TY - JOUR

T1 - LR B-splines to approximate bathymetry datasets

T2 - An improved statistical criterion to judge the goodness of fit

AU - Skytt, Vibeke

AU - Kermarrec, Gaël

AU - Dokken, Tor

N1 - Funding Information: The authors declare the following financial interests/personal relationships which may be considered as potential competing interests: Gael Kermarrec reports financial support was provided by Deutsche Forschungsgemeinschaft. This study is supported by the Deutsche Forschungsgemeinschaft under the project KE2453/2-1 and the Norwegian research council under grant number 270922. The data set is provided by the Norwegian map authorities, division Sjøkartverket.

PY - 2022/8

Y1 - 2022/8

N2 - The task of representing remotely sensed scattered point clouds with mathematical surfaces is ubiquitous to reduce a high number of observations to a compact description with as few coefficients as possible. To reach that goal, locally refined B-splines provide a simple framework to perform surface approximation by allowing an iterative local refinement. Different setups exist (bidegree of the splines, tolerance, refinement strategies) and the choice is often made heuristically, depending on the applications and observations at hand. In this article, we introduce a statistical information criterion based on the t-distribution to judge the goodness of fit of the surface approximation for remote sensing data with outliers. We use a real bathymetry dataset and illustrate how concepts from model selection can be used to select the most adequate refinement strategy of the LR B-splines.

AB - The task of representing remotely sensed scattered point clouds with mathematical surfaces is ubiquitous to reduce a high number of observations to a compact description with as few coefficients as possible. To reach that goal, locally refined B-splines provide a simple framework to perform surface approximation by allowing an iterative local refinement. Different setups exist (bidegree of the splines, tolerance, refinement strategies) and the choice is often made heuristically, depending on the applications and observations at hand. In this article, we introduce a statistical information criterion based on the t-distribution to judge the goodness of fit of the surface approximation for remote sensing data with outliers. We use a real bathymetry dataset and illustrate how concepts from model selection can be used to select the most adequate refinement strategy of the LR B-splines.

KW - AIC

KW - Bathymetry dataset

KW - Full span refinement strategy

KW - Information criteria

KW - LR B-splines

KW - Optimality

KW - Surface fitting

KW - T-distribution

UR - http://www.scopus.com/inward/record.url?scp=85133311219&partnerID=8YFLogxK

U2 - 10.1016/j.jag.2022.102894

DO - 10.1016/j.jag.2022.102894

M3 - Review article

AN - SCOPUS:85133311219

VL - 112

JO - International Journal of Applied Earth Observation and Geoinformation

JF - International Journal of Applied Earth Observation and Geoinformation

SN - 1569-8432

M1 - 102894

ER -