Topology Density Map for Urban Data Visualization and Analysis

Digital Object Identifier: xx.xxxx/TVCG.201x.xxxxxxx for urban traffic data, by carefully considering the constraints implied by underlying road networks.

Density map, as an effective visualization technique [14], is widely used in urban analysis, which involves spatial distribution patterns [50], such as anomaly detection [41], risk analysis [33] and air pollution propagation analysis [9]. A density map depicts the continuous distribution of scalar field in a 2D planar space by assigning a unique color to each individual scalar value [16,37]. The scalar field is computed from the premise of the finite observation of the data [37]. The process is referred as density estimation, which can be parametric or nonparametric. Kernel density estimation (KDE) is a common nonparametric model, which typically applies a kernel (e.g., parabolic, Gaussian, and Sigmoid) to the proximity between two locations. The proximity is typically computed as Euclidean distance in a Cartesian coordinate system. Due to its simplicity, KDE has been widely adopted in movement visualization, such as vessel movements [33,46] and flight trails [18,19].

Nevertheless, the KDE based on Euclidean distance is inappropriate for many urban analyses that should take road networks into consideration, simply because most movements in cities are constrained by road networks [5]. Fig. 1 illustrates a real-world scenario, where domain experts would like to analyze how easy to access points-of-interest (POIs), i.e., the POI accessibility. For accurate accessibility measurement, we shall consider the following properties of a road network when measuring the proximity between two locations: