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Geometric Algorithms for Deep Point Networks


Point networks have recently enjoyed a lot of success due to the significant growth in 3D data and the development of novel point network architectures focusing on new applications. In this dissertation, I show that the performance of existing point networks can be improved by using insights from classical geometry processing algorithms. I demonstrate this first by proposing a new point-surface loss function called Quadric loss, which preserves sharp features such as edges and corners of 3D shapes. Inspired by the classical quadric simplification, Quadric loss minimizes the quadric error between the reconstructed points and the input surface. I show that combining Quadric loss with other popular point based loss functions can achieve better reconstruction results than existing approaches. Next, I propose a new meshing algorithm called Guided and Augmented Meshing, GAM, which generates a surface for the output points of a point network using a mesh prior. GAM decouples the geometry from the topology by making the point network solely responsible for geometry and the mesh prior responsible for topology. I show the benefits of such a disentanglement for single-view shape prediction and fair evaluation of deep point networks. Finally, I also present a novel 3D mesh dataset which was curated during this research, along with its several promising future applications.

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