Since September 2010, I am a Ph.D. student in the Algorithms Group at the Department of Mathematics and Computer Science of the Eindhoven University of Technology.

The topic of my Ph.D. thesis is “algorithms for cartographic generalization”. For more details on my research, see research.

Office: HG 7.33

Computational geometry
Schematization and simplification
Visualization

Many problems ask for a comparison between curves. Many measures have been proposed to quantify similarity, for example, the Hausdorff and Fréchet distance. These measures result in a single number. However, many applications require a matching of the curves, a description of the actual similarity.

In order to specify and compute high quality matchings for polygonal curves, we introduced a criterion called local correctness. This criterion describes a ``good matching'' for matching-based similarity measures such as the Fréchet distance. Informally, it states that a good matching for two curves predicts the similary (according to the measure) for any matched subcurves.

Most recent publication: Locally Correct Fréchet Matchings [W3]

An interesting problem is the simplification (detail reduction) of shapes. For simplification, it is important to maintain recognizability of the original shape while trying to achieve the simplification goals. Schematization is a special kind of simplification where not only detail reduction is desired but also a more stylistic shape. This is often encountered for network and metro maps, but is also worthwhile for shapes. Generalization takes detail reduction a step further by allowing more operators, such as aggregation of shapes.

We developed an algorithm that can produce simplifications of polygons and subdivisions, such that each face maintains its original area. With some additional preprocessing, the algorithm is also suitable for schematization and generalization.

Most recent publication: A New Method for Subdivision Simplification with Applications to Urban-Area Generalization [C3]

A vernacular region is a region without a precise or administrative boundary. A formalization is needed to model these regions for automated usage. This allows for more intelligent treatment of search queries like “hotels in the British Midlands”. A common approach is to use the internet as a source of information, using search engines to relate exact geographical locations to vernacular regions. The question arises how to find the (approximate) boundary of a region, given a set of points that are likely to be inside or near the region.

We developed a new geometric model that straightforwardly extends to include geographic context. This same extension can also be applied to the popular KDE method.

Most recent publication: Delineating Imprecise Regions via Shortest-Path Graphs [C2]