Adaptive Regularization of B-Spline Models for Scientific Data

TL;DR

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

Contribution

It proposes a novel adaptive smoothing method that varies regularization strength across the domain to better preserve important features in scientific data.

Findings

Effective artifact reduction in non-uniform data regions

Preservation of key data features during smoothing

Validated on multi-dimensional scientific simulation data

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 behavior of our method is validated on a collection of two- and three-dimensional data sets produced by scientific simulations.