Identification of Change in a Dynamic Dot Pattern and its use in the Maintenance of Footprints

Examples of spatio-temporal data that can be represented as sets of points (called dot patterns) are pervasive in many applications, for example when tracking herds of migrating animals, ships in busy shipping channels and crowds of people in everyday life. The use of this type of data extends beyond the standard remit of Geographic Information Science (GISc), as classification and optimisation problems can often be visualised in the same manner. A common task within these fields is the assignment of a region (called a footprint) that is representative of the underlying pattern. The ways in which this footprint can be generated has been the subject of much research with many algorithms having been produced. Much of this research has focused on the dot patterns and footprints as static entities, however for many of the applications the data is prone to change. This thesis proposes that the footprint need not necessarily be updated each time the dot pattern changes; that the footprint can remain an appropriate representation of the pattern if the amount of change is slight. To ascertain the appropriate times at which to update the footprint, and when to leave it as it is, this thesis introduces the concept of change identifiers as simple measures of change between two dot patterns. Underlying the change identifiers is an in-depth examination of the data inherent in the dot pattern and the creation of descriptors that represent this data. The experimentation performed by this thesis shows that change identifiers are able to distinguish between different types of change across dot patterns from different sources. In doing so the change identifiers reduce the number of updates of the footprint while maintaining a measurably good representation of the dot pattern

Collection of abstracts of the 24th European Workshop on Computational Geometry

International audienceThe 24th European Workshop on Computational Geomety (EuroCG'08) was held at INRIA Nancy - Grand Est & LORIA on March 18-20, 2008. The present collection of abstracts contains the 63 scientific contributions as well as three invited talks presented at the workshop

Large bichromatic point sets admit empty monochromatic 4-gons

We consider a variation of a problem stated by Erd˝os and Szekeres in 1935 about the existence of a number fES(k) such that any set S of at least fES(k) points in general position in the plane has a subset of k points that are the vertices of a convex k-gon. In our setting the points of S are colored, and we say that a (not necessarily convex) spanned polygon is monochromatic if all its vertices have the same color. Moreover, a polygon is called empty if it does not contain any points of S in its interior. We show that any bichromatic set of n ≥ 5044 points in R2 in general position determines at least one empty, monochromatic quadrilateral (and thus linearly many).Postprint (published version

LIPIcs, Volume 274, ESA 2023, Complete Volume

LIPIcs, Volume 274, ESA 2023, Complete Volum