Customizable Adaptive Regularization Techniques for B-Spline Modeling

TL;DR

This paper introduces a customizable adaptive regularization method for B-spline models that automatically adjusts smoothing to preserve key data features while reducing artifacts, validated on scientific simulation data.

Contribution

It presents a novel adaptive regularization technique that varies smoothing strength across the domain to better preserve data features in B-spline modeling.

Findings

Effective artifact reduction in non-uniform data regions

Preservation of key data features during smoothing

Validated on scientific simulation datasets

Abstract

B-spline models are a powerful way to represent scientific data sets with a functional approximation. However, these models can suffer from spurious oscillations when the data to be approximated are not uniformly distributed. Model regularization (i.e., smoothing) has traditionally been used to minimize these oscillations; unfortunately, it is sometimes impossible to sufficiently remove unwanted artifacts without smoothing away key features of the data set. In this article, we present a method of model regularization that preserves significant features of a data set while minimizing artificial oscillations. Our method varies the strength of a smoothing parameter throughout the domain automatically, removing artifacts in poorly-constrained regions while leaving other regions unchanged. The proposed method selectively incorporates regularization terms based on first and second derivatives to maintain model accuracy while minimizing numerical artifacts. The behavior of our method is validated on a collection of two- and three-dimensional data sets produced by scientific simulations. In addition, a key tuning parameter is highlighted and the effects of this parameter are presented in detail. This paper is an extension of our previous conference paper at the 2022 International Conference on Computational Science (ICCS) [Lenz et al. 2022].