Kernel Estimates as General Concept for the Measuring of Pedestrian Density

The standard density definition produces scattered values. Hence approaches improving features of the density estimates has been invented for many use cases. Presented general framework evaluating density using various kernels brings desired properties of density estimates and incorporates the most of ordinarily used methods. Extensive parametric study is performed on experimental data to illustrate effects of kernel selection (e.g. Gauss, cone) and its parametrization (blur). Quantitative evaluation of introduced quality criteria illustrates that kernel densities satisfy user requirements, e.g. conic kernel with radius in $[0.7, 1.2]$ m. These parametric values are also interpretable from proxemic theory indicating correctness of the whole concept. Besides, the kernel approach is directly compared to Voronoi approximation and customized distance to the nearest pedestrian - the comparison indicates a relevant correspondence. Furthermore, the kernel approach is supposed to be valid from mathematical perspective, since introduced Borsalino kernel has promising mathematical properties enabling future analytical research.