Vision Modeling and Computation

Vision, whether biological or computational , is the science and technology of perception generation from observed optical signals (or popularly referred to as images).  It allows a human being or an intelligent robot to sense, interpret, communicate with, and react to the environment (i.e., time+space). 

From quantum mechanics, Einstein's relativity theories, to nanotechnology and photonics, the role of light or photons has always been critical. Light (or electromagnetic waves), traveling in space and time, allows us to see the images of distant galaxies and stars millions of light-years away (or rather, ago), to feel the black hole ghosts from their gravity images, to watch the functioning organs of our own bodies (e.g., 2003 Nobel Prize in Physiology or Medicine was awarded to Paul Lauterbur and Peter Mansfield for magnetic resonance imaging (MRI)), and to take pictures for individual molecules in the nano- or meso-scales.

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Beneath all these sciences and technologies, lie the fundamental, counterintuitively technical, and often even more profoundly philosophical, questions: What do we mean by seeing? What do we mean by seeing some patterns (as Scott Russell discovered the first soliton pattern on the Edinburg-Glasgow canal when riding on his horse in 1834)? How much trust shall we put in our own seeing? Does seeing faithfully reflect existence and reality, or only come from the biased believing (or computation) of our mind? But what on earth is reality or existence? If even light cannot escape the core of a black hole and thus you cannot see it nor measure it, do you still believe it is meaningful to discuss its existence, time, or other features ? Travelling near the speed of light, are we still able to see the same world (Einstein claimed that nothing in this universe can exceed the light speed)? ...

This digital and information age further pushes those questions to the frontier. What is the chance in this universe for a natural area on the Mars' surface to bear the pattern of a human face? How much trust shall we invest in a doctor's words when s/he observes abnormalities from CT/MRI/PET images? Could a new bright spot in an astronomical image be a star missed by all the previous observations (e.g., the tenth newly discovered planet-Sedna- of our solar system)?

Naturally, vision modeling has to be interdisciplinary, cutting across vision psychology, cognitive science, computational neuron science, learning theory, pattern theory, image processing, computer vision, artificial intelligence, and so on. As applied mathematicians,  our goals are to develop models based on all the experimental results and data, analyze the models (existence, uniqueness, well-posedness, stability etc.), efficiently compute the models, and validate and improve them.

We closely follow and are deeply inspired by the pioneering works of Brown's Pattern Theory Group.

by Jianhong (JACKIE) Shen

First created in December 2002. Last modified in June 2003.  Here to the UCLA Imagers .