Moments and Moment Invariants in Pattern Recognition (eBook)

Professor Jan Flusser, PhD, Dsc, is a director of the Institute of Information Theory and Automation of the ASCR, Prague, Czech Republic, and a full professor of Computer Science at the Czech Technical University, Prague, and at the Charles University , Prague. Jan Flusser's research areas are moments and moment invariants, image regristration, image fusion, multichannel blind deconvolution and super-resolution imaging. He has authored and coauthored more than 150 research publications in these areas, including tutorials (ICIP'05, ICIP'07, EUSIPCO'07, CVPR'08, FUSION'08, SPPRA'09, SCIA'09) and invited/keynote talks (ICCS'06, COMPSTAT'06, WIO'06, DICTA'07, CGIM'08) at major international conferences. He gives undergraduate and graduate courses on digital image processing, pattern recognition, and moment invariants and wavelets. Personal webpage http://www.utia.cas.cz/people/flusser. TomáS Suk, PhD, is a research fellow of the same Institute. His research interests include invariant features, moment and point-based invariants, color spaces and geometric transformations. He has authored and coauthored more than 50 research publications in these areas, some of which have elicited a considerable citation response. Tomás Suk coauthored tutorials on moment invariants held at international conference ICIP'07 and SPPR'09. Personal webpage href="http://zoi.utia.cas.cz/suk">http://zoi.utia.cas.cz/suk. Barbara Zitová, PhD, is Head of the Department of Image Processing at the same Institute. Her research interest is mainly in image regi8stration, invariants, wavelets, and image processing applications in cultural heritage. She has authored and coauthored more that 30 research publications in these areas, including tutorials at international conferences (ICIP'05, ICIP'07, EUSIPCO'07, FUSION'08 and CVPR'08). Her paper "Image Registration Methods: A Survey," Image and Vision Computing, vol. 21, pp. 977-1000, 2003, has become a major reference work in image registration . She teaches a specialized graduate course on moment invariants and wavelets at the Czech Technical University. Personal webpage href="http://zoi.utia.cas.cz/zitova">http://zoi.utia.cas.cz/zitova.

Authors' biographies.

Preface.

Acknowledgments.

1 Introduction to moments.

1.1 Motivation.

1.2 What are invariants?

1.3 What are moments?

1.4 Outline of the book.

References.

2 Moment invariants to translation, rotation and
scaling.

2.1 Introduction.

2.2 Rotation invariants from complex moments.

2.3 Pseudoinvariants.

2.4 Combined invariants to TRS and contrast changes.

2.5 Rotation invariants for recognition of symmetric
objects.

2.6 Rotation invariants via image normalization.

2.7 Invariants to nonuniform scaling.

2.8 TRS invariants in3D.

2.9 Conclusion.

References.

3 Affine moment invariants.

3.1 Introduction.

3.2 AMIs derived from the Fundamental theorem.

3.3 AMIs generated by graphs.

3.4 AMIs via image normalization.

3.5 Derivation of the AMIs from the Cayley-Aronhold
equation.

3.6 Numerical experiments.

3.7 Affine invariants of color images.

3.8 Generalization to three dimensions.

3.9 Conclusion.

Appendix.

References.

4 Implicit invariants to elastic transformations.

4.1 Introduction.

4.2 General moments under a polynomial transform.

4.3 Explicit and implicit invariants.

4.4 Implicit invariants as a minimization task.

4.5 Numerical experiments.

4.6 Conclusion.

References.

5 Invariants to convolution.

5.1 Introduction.

5.2 Blur invariants for centrosymmetric PSFs.

5.3 Blur invariants for N-fold symmetric PSFs.

5.4 Combined invariants.

5.5 Conclusion.

Appendix.

References.

6 Orthogonal moments.

6.1 Introduction.

6.2 Moments orthogonal on a rectangle.

6.3 Moments orthogonal on a disk.

6.4 Object recognition by ZMs.

6.5 Image reconstruction from moments.

6.6 Three-dimensional OG moments.

6.7 Conclusion.

References.

7 Algorithms for moment computation.

7.1 Introduction.

7.2 Moments in a discrete domain.

7.3 Geometric moments of binary images.

7.4 Geometric moments of graylevel images.

7.5 Efficient methods for calculating OG moments.

7.6 Generalization to n dimensions.

7.7 Conclusion.

References.

8 Applications.

8.1 Introduction.

8.2 Object representation and recognition.

8.3 Image registration.

8.4 Robot navigation.

8.5 Image retrieval.

8.6 Watermarking.

8.7 Medical imaging.

8.8 Forensic applications.

8.9 Miscellaneous applications.

8.10 Conclusion.

References.

9 Conclusion.

Index.

"This text is a little gem in the vast amount of literature on
pattern recognition...In conclusion, this is an excellent text on
pattern recognition that I highly recommend to practitioners and
students in signal and image processing." (Computing
Reviews, October 2010)