English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

Accurate interpolation and approximation techniques for functions withdiscontinuities are key tools in many applications as, for instance, medicalimaging. In this paper, we study an RBF type method for scattered datainterpolation that incorporates discontinuities via a variable scalingfunction. For the construction of the discontinuous basis of kernel functions,information on the edges of the interpolated function is necessary. Wecharacterize the native space spanned by these kernel functions and study errorbounds in terms of the fill distance of the node set. To extract the locationof the discontinuities, we use a segmentation method based on a classificationalgorithm from machine learning. The conducted numerical experiments confirmthe theoretically derived convergence rates in case that the discontinuitiesare a priori known. Further, an application to interpolation in magneticparticle imaging shows that the presented method is very promising.

Shape-Driven Interpolation with Discontinuous Kernels: Error Analysis, Edge Extraction and Applications in MPI