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This volume comprises some of the key work presented at two IMA Workshops on Computer Vision during fall of 2000. Recent years have seen significant advances in the application of sophisticated mathematical theories to the problems arising in image processing. Basic issues include image smoothing and denoising, image enhancement, morphology, image compression, and segmentation (determining boundaries of objectsùincluding problems of camera distortion and partial occlusion). Several mathematical approaches have emerged, including methods based on nonlinear partial differential equations, stochastic and statistical methods, and signal processing techniques, including wavelets and other transform theories. Shape theory is of fundamental importance since it is the bottleneck between high and low level vision, and formed the bridge between the two workshops on vision. The recent geometric partial differential equation methods have been essential in throwing new light on this very difficult problem area. Further, stochastic processes, including Markov random fields, have been used in a Bayesian framework to incorporate prior constraints on smoothness and the regularities of discontinuities into algorithms for image restoration and reconstruction. A number of applications are considered including optical character and handwriting recognizers, printed-circuit board inspection systems and quality control devices, motion detection, robotic control by visual feedback, reconstruction of objects from stereoscopic view and/or motion, autonomous road vehicles, and many others.
This volume comprises some of the key work presented at two IMA
Workshops on Computer Vision during fall of 2000. Recent years have
seen significant advances in the application of sophisticated
mathematical theories to the problems arising in image processing.
Basic issues include image smoothing and denoising, image
enhancement, morphology, image compression, and segmentation
(determining boundaries of objects-including problems of camera
distortion and partial occlusion). Several mathematical approaches
have emerged, including methods based on nonlinear partial
differential equations, stochastic and statistical methods, and
signal processing techniques, including wavelets and other
transform theories. Shape theory is of fundamental importance since
it is the bottleneck between high and low level vision, and formed
the bridge between the two workshops on vision. The recent
geometric partial differential equation methods have been essential
in throwing new light on this very difficult problem area. Further,
stochastic processes, including Markov random fields, have been
used in a Bayesian framework to incorporate prior constraints on
smoothness and the regularities of discontinuities into algorithms
for image restoration and reconstruction. A number of applications
are considered including optical character and handwriting
recognizers, printed-circuit board inspection systems and quality
control devices, motion detection, robotic control by visual
feedback, reconstruction of objects from stereoscopic view and/or
motion, autonomous road vehicles, and many others.
Since its inception in the early 1980s, H( optimization theory has
become the control methodology of choice in robust feedback
analysis and design. The purpose of this monograph is to present,
in a tutorial fashion, a self contained operator theoretic approach
to the H( control for disturbed parameter systems, that is, systems
which admit infinite dimensional state spaces. Such systems arise
for problems modelled by partial differential equations or which
have time delays. Besides elucidating the mathematics of H(
control, extensive treatment is given to its physical and
engineering underpinnings. The techniques given in the book are
carefully illustrated by two benchmark problems: an unstable system
with a time delay which comes from the control of the X-29, and the
control of a Euler-Bernoulli flexible beam with Kelvin-Voigt
damping.
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