TayloRF: Approximate Volume Integral Using Explicit Polynomials Representation

Area of Science:

• Computer Vision
• Computer Graphics
• Machine Learning

Background:

• Neural Radiance Fields (NeRFs) excel at synthesizing novel views from images.
• Current NeRFs use Riemann sums for ray integration, limiting reconstruction quality due to piecewise constant approximations.
• This approximation fails to capture high-order variations within integration intervals, causing ambiguity.

Purpose of the Study:

• To enhance NeRFs' reconstruction quality by addressing limitations in volume rendering integral approximation.
• To introduce a novel method for modeling distributions within integration intervals more accurately.
• To improve the disambiguation of interval distributions and mitigate approximation errors in NeRF rendering.

Main Methods:

• Proposed modeling interval distributions using explicit Taylor-like polynomials parameterized by spatial gradients.
• Developed a learnable gradient estimator regularized by an interval boundary loss for numerical consistency.
• Implemented an adaptive interval scaling module for enhanced stability and handling of varying interval sizes.

Main Results:

• The proposed method significantly boosts rendering quality across various NeRF models.
• Achieved state-of-the-art performance on both synthetic and real-world scene datasets.
• Demonstrated effective disambiguation of interval distributions and mitigation of integral approximation errors.

Conclusions:

• Explicit polynomial modeling of interval distributions offers a significant improvement over piecewise constant approximations in NeRFs.
• The proposed framework is easily integrable with existing NeRF-based rendering systems.
• This approach leads to superior novel view synthesis and reconstruction quality in computer graphics applications.