Author: Michael E. Farmer

Application of Chaos and Fractals to Computer Vision

eBook: US $69 Special Offer (PDF + Printed Copy): US $163
Printed Copy: US $129
Library License: US $276
ISBN: 978-1-60805-901-0 (Print)
ISBN: 978-1-60805-900-3 (Online)
Year of Publication: 2014
DOI: 10.2174/97816080590031140101


Application of Chaos and Fractals to Computer Vision

This book provides a thorough investigation of the application of chaos theory and fractal analysis to computer vision. The field of chaos theory has been studied in dynamical physical systems, and has been very successful in providing computational models for very complex problems ranging from weather systems to neural pathway signal propagation. Computer vision researchers have derived motivation for their algorithms from biology and physics for many years as witnessed by the optical flow algorithm, the oscillator model underlying graphical cuts and of course neural networks. These algorithms are very helpful for a broad range of computer vision problems like motion segmentation, texture analysis and change detection.

The contents of this book include chapters in biological vision systems, foundations of chaos and fractals, behavior of images and image sequences in phase space, mathematical measures for analyzing phase space, applications to pre-attentive vision and applications to post-attentive vision.

This book is intended for graduate students, upper division undergraduates, researchers and practitioners in image processing and computer vision. The readers will develop a solid understanding of the concepts of chaos theory and their application to computer vision. Readers will be introduced to a new way of thinking about computer vision problems from the perspective of complex dynamical systems. This new approach will provide them a deeper understanding of the various phenomena present in complex image scenes.

Indexed in: Book Citation Index, Science Edition, EBSCO, Ulrich's Periodicals Directory.


Computer Science, Computer Engineering, Electrical Engineering, Biomedical Engineering, Mechanical Engineering, and Civil Engineering, together with physics, cognitive psychology, evolutionary biology and mathematics have been involved in computer vision to solve many theoretical and practical problems. For example, understanding of human vision as well as vision of terrestrial animals, underground creatures, underwater animals, and flying animals could be very helpful in developing improved computer vision algorithms for various "smart" autonomous machines such as terrestrial vehicles, mobile robots, underground drones, submersibles, and constellations of small satellites, including nano-, pico-, and femto¬satellites. Another fundamental reason for the quest to develop better computer vision is the expanding interest in cognitive dynamical systems. While adaptive control systems constituted the foundation of the previous revolution in systems, cognitive dynamical systems appear to be the next.

This book is right in the center of such developments. It is motivated by the need to solve many fundamental issues in computer vision, including static and moving object segmentation, scene registration and tracking, as well as object classification. Its approach is also matching the requirements of dynamic systems by including not only the three classic stable states (point, cyclic and toroidal stability), but also the fourth stable state, chaos. Under special conditions and driving functions, chaos can develop in a system to affect its behavior either negatively or positively. The positive impact is explored in the book using aperiodic forcing functions to induce temporal chaotic-like behavior (in image sequences) and spatial chaotic-like behavior (in image textures). This approach is of interest to many researchers today. Since the phase-space trajectories (behavior) of chaotic systems is fractal and multi-fractal, their analysis must also be multi-fractal. The book uses this approach to detect chaotic behavior in a system. This approach could also be used to quantify the behavior in order to improve it. Since a multi-fractal analysis is necessarily based on information-theoretic arguments, it often is superior to energy-based approaches in quantification of complexity of systems and their behavior. An example of the use of a unified approach to multi-fractal analysis of phase-space self-affine objects is presented in Chapter 5.

Since this well-crafted and unique book is supported by many examples, illustrations and images, it is easy to read and understand even though it deals with very difficult scientific and technical matters. It should be of interest to many students, researchers and practitioners not only in the area of computer vision, but also to the broader audience of mechatronics, robotics, secure and resilient systems, as well as adaptive, perceptual and cognitive systems.

Witold Kinsner
Cognitive Systems Laboratory
Department of Electrical and Computer Engineering
University of Manitoba