Curvature Regularized Surface Reconstruction from Point Cloud

01/22/2020
by   Yuchen He, et al.
0

We propose a variational functional and fast algorithms to reconstruct implicit surface from point cloud data with a curvature constraint. The minimizing functional balances the distance function from the point cloud and the mean curvature term. Only the point location is used, without any local normal or curvature estimation at each point. With the added curvature constraint, the computation becomes particularly challenging. To enhance the computational efficiency, we solve the problem by a novel operator splitting scheme. It replaces the original high-order PDEs by a decoupled PDE system, which is solved by a semi-implicit method. We also discuss approach using an augmented Lagrangian method. The proposed method shows robustness against noise, and recovers concave features and sharp corners better compared to models without curvature constraint. Numerical experiments in two and three dimensional data sets, noisy and sparse data are presented to validate the model.

READ FULL TEXT
POST COMMENT

Comments

There are no comments yet.

Authors

page 17

05/26/2019

Efficient Curvature Estimation for Oriented Point Clouds

There is an immense literature focused on estimating the curvature of an...
07/02/2019

Fast Algorithms for Surface Reconstruction from Point Cloud

We consider constructing a surface from a given set of point cloud data....
04/17/2022

Fast Multi-grid Methods for Minimizing Curvature Energy

The geometric high-order regularization methods such as mean curvature a...
10/19/2020

Mean curvature motion of point cloud varifolds

This paper investigates a discretization scheme for mean curvature motio...
02/21/2019

A Fully Lagrangian Meshfree Framework for PDEs on Evolving Surfaces

We propose a novel framework to solve PDEs on moving manifolds, where th...
09/10/2020

CAD-PU: A Curvature-Adaptive Deep Learning Solution for Point Set Upsampling

Point set is arguably the most direct approximation of an object or scen...
07/20/2020

GarNet++: Improving Fast and Accurate Static3D Cloth Draping by Curvature Loss

In this paper, we tackle the problem of static 3D cloth draping on virtu...
This week in AI

Get the week's most popular data science and artificial intelligence research sent straight to your inbox every Saturday.