Abstract

Much of what we call big data consists of visual data such as photographs or videos, acquired and stored in various contexts, ranging from online image databases in libraries, security applications such as CCTV or security screening on airports, to clinical imaging data in hospitals. This data needs to be processed, analysed, and classified, and very often is used to inform decisions based on the information extracted. Image data plays a special role in data science, as the information that it encodes is usually very complex and structured, and is prone for access by mathematical models and techniques. Indeed, images are a rich source of beautiful mathematical formalism and analysis.

In this talk we will discuss a collection of mathematical approaches and their use and realisation for solving particular image analysis and processing tasks such as image de-noising, de-blurring and segmentation, object tracking and motion estimation, as well as image classification. The talk is furnished with applications of the introduced models in biomedical and clinical imaging, remote sensing for forest ecology, and restoration of paintings and illuminated manuscripts.