An expert team with diverse mathematical backgrounds will build the mathematical foundations for image classification using iterated-integrals signature in the context of rough paths theory. This represents a significant mathematical challenge at the intersection of algebra, stochastic analysis, and geometry. Involving researchers with expertise in machine learning, we will explore signatures of images with a view towards real world applications. Related questions regarding statistical properties of signatures of images will be investigated and answered. The project will provide a platform for interdisciplinary research, reaching from pure mathematics into data science, and aiming at preparing applications for RCN and ERC projects.