Mathematical Methods in Computer Vision

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.

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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 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.