A Generalized Distance Transform: Theory and Applications to Weather Analysis and Forecasting

The distance transform (DT) (also known as distance map or distance field) is a fundamental tool of mathematical morphology. We introduce a generalized DT (GDT) that is smoother than the classical DT. This transform can be used to define a generalized Hausdorff metric that is shown to be more robust to noise while preserving all metric properties. It is also shown to lead to smoother level sets, allowing contour evolution without having to solve a partial differential equation. Two applications in weather analysis and forecasting demonstrate the usefulness of this proposed GDT. In particular, the dilation of sets according to the GDT allows the simplification of numerical weather forecasts and analysis into geometric objects, called MetObjects, and the generalized Hausdorff distance can be used as a forecast verification metric.