This book is about the use of modern geometric methods for signal and image analysis. It provides a comprehensive coverage of the subject from the basic principles to state-of-the-art concepts and applications. The objective is to give the reader a sound understanding of the major theoretical concepts and computational approaches for applying geometric techniques and methodologies in solving various problems that arise naturally in signal and image processing, computer graphics, computer-aided design, bioinformatics, and other disciplines. The emphasis throughout is on intuitive and application-driven arguments. All methods are illustrated by well-chosen examples and applications, and are selected from core areas of modern geometric and topological computing. Furthermore, the purpose is for the reader to become aware of some recent developments in this fast-growing field.

Audience

The book is intended as a comprehensive and concise reference for geometric and topological methods in signal and image processing. The topics covered in this book are essential for research in numerical geometry and computational algebraic topology, and desirable for students, researchers, and practitioners pursuing research in signal and image processing, computer vision, computer graphics, computer-aided design, and other related fields.

The content grew from notes developed for graduate and undergraduate courses in signal processing, image processing, and computer graphics given at North Carolina State University and Concordia University, primarily targeted at electrical engineering, computer science, and software engineering students.

Chapter organization and topics covered

This book abandons the classical definition–theorem–proof model, and instead heavily relies on effective computational techniques with concrete applications to image analysis, computer vision, geometry processing, and computer graphics. The pitfalls of including all the technical details at the expense of foregone physical intuition of many heavily mathematical texts are largely avoided. The first chapter presents a brief motivation behind geometric methods and their various applications in imaging and computer graphics. Chapters 2 and 3 lay the foundations for our coverage of geometry and topology, and are essential to the rest of the book. The remaining three chapters are, however, almost completely independent of each other.