Geometric Methods in Signal and Image Analysis

This comprehensive guide offers a new approach for developing and implementing robust computational methodologies that uncover the key geometric and topological information from signals and images. With the help of detailed real-world examples and applications, readers will learn how to solve complex signal and image processing problems in fields ranging from remote sensing to medical imaging, bioinformatics, robotics, security, and defence. With an emphasis on intuitive and application-driven arguments, this text covers not only a range of methods in use today, but also introduces promising new developments for the future, bringing the reader up-to-date with the state of the art in signal and image analysis. Covering basic principles as well as advanced concepts and applications, and with examples and homework exercises, this is an invaluable resource for graduate students, researchers, and industry practitioners in a range of fields including signal and image processing, biomedical engineering, and computer graphics.

1. Introduction; 2. Fundamentals of group theory; 3. Vector spaces; 4. Differential geometry of curves and surfaces; 5. Geometric and differential topology of manifolds; 6. Computational algebraic topology.

H. Krim is Professor of Electrical and Computer Engineering and Director of the Vision, Information and Statistical Signal Theories and Applications group at North Carolina State University. Previously he was a Member of Technical Staff at AT&T Bell Labs and has spent nearly two decades bringing geometric and topological tools to solve real-world and applied problems in signal and image analysis, developing innovative tools which are being used in industry and government alike.
Abdessamad Ben Hamza is Associate Professor and Associate Director of the Concordia Institute for Information Systems Engineering (CIISE) at Concordia University, Montreal. Previously he was a postdoctoral research associate at Duke University in North Carolina, affiliated with both the Department of Electrical and Computer Engineering and the Fitzpatrick Center for Photonics and Communications Systems. He is also a licensed Professional Engineer and a Senior Member of the IEEE.