Deriving scale-transition matrices from map samples for simulated annealing-based aggregation

Abstract

The goal of the research described in this article is to derive parameters necessary for the automatic generalization of land-cover maps. A digital land-cover map is often given as a partition of the plane into areas of different classes. Generalizing such maps is usually done by aggregating small areas into larger regions. This can be modelled using cost functions in an optimization process, where a major objective is to minimize the class changes. Thus, an important input parameter for the aggregation is the information about possible aggregation partners of individual object classes. This can be coded in terms of a transition matrix listing costs that are charged for changing a unit area from one class into another one. In our case we consider the problem of determining the transition matrix based on two data sets of different scales. We propose three options to solve the problem: (1) the conventional way where an expert defines manually the transition matrix, (2) to derive the transition matrix from an analysis of an overlay of both data sets, and (3) an automatic way where the optimization is iterated while adapting the transition matrix until the difference of the intersection areas between both data sets before and after the generalization is minimized. As underlying aggregation procedure we use an approach based on global combinatorial optimization. We tested our approach for two German topographic data sets of different origin, which are given in the same areal extent and were acquired at scales 1:1000 and 1:25,000, respectively. The evaluation of our results allows us to conclude that our method is promising for the derivation of transition matrices from map samples. In the discussion we describe the advantages and disadvantages and show options for future work.