From medical imaging (CT, X-ray, MRI, fMRI), atomic and molecular imaging,  underwater imaging, cosmological imaging, Internet  image  and  video  communication, computer graphics in the multi-billion industries of movies, games, and advertisements, and computer vision and artificial intelligence for mobile robots, to the scientific understanding of the most delicate (and wonderful) design of our Mother Nature - the biological vision system,  images are seen everywhere.

From the early rosy dawn when one wakes up into the REAL world, to the late neon night when one escapes into the DREAM world, the information of  both the exterior and interior worlds of the human race, is projected through "the window to the soul" (quoting da Vinci) - the two eyes, onto the conscious or subconscious layers of the Brain. Thus the worlds reveal themselves, and we perceive; and images are the messengers.

From the intriguing surface features of a distant planet, the double-helix structure of DNA chains under X-rays, the puzzling folding patterns of proteins, a heart-shattering greyish block in a CT medical scan, and a knife shape on the computer screen at an airport security gate, to a human figure in a remote mountain valley spotted high above by a night-vision goggle from a rescuing helicopter, images are all about patterns.

We see, but do we truly understand our seeing? We watch, but are we watching consciously our own watching? Buddha says: Seeing Blinds You.

What are Images? What are Patterns? How can They be Analyzed? Is There a Consistent Theory? What are the Coherent Logical Structures behind all Above Image Analysis and Processing?  This book is devoted to the partial answering of all these questions.

We are standing on the shoulders of many giants and pioneers in this exciting field, to whom we are profoundly indebted, and to whom we dedicate this monograph ...                      September, 2005.