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Mathematics Of Shapes And Applications (Hardcover)
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Mathematics Of Shapes And Applications (Hardcover)
Series: Lecture Notes Series, Institute for Mathematical Sciences, National University of Singapore, 37
Expected to ship within 10 - 15 working days
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Understanding how a single shape can incur a complex range of
transformations, while defining the same perceptually obvious
figure, entails a rich and challenging collection of problems, at
the interface between applied mathematics, statistics and computer
science. The program on Mathematics of Shapes and Applications, was
held at the Institute for Mathematical Sciences at the National
University of Singapore in 2016. It provided discussions on
theoretical developments and numerous applications in computer
vision, object recognition and medical imaging.The analysis of
shapes is an example of a mathematical problem directly connected
with applications while offering deep open challenges to
theoretical mathematicians. It has grown, over the past decades,
into an interdisciplinary area in which researchers studying
infinite-dimensional Riemannian manifolds (global analysis)
interact with applied mathematicians, statisticians, computer
scientists and biomedical engineers on a variety of problems
involving shapes.The volume illustrates this wealth of subjects by
providing new contributions on the metric structure of
diffeomorphism groups and shape spaces, recent developments on
deterministic and stochastic models of shape evolution, new
computational methods manipulating shapes, and new statistical
tools to analyze shape datasets. In addition to these
contributions, applications of shape analysis to medical imaging
and computational anatomy are discussed, leading, in particular, to
improved understanding of the impact of cognitive diseases on the
geometry of the brain.
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