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

• URL: http://arxiv.org/abs/2512.05783v1
• Date: Fri, 05 Dec 2025 15:11:04 GMT
• Title: Curvature-Regularized Variational Autoencoder for 3D Scene Reconstruction from Sparse Depth
• Abstract summary: We propose curvature regularization through a discrete Laplacian operator, achieving 18.1% better reconstruction accuracy than standard variational autoencoders.<n>Our contribution challenges an implicit assumption in geometric deep learning: that combining multiple geometric constraints improves performance.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• 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.

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