In this paper, we develop a methodology for the local estimation of multifractal properties in random 2D fields. The main novelty of our approach lies in introducing a local average of one-dimensional increments, rendering the analysis applicable not only for fully defined images but also for any marked point process where information is not ubiquitously available, e.g. in the context of geospatial data analysis and modeling. We demonstrate the robustness of the estimation by deploying the methodology on a multifractal random field defined as a marked 2D point pattern with three different underlying supports: an equidistant grid (or image), a self-similar and a multifractal Sierpinski carpet. We show that the estimation of obtained scaling characteristics is statistically concurrent on these three spatial distributions. We conclude by presenting a real-world application using geospatial data.