Getting Topology and Point Cloud Generation to Mesh
This work addresses the challenge of creating realistic 3D shapes for applications in computer graphics and AI, representing an incremental improvement by integrating topology and geometry insights.
The paper tackles the problem of generating point clouds by proposing a generative model that deforms a uniform sphere to approximate target point clouds, resulting in efficient generation of quality meshes.
In this work, we explore the idea that effective generative models for point clouds under the autoencoding framework must acknowledge the relationship between a continuous surface, a discretized mesh, and a set of points sampled from the surface. This view motivates a generative model that works by progressively deforming a uniform sphere until it approximates the goal point cloud. We review the underlying concepts leading to this conclusion from computer graphics and topology in differential geometry, and model the generation process as deformation via deep neural network parameterization. Finally, we show that this view of the problem produces a model that can generate quality meshes efficiently.