Curvature-Regularized Variational Autoencoder for 3D Scene Reconstruction from Sparse Depth

TL;DR

This paper introduces a curvature regularization method using a discrete Laplacian in a variational autoencoder to improve 3D scene reconstruction accuracy from sparse depth data, outperforming complex multi-constraint approaches.

Contribution

It demonstrates that a single, well-designed regularization term can surpass multi-term geometric constraints in 3D reconstruction tasks.

Findings

Achieved 18.1% better accuracy than standard VAEs.

Single regularization term outperforms complex multi-term formulations.

Provides stable gradients and noise suppression with minimal overhead.

Abstract

When depth sensors provide only 5% of needed measurements, reconstructing complete 3D scenes becomes difficult. Autonomous vehicles and robots cannot tolerate the geometric errors that sparse reconstruction introduces. We propose curvature regularization through a discrete Laplacian operator, achieving 18.1% better reconstruction accuracy than standard variational autoencoders. Our contribution challenges an implicit assumption in geometric deep learning: that combining multiple geometric constraints improves performance. A single well-designed regularization term not only matches but exceeds the effectiveness of complex multi-term formulations. The discrete Laplacian offers stable gradients and noise suppression with just 15% training overhead and zero inference cost. Code and models are available at https://github.com/Maryousefi/GeoVAE-3D.