# N-dimensional Data-Dependent Reconstruction Using Topological Changes

## Abstract

We introduce a new concept for a geometrically based feature preserving reconstruction technique of n-dimensional scattered data. Our goal is to generate an n-dimensional triangulation, which preserves the high frequency regions via local topology changes. It is the generalization of a 2D reconstruction approach based on data-dependent triangulation and Lawson's optimization procedure. The definition of the mathematic optimum of the reconstruction is given. We discuss an original cost function and a generalization of known functions for the n-dimensional case.

Z. Toth, I. Viola, A. Ferko, and M. E. Gröller, "N-dimensional Data-Dependent Reconstruction Using Topological Changes," in Topology-based Methods in Visualization (Proc. of TopoInVis 2005), 2007, p. 183–198.

[BibTeX]

We introduce a new concept for a geometrically based feature preserving reconstruction technique of n-dimensional scattered data. Our goal is to generate an n-dimensional triangulation, which preserves the high frequency regions via local topology changes. It is the generalization of a 2D reconstruction approach based on data-dependent triangulation and Lawson's optimization procedure. The definition of the mathematic optimum of the reconstruction is given. We discuss an original cost function and a generalization of known functions for the n-dimensional case.

```
@INPROCEEDINGS {toth2007ndd,
author = "Zsolt Toth and Ivan Viola and Andrej Ferko and Meister Eduard Gr{\"o}ller",
title = "N-dimensional Data-Dependent Reconstruction Using Topological Changes",
booktitle = "Topology-based Methods in Visualization (Proc. of TopoInVis 2005)",
year = "2007",
editor = "H. Hauser, H. Hagen, H. Theisel",
pages = "183--198",
month = "sep",
publisher = "Springer",
abstract = "We introduce a new concept for a geometrically based feature preserving reconstruction technique of n-dimensional scattered data. Our goal is to generate an n-dimensional triangulation, which preserves the high frequency regions via local topology changes. It is the generalization of a 2D reconstruction approach based on data-dependent triangulation and Lawson's optimization procedure. The definition of the mathematic optimum of the reconstruction is given. We discuss an original cost function and a generalization of known functions for the n-dimensional case.",
images = "images/toth07ndd.jpg",
thumbnails = "images/toth07ndd_thumb.jpg",
location = "Budmerice, Slovakia",
url = "//www.cg.tuwien.ac.at/research/publications/2007/toth-2007-ndd/"
}
```