The key idea is to develop a proper notion of distance between shapes themselves rather than between points in space. We make this notion rigorous by defining the set of all possible oil spill models as a metric space:
For those unfamiliar with topology, you can think of a topological space as an abstraction of the human perception of space. By making the set of all oil spill models into a metric space, we are giving ourselves a way to actually measure how “close” or “far” two models are from one another, and we are guaranteed by the restrictions (1)-(3) on our distance function that this notion of distance is free of pathological cases. We are essentially creating a very abstract space (which is impossible to visualize) in which the points themselves are oil spills, and in which we can measure a natural notion of distance between these points. This provides a simple framework in which to rank the goodness of fit of various proposed models.
My current efforts have been focused on what is called the modified Hausdorff distance:
SINTEF in Norway.
|Jon Ubnoske, Florida State University|