Point Cloud Surface Parametrization with HAND and LEG: Hausdorff Approximation from Node-wise Distances and Localized Energy for Geometry

TL;DR

This paper introduces a neural network-based optimization method for point cloud surface parametrization, utilizing novel loss functions and theoretical insights to improve quality without relying on extrinsic data.

Contribution

It presents a new neural network approach with innovative loss functions and theoretical analysis for point cloud surface parametrization, addressing a less explored area.

Findings

Effective parametrization of open surfaces achieved

Landmark matching can be enforced within the framework

Applications demonstrated in surface reconstruction and boundary detection

Abstract

Surface parametrization is a crucial part in various fields, having applications in computer graphic, medical imaging, scientific computing and computational engineering. The majority of surface parametrization approaches are performed on triangular meshes. On the contrary, the theories and methods of point cloud surface parametrization are less researched, despite its rising significance. In this work, we compute surface parametrization in an optimization approach using neural networks, with novel loss functions introduced without extrinsic information, together with theoretical analyses. Based on the theory, we develop an optimization algorithm to improve the parametrization quality. Using our methods, general open surfaces can be parametrized in either free-boundary manner or with arbitrary domain constraints. Landmark matching can also be enforced under our framework. Numerical experiments are conducted and presented, along with applications including surface reconstruction and boundary detection.