Image analysis is the quantitative analysis of images. It feeds on advances in mathematics, signal processing and machine learning to apply them to information extraction from images, N-dimensional sampled signals. In this talk we will attempt to explore applications of mathematics to different areas of image analysis, from acquisition, to processing, to data exploration. We will see how advances in sensing equipment creates additional challenges for processing and extracting scientific insights. Thomas obtained his BSc and MSc in Computer Engineering at Politecnico di Milano in 2005. His PhD was defended in 2010 at the University of Navarra, with the title "Automation of Early Lung Cancer Detection", a work he developed at the Center for Applied Medical Research in Pamplona. During his Ph.D. he was a visiting scientist at the CBIA in Brno and at Sudar Lab in the Lawrence Berkeley National Laboratory. After a two years postdoc at the Ecole Polytechnique Federale de Lausanne working on the analysis of super-resolution microscopy images at the LEB he worked as an image analyst at the Center for Genomic Regulation in Barcelona in the Advanced Light Microscopy Unit and in the laboratory of Luis Serrano, before moving to the U of M.