The main objective of work package 3 is to improve the understanding of the transition between discrete and continuum nonlocal models, which are investigated as part of the first two main objectives of this project. In particular, the relation of infinite limit processes of discrete models to nonlocal variational formulations in the continuum has yet to be explored. Our goal is to study the relationship between discrete and continuum descriptions of the problems related to analysis of data clouds (which are seen as random samples of a measure describing the ground truth), and more broadly variational problems with nonlocal regularization and general-graph based variational problems. We aim to fully understand the scaling of the discrete problems under which there is a well-defined continuum limit and understand the nature of the discrete-to-continuum convergence. This includes building mathematical tools to study the convergence of graph based variational problems to their continuum limit. Although pointwise convergence results have been known for some time, convergence in distance is very recent. In particular, the topology (and distance) to analyse the discrete and continuum models was proposed only in 2016. This breakthrough paves the way for further convergence results and a better understanding of the discrete-to-continuum limit. Results of our investigations are important for ensuring the reliability and improving the performance of current, and guiding development of new models and algorithms for data analysis tasks. In particular, we will deduce theoretical justifications for methods developed on finite weighted graphs. In this context we focus on the theory of optimal transport to make the passage from discrete graphs to the continuum limit of discrete operators such as the graph p- and infinity-Laplacian operators. Furthermore, we will establish consistency results for different graph-cut algorithms, which are important for segmentation tasks in real world problems.