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

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.