Signal Representation and Signal Processing Using Operators Signal Representation and Signal Processing Using Operators

The topic of this report is signal representation in the context of hierarchical image processing. An overview of hierarchical processing systems is included as well as a presentation of various approaches to signal representation, feature representation and feature extraction. It is claimed that image hierarchies based on feature extraction, so called feature hierarchies, demand a signal representation other than the standard spatial or linear representation used today. A new representation, the operator representation is developed. It is based on an interpretation of features in terms of signal transformations. This representation has no references to any spatial ordering of the signal element and also gives an explicit representation of signal features. Using the operator representation, a generalization of the standard phase concept in image processing is introduced. Based on the operator representation, two algorithms for extraction of feature values are presented. Both have the capability of generating phase invariant feature descriptors. It is claimed that the operator representation in conjunction with some appropriate feature extraction algorithm is well suited as a general framework for de ning multi level feature hierarchies. The report contains an appendical chapter containing the mathematical details necessary to comprehend the presentation. Acknowledgement There are a number of people who have inspired and helped me in the work documented in this report. First of all, I would like to express my gratitude to professor Gosta Granlund. It is his ideas regarding information representation and hierarchical signal processing which have inspired the present work. The results of this work would not have been possible without stimulating discussions with the members of the Computer Vision Laboratory, of which I would like to mention Hans Knutsson, Andrew Calway (now at University of Wales) and H akan B arman. A number of people have helped me with the mathematical details which are found in the last chapter. In particular Reiner Lenz at the Department of Electrical Engineering, Magnus Herberthson, Anders Carlsson, professor Lars Eld en, Peter Hackman at the Department of Mathematics, and Frank Uhlig at Auburn University, have contributed. I owe specially to Peter for suggesting the textbook by Curtis which has been a great source of inspiration in the beginning of this work and also for proof reading the manuscript of Chapter 5 and making several suggestions which improved the nal result. Many thanks also to Tomas Landelius who proof read some of the chapters. Finally, I would like to thank Annika and the people of Iceland. I believe that a holiday with these wonderful people was a major inspiration to this work. The present work is nancially supported in full by the Swedish Board of Technical Development.