An image-map is a compromise between an image and a map. The quality of such maps is affected by several factors, such as (a) the matching between the features on images and the graphic symbols from maps, (b) the complexity of background images, and (c) the representation of graphic and text symbols on the images. This project deals with the first issue. The current solution is that the accuracy of images should satisfy the accuracy standard of maps. However, images with different resolutions can satisfy the standard for a specific map scale. This may lead to a situation in which the levels of detail (LoD) in images may not match the complexity of map features although the planimetric accuracy is matched. To solve this problem, we developed a complexity-based matching between the image resolution and map scale. More precisely, the matching is based on the complexity of line features. Experimental evaluations were conducted in 15 representative areas in Hong Kong using maps at seven scales and eight image resolutions. Results show that the proposed complexity-based method is capable of obtaining good matching between image resolution and map scale in terms of both accuracy and users’ preference.

Allometric scaling originates in biology, where it refers to scaling relations between the size of a body part and the size of the whole body when an organism grows. In cities, various allometric relations have also been discovered, such as those between the complexity of traffic networks and urban quantities. Metro networks are typical traffic networks in cities. However, whether allometric relations with metro networks exist is still uncertain. In this study, “fractal dimension” was employed as the complexity measure of metro networks, and potential allometric relations between fractal dimensions and urban indicators in 26 main cities in China were explored. It was found that fractal dimensions of metro networks had positive allometric relations with gross domestic product (GDP), population, particulate matter with a diameter less than 2.5 microns (PM_2.5), the road congestion index and the average price of second-hand housing (with Spearman’s R of 0.789, 0.806, 0.273, 0.625 and 0.335, respectively) but inverse allometric relations with sulfur dioxide (SO₂) and residential satisfaction (with Spearman’s R of −0.270 and −0.419, respectively). Such discoveries imply that allometric relations do exist with metro networks, which is helpful in deepening our understanding of how metro systems interact with urban quantities in the self-organized evolution of cities.

Schematization is a process of generating schematic network maps (e.g., metro network maps), where the graphic complexity of networks is usually reduced. In the past two decades, various automated schematization methods have been developed. A quantitative and accurate description of the complexity variation in the schematization is critical to evaluate the usability of schematization methods. It is noticed that fractal dimension ($F$) has been widely used to analyze the complexity of geographic objects, and this indicator may be appropriate for this purpose. In some existing studies, although $F$ has been employed to describe the complexity variation, the theoretical and experimental basis for adopting this approach is inadequate. In this study, experiments based on 26 Chinese cities’ metro networks showed that the $F$ of all these metro networks have decreased in schematization, and a significant positive correlation exists between the $F$ of original networks and the reduction of $F$ after schematization. The above results were verified to have similar trends with the subjective opinions of participants in a psychological questionnaire. Therefore, it can be concluded that $F$ can quantitatively measure the complexity change of networks in schematization. These discoveries provide the basis for using $F$ to evaluate the usability of schematization methods.