Automatic object recognition has become an established discipline inside image analysis. Moments and moment invariants play a very important role as features in invariant recognition. They were introduced to the pattern recognition community almost 50 years ago and the mathematical background they utilized is even older, it originates from the second half of the 19th century. Nowadays, we may find thousands of references to journal and conference papers when searching SCOPUS, Web of Science, or IEEE Xplore databases for the keyword "moment invariants" and this number grows every year. Despite this, any comprehensive monograph covering the current state-of-the-art and presenting the latest development on this field in a consistent form has not so far been published. Our main purpose in writing this book was to bridge this gap. In this book, the reader finds both a survey of all important theoretical results as well as a description of how to use them in various image analysis tasks.

The book presents a unique overview of recent as well as traditional image analysis and pattern recognition methods based on image moments. Invariants to traditional transforms - translation, rotation, scaling, and affine transform - are studied in-depth from a new point of view. Recent results on invariants to linear filtering of the image and on implicit moment invariants to elastic deformations are clearly presented and well explained. Various classes of orthogonal moments (Legendre, Zernike, Pseudo-Zernike, Chebyshev, Fourier-Mellin, Krawtchouk, and other moments) are reviewed and compared and their application to image reconstruction from moments is demonstrated. We reviewed efficient numerical algorithms that can be used for moment computation in a discrete domain. Finally, we demonstrated practical examples of using moment invariants in real applications from the area of computer vision, remote sensing, and medical imaging. Most of the book is related to 2D images but generalization to 3D is also shown in most cases.

The book is based on our deep experience with moments and moment invariants gained from 15 years of research in this area, from teaching the graduate courses on moment invariants and related fields of image analysis at the Czech Technical University and at the Charles University, Prague, Czech Republic, and from presenting several tutorials on moments at major international conferences.

The target readership of the book are academic researchers and R&D engineers from all application areas who need to recognize 2D objects extracted from binary/graylevel/color images and who look for invariant and robust object descriptors, as well as specialists in moment-based image analysis interested in a new development on this field. Last but not least, the book is also intended for university lecturers and graduate students of image analysis and pattern recognition. It can be used as a textbook for advanced graduate courses on Invariant Pattern Recognition. The first two Chapters can be even utilized as supplementary reading to undergraduate courses on Pattern Recognition and Image Analysis.