Jan Flusser & Barbara Zitova 
Moments and Moment Invariants in Pattern Recognition [PDF ebook] 

Moments as projections of an image’s intensity onto a proper
polynomial basis can be applied to many different aspects of image
processing. These include invariant pattern recognition, image
normalization, image registration, focus/ defocus measurement, and
watermarking. This book presents a survey of both recent and
traditional image analysis and pattern recognition methods, based
on image moments, and offers new concepts of invariants to linear
filtering and implicit invariants. In addition to the theory,
attention is paid to efficient algorithms for moment computation in
a discrete domain, and to computational aspects of orthogonal
moments. The authors also illustrate the theory through practical
examples, demonstrating moment invariants in real applications
across computer vision, remote sensing and medical imaging.



Key features:



* Presents a systematic review of the basic definitions and
properties of moments covering geometric moments and complex
moments.

* Considers invariants to traditional transforms —
translation, rotation, scaling, and affine transform — from a new
point of view, which offers new possibilities of designing optimal
sets of invariants.

* Reviews and extends a recent field of invariants with respect
to convolution/blurring.

* Introduces implicit moment invariants as a tool for recognizing
elastically deformed objects.

* Compares various classes of orthogonal moments (Legendre,
Zernike, Fourier-Mellin, Chebyshev, among others) and demonstrates
their application to image reconstruction from moments.

* Offers comprehensive advice on the construction of various
invariants illustrated with practical examples.

* Includes an accompanying website providing efficient numerical
algorithms for moment computation and for constructing invariants
of various kinds, with about 250 slides suitable for a graduate
university course.

Moments and Moment Invariants in Pattern Recognition is
ideal for researchers and engineers involved in pattern recognition
in medical imaging, remote sensing, robotics and computer vision.
Post graduate students in image processing and pattern recognition
will also find the book of interest.

Содержание

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.

Об авторе

Professor Jan Flusser, Ph D, 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, Ph D, 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, Ph D, 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.