2022/03/23 by David E. Lenz, Lenz, David, Raine Yeh +7 · 1 citation
Computer Science · Engineering · Medicine · #AI in cancer detection #Advanced Numerical Analysis Techniques #FOS: Mathematics #G.1.2 #Medical Imaging Techniques and Applications #Numerical Analysis (math.NA)
paper · pdf · doi:10.48550/arxiv.2203.12730
openalex publication_date 2022/03/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.