Group-Theoretical Methods in Image Understanding

This book presents the mathematics relevant to image understanding by

computer vision and gives examples of actual applications. Group

representation theory, Lie groups and Lie algebras, the theory of

invariance, tensor calculus, differential geometry and projective

geometry are used for three-dimensional shape and motion analysis from

images, making use of techniques such as shape from motion, shape from

texture, shape from angle and shape from surface. Although the

mathematics itself may be well known to mathematicians, people working

in areas related to computer science, image understanding, computer

vision and image processing have usually never studied such

mathematics, and so may be surprised to learn that abstract

mathematical concepts can be of enormous help in building intelligent

computer vision systems.