Beyond Abstract Measures: geometry and computation

Measures are a central concept in science, quantifying any notion and making results comparable. This workshop concentrates on geometric measures as known in foundational research areas, and on such measures in certain application areas: information visualization, cell and plant biology, and shape reconstruction. Typical measures are similarity measures, density measures, quality measures, etc. Measures as known in mathematics, and computational geometry and topology, are typically abstract and allow efficient computation, but they often do not directly apply to specific applications. There are multiple reasons for this: they may not be robust to noise, they may be based on a bottleneck distance instead of an averaging distance, and they may be too abstract altogether. Furthermore, certain measures known in application areas have not been considered in computational geometry and topology at all. In this workshop we will address and overcome this problem by bringing together researchers in all of the relevant research fields.

The workshop will feature survey presentations on all of the relevant topics, which include all of the applications and more formal aspects of geometric and topological measures. Participants will be given the opportunity for short presentations of their most interesting, relevant experiences with measures, be it applied or theoretical. A large part of the time at the workshop will be spent in break-out groups where discussions and joint research will take place.

The main purpose of the workshop is information exchange between researchers from different fields. In particular, we hope for a better understanding among foundational researchers for issues of practical measures and a better understanding among applied researchers for possibilities of abstract measures. We hope to see new measures arising that can help science forward, and new collaborations among researchers in general.