MSLF: multi-scale legibility function to estimate the legible scale of individual line features

Modern technology has given thousands of amateur cartographers not only the opportunity but also the means to make a valuable contribution to mapping at all scales. However, web maps made by amateurs are prone to legibility shortcomings, such as coalescence, complexity, and congestion. These problems can be solved by map generalization; however, for amateurs participating in web mapping, the crucial decision is when to activate generalization. Such a decision is difficult, as the original and target map scales are sometimes uncertain owing to heterogeneous data quality and different output devices. In this study, starting from the identification of different pixels in a rasterized line, we developed a new scale-specific measure to evaluate the degree of legibility (DoL) of individual lines. Our experimental results showed that this measure could reflect the legibility of a line at a given map scale effectively, and could facilitate accurate decisions on whether generalization is necessary. In addition, we fitted a multi-scale legibility function (MSLF) for each line based on DoLs at multiple scales. This function can be used to estimate the legible scale for each line accurately. Our measures are easy to understand, tolerant of data quality, and have great potential for multi-scale spatial data processing.