Geometric Generative Model

Geometric generative models aim to create realistic data by leveraging geometric principles, focusing on representing and manipulating data as geometric objects rather than solely relying on statistical properties. Current research explores various architectures, including those based on signed distance functions (SDFs) for 3D modeling, morphological operations within equivariant neural networks for improved feature extraction and geometric interpretability, and neural networks that generate polytope approximations of complex shapes. This approach offers advantages in generating high-fidelity 3D models and images, particularly for complex objects like human heads, and provides new tools for data analysis tasks like clustering and visualization through the development of novel geometric metrics.