Probabilistic Directed Distance Fields for Ray-Based Shape Representations

Area of Science:

• Computer Vision
• 3D Shape Representation
• Geometric Deep Learning

Background:

• Optimal 3D shape representation is task-dependent in computer vision.
• Differentiable rendering is crucial for inverse graphics but faces challenges with explicit (low fidelity) and implicit (rendering difficulties) representations.

Purpose of the Study:

• Introduce Directed Distance Fields (DDFs) as a novel 3D shape representation.
• Enable efficient and high-fidelity differentiable rendering for various computer vision tasks.

Main Methods:

• Devised Directed Distance Fields (DDFs) mapping rays/oriented points to surface visibility and depth.
• Utilized probabilistic DDFs (PDDFs) to model field discontinuities.
• Applied DDFs to single-shape fitting, generative modeling, and 3D reconstruction.
• Investigated theoretical constraints for view consistency in DDFs.

Main Results:

• Achieved efficient differentiable rendering with a single forward pass for depth and backward passes for higher-order geometry.
• Demonstrated strong performance in shape fitting, generative modeling, and 3D reconstruction using DDFs.
• Identified sufficient field properties for guaranteed view consistency.

Conclusions:

• DDFs provide a versatile and efficient representation for 3D shapes, overcoming limitations of existing methods.
• The proposed method facilitates advanced inverse graphics and 3D reconstruction tasks.
• Theoretical analysis ensures view consistency, enhancing the robustness of DDFs.