Reproduce “Implicit Geometric Regularization for Learning Shapes” on OpenResearch

About this paper

Amos Gropp, Lior Yariv, Niv Haim, Matan Atzmon, Yaron Lipman

Researchers at the Weizmann Institute of Science developed a method for learning neural implicit 3D shape representations directly from raw point clouds using a loss function with an Eikonal term. This approach implicitly regularizes the learned surface, allowing it to achieve state-of-the-art fidelity and detail in reconstructions, outperforming existing explicit regularization or regression-based methods.

Key insights

• A simple Eikonal term in the loss function can implicitly regularize the training of neural implicit representations, effectively guiding the network to approximate a signed distance function.
• This implicit geometric regularization leads to superior high-fidelity and detailed 3D surface reconstructions directly from raw point cloud data, avoiding undesirable irregular solutions.
• Theoretical analysis for a simplified linear model demonstrates that gradient descent on the proposed loss converges with high probability to the underlying signed distance function, providing formal justification for the implicit regularization phenomenon.

Summary by alphaXiv.