Curvature Regularized Surface Reconstruction from Point Cloud
This work addresses surface reconstruction challenges in computer graphics and vision, offering incremental improvements for handling noisy and sparse point cloud data.
The authors tackled the problem of reconstructing implicit surfaces from point clouds by introducing a curvature constraint to improve feature recovery, resulting in a method that shows robustness against noise and better reconstruction of concave features and sharp corners compared to models without such constraints.
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.