RAIN-FIT: Learning of Fitting Surfaces and Noise Distribution from Large Data Sets

TL;DR

This paper introduces RAIN-FIT, a computationally efficient method for fitting surfaces and noise distributions from large, noisy datasets, applicable in high dimensions without hyperparameter tuning.

Contribution

The paper presents a novel, generalizable algorithm that estimates surfaces and noise parameters simultaneously with proven convergence and superior performance over existing methods.

Findings

The method achieves linear complexity in sample size.

It effectively handles high-dimensional data beyond 2D and 3D.

Numerical results show it outperforms Poisson Reconstruction and Encoder-X.

Abstract

This paper proposes a method for estimating a surface that contains a given set of points from noisy measurements. More precisely, by assuming that the surface is described by the zero set of a function in the span of a given set of features and a parametric description of the distribution of the noise, a computationally efficient method is described that estimates both the surface and the noise distribution parameters. In the provided examples, polynomial and sinusoidal basis functions were used. However, any chosen basis that satisfies the outlined conditions mentioned in the paper can be approximated as a combination of trigonometric, exponential, and/or polynomial terms, making the presented approach highly generalizable. The proposed algorithm exhibits linear computational complexity in the number of samples. Our approach requires no hyperparameter tuning or data preprocessing and effectively handles data in dimensions beyond 2D and 3D. The theoretical results demonstrating the convergence of the proposed algorithm have been provided. To highlight the performance of the proposed method, comprehensive numerical results are conducted, evaluating our method against state-of-the-art algorithms, including Poisson Reconstruction and the Neural Network-based Encoder-X, on 2D and 3D shapes. The results demonstrate the superiority of our method under the same conditions.