EG3D and represent signed distance fields as a mixture of tri-planes and MLPs instead of representing it with MLPs only. Using tri-planes leads to a more expressive data structure but will also introduce noise in the reconstructed surface. The second component is to use a new type of positional encoding with learnable weights to combat noise in the reconstruction process. We divide the features in the tri-plane into multiple frequency scales and modulate them with sin and cos functions of different frequencies. The third component is to use learnable convolution operations on the tri-plane features using self-attention convolution to produce features with different frequency bands. The experiments show that PET-NeuS achieves high-fidelity surface reconstruction on standard datasets. Following previous work and using the Chamfer metric as the most important way to measure surface reconstruction quality, we are able to improve upon the NeuS baseline by 57% on Nerf-synthetic (0.84 compared to 1.97) and by 15.5% on DTU (0.71 compared to 0.84). The qualitative evaluation reveals how our method can better control the interference of high-frequency noise. Code available at \url{https://github.com/yiqun-wang/PET-NeuS}.

• The paper introduces PET-NeuS, which integrates tri-plane representations, learnable positional encoding, and self-attention convolution to improve neural surface reconstruction.
• It demonstrates a 57% reduction in Chamfer error on the NeRF-synthetic dataset compared to baseline methods.
• The approach paves the way for more robust 3D reconstructions in applications like medical imaging and environmental modeling.

Analysis of "PET-NeuS: Positional Encoding Tri-Planes for Neural Surfaces"

In the paper titled "PET-NeuS: Positional Encoding Tri-Planes for Neural Surfaces," the authors introduce innovations in the field of neural surface reconstruction, specifically by extending the approach of NeuS with enhancements aimed at improving the expressiveness and resilience to noise. Their work integrates tri-plane data structures, learnable positional encoding weights, and self-attention convolution to improve the fidelity of surface reconstruction.

Methodological Advancements

The authors propose three key components:

1. Tri-Plane Representation: Leveraging ideas from EG3D, the representation of signed distance functions (SDF) as a combination of tri-plane and multilayer perceptrons (MLPs) marks a departure from solely using MLPs. The tri-plane data structure is lauded for its expressive capacity, potentially enhancing the fitting of local details. However, it introduces challenges such as higher noise levels in reconstructions due to the increased complexity.
2. Positional Encoding with Learnable Weights: To mitigate reconstruction noise, a novel positional encoding method is introduced. It supports multiple frequency scales modulated by sinusoidal functions. This encoding is designed to interpolate information across the tri-plane features, effectively suppressing high-frequency noise and contributing to the smoothness and accuracy of the reconstructed surfaces.
3. Self-Attention Convolution: Adapting self-attention mechanisms in conjunction with convolution operations allows the generation of feature maps with varying frequency bands. This technique aims to handle the diverse positional encodings effectively, offering flexibility and fine-tuning that improve the surface reconstruction quality further.

Empirical Results

Empirical evaluation conducted on standard datasets, including NeRF-synthetic and DTU, demonstrates significant improvements over existing methods like NeuS, HF-NeuS, and VolSDF. For instance, improvements measured by the Chamfer metric show a 57% reduction on the NeRF-synthetic dataset compared to the NeuS baseline, indicating superior handling of high-frequency noise and detailed feature reconstruction.

Implications and Future Directions

The integration of tri-plane data structures with neural implicit surfaces can greatly enhance the fidelity of 3D reconstructions, particularly in applications requiring fine-grain detail and noise resilience. This work opens new avenues for exploring hybrid neural representations, merging discrete and continuous models to leverage their respective strengths.

The self-attention convolution's role in modulating frequency information suggests potential cross-applications in fields where spatial frequency plays a critical role, such as medical imaging and high-resolution environmental modeling.

Future research could focus on reducing computational overhead inherent in handling self-attention mechanisms and explore further optimizations at the algorithmic level to extend the applicability of PET-NeuS in real-time scenarios. Additionally, investigating the trade-offs between detail preservation and noise introduction may yield insights into more dynamic control methods during reconstruction processes.

In summary, "PET-NeuS: Positional Encoding Tri-Planes for Neural Surfaces" contributes notable advancements to the discipline of neural surface reconstruction, offering methodologies that enhance both theoretical understanding and practical effectiveness of neural fields in complex environments.