## 4 Conclusions
In addition to that, the variety of map styles in the Atlanta map composite is higher. A careful interpretation of this difference would be that the proposed method works better for map collections of homogeneous map styles with a minimum of complexity (i.e., when fewer colors are used in the historical maps), which is typically the case for older maps. This seems plausible, though it is in contrast to remotely sensed observations, where more recent data are typically more reliable than earlier measurements. However, in order to confidently formulate recommendations related to such properties, and to assess the influence of building representations in the historical maps (individual building outlines, city blocks, etc. ), statistical evidence would be required by systematically analyzing a larger sample of maps from different points in time and of different map styles. From a methodological point of view, we followed the principle of parsimony and implemented a simplistic, rule-based color clustering method to extract the features of interest, and observed satisfactory levels of performance (i.e., high levels of receptiveness with respect to historical building densities--AUC > 0.9; and consistency with model-based estimates of historical urban area) and efficiency. Future work will include the use of more advanced extraction methods, taking into account shape and textural characteristics, or more complex rule-based systems, potentially able to distinguish between high-density and low-density urban/built-up areas. The concept of contemporary spatial constraints such as delineating the results to the 1975 GHSL built-up areas, could also be incorporated into an automated training data collection procedure, which could then be used for a supervised, deep-learning approach to extract urban areas and human settlement patterns at finer spatial granularity (cf. [61]). Concluding, we find that the presented approach appears to perform better on maps of few map colors (3-color prints) and shows lower performance on 5-color prints, even though the 3-color maps are older. When using composites of multiple individual historical maps, the method seems to work better on map composites consisting of homogeneous map styles. As our results seem plausible across all study areas, we find that the graphical quality of the underlying maps, manifested in their spatial resolution (cf. Table 1), does not affect the quality of the results drastically. As the use of k-means color space clustering requires the manual choice of the number of clusters k, the results depend on this choice (Figure A5). Future work will include the test of alternative clustering or unsupervised classification techniques that infer the optimum number of clusters from the data [94; 95], as well as the use of different color space representations [96]. Future work will also include the performance of object-based methods [57; 64] as compared to the pixel-based extraction method presented herein. Spatially explicit, historical data on built-up or urban area can enhance our understanding of the efficiency of a city over time (e.g., urban scaling analysis [97]), reduce manual labor involved in the analysis of urban-spatial trajectories [14], and allow for studying long-term urban development and land consumption processes. From a city planning perspective, however, historical information on functional properties of city elements (e.g., historical, spatially explicit urban land use, or building function) would be more beneficial than area-related information alone. While most historical topographic maps only contain limited information on land use and building functions, some map collections such as the Sanborn Fire Insurance maps [20] contain such information. However, the extraction of such information requires more complex information extraction methods, such as deep learning [98]. Future work could also focus on the extraction of functional properties from such historical maps, facilitated by contemporary remote sensing data.