Mathematical imaging and spatial pattern analysis

Mathematical imaging and spatial pattern analysis are mature but exciting and fast developing fields, which underpin developments in cognate fields such as computer vision, image processing, text and document analysis and neural networks. It is closely akin to machine learning, and also finds applications in fast emerging areas such as biometrics, bioinformatics, multimedia data analysis and most recently data science.

The objective is to know the necessary mathematical and computational tools and master the concepts of processing and geometrical characterization of shapes (signals, images, point patterns) to get basic knowledge about image and pattern analysis for real applications.

At the end of this toolbox, the student will be able to manipulate the main aspects of modern geometry, use concepts and results to solve concrete problems, such as the processing of binary, gray-level and color images, the extraction of geometrical, morphometrical and textural information in image analysis as well as the characterization, modeling and simulation of point patterns or spatial object distributions. He will also be able to use some basic machine learning techniques to answer image and pattern recognition applicative problems, such as the automatic detection of cancerous skin lesions in biomedical imaging.

"Introduction to image processing" is a short general introduction from the image acquisition to image characterization

"Image and pattern recognition" is focused on shapes and binary images

"Advanced image processing" is focused on gray-level images

"Color image processing" is focused on color images

"Bibliographical study and project" takes up the previous theoretical and practical notions