Visualizing the Planimetric Accuracy of Historical Maps with MapAnalyst

MapAnalyst is a new software application for the visualization and study of the planimetric accuracy of old maps. It illustrates local map distortion by generating distortion grids, displacement vectors, and new isolines of scale and rotation. MapAnalyst additionally computes the old map’s scale and rotation, as well as statistical indicators summarizing the map’s geometric accuracy. It offers a user-friendly interface and is freely available for all major computer platforms at http:// mapanalyst.cartography.ch/. Map historians are invited to use MapAnalyst, and are encouraged to consult and improve the free Java source-code. This article describes the steps leading to visualizations of a map’s planimetric accuracy. It provides basic algorithmic information that is necessary for the understanding and correct interpretation of displacement vectors and distortion grids. It also introduces isolines of equal scale and rotation, a new type of accuracy visualization. The last section interprets sample visualizations for an eighteenth century map. Visualizing Accuracy The planimetric accuracy of a historical map is the extent to which distances and bearings between identifiable objects on a map coincide with their true value (Blakemore and Harley 1980). Visualizations of planimetric accuracy illustrate how rotation, shearing, shrinkage, and stretching vary locally on the map. The applications of accuracy analyses are twofold. An analysis may support or refute a hypothesis about technical aspects of map creation. The map historian may, for example, verify assumptions about the surveying methods and source maps used to compile the map or examine its underlying projection and geodetic reference. Alternatively, an analysis may indicate the geometric reliability of information extracted for historical research (e.g., studies of changes in land use, vegetation, or coastal erosion; Blakemore and Harley 1980). Graphic presentations of the planimetric accuracy allow for discovering and understanding new facts about a map and are an excellent means to illustrate these findings. It is thus essential to have available a range of complementary visualizations that illustrate the local geometric characteristics of the map and emphasize punctiform or spatially limited outliers. Various computer-aided techniques exist for the visualization of planimetric distortion and accuracy. Gustav Forstner and Markus Oehrli (1998), as well as Evangelos Livieratos (2006), provide concise overviews of techniques developed for the graphical analysis of old maps. Most visualizations derive from two sets of corresponding points; that is, one set originates from a modern reference map and is considered to be perfectly accurate, while the points of the other set is drawn from the old map and is supposed to be inaccurate. Before a visualization can be generated, the two sets of points must share a common coordinate system. Affine transformations bring the two coordinate systems into coincidence by converting one set of points to the coordinate system of the other set. This is achieved by scaling, shifting, and rotating one set in such a way that the differences between the two sets are minimal according to the leastsquares method. Compared to other types of transformations, affine transformations offer the advantage of cartographica (volume 42, issue 1) 89 providing estimations of the scale and the rotation of the old map. An analysis with MapAnalyst begins by importing images of an old map and a georeferenced modern map (see Figure 1). The user then identifies corresponding locations on the two maps and interactively places pairs of points at these locations. Finally, he or she chooses the appropriate type of affine transformation and selects the parameters for the desired accuracy visualization. The computation of the various visualizations is quick, which facilitates an iterative approach. For example, changing the mesh size of a distortion grid or computing the scale of a sub-area of the map is a matter of seconds. MapAnalyst can then export the visualizations it has generated to various graphics formats. DISPLACEMENT VECTORS Displacement vectors are algorithmically the simplest visualization technique and are easy to understand (see Figure 2a). Each vector line starts at a point previously identified in the old map and ends at the position where the point would be if the old map were as accurate as the modern reference map. This endpoint results from an affine transformation between the two sets of points. Exceedingly long vectors are easily identifiable; these indicate outliers that are due to gross positional errors in the map.