Mathematics Of Shapes And Applications

by Sergey Kushnarev, Anqi Qiu, Laurent Younes

Overview

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.

Product Details

ISBN-13:	9789811200120
Publisher:	World Scientific Publishing Company, Incorporated
Publication date:	11/28/2019
Series:	Lecture Notes Series, Institute For Mathematical Sciences, National University Of Singapore , #37
Pages:	220
Product dimensions:	6.00(w) x 9.00(h) x 0.56(d)

Table of Contents

3D Normal Coordinate Systems for Cortical Areas; Piecewise Rigid Motion in Diffeomorphism Groups with Strong Right-Invariant Metrics; Variational Second-Order Interpolation on the Group of Diffeomorphisms with a Right-Invariant Metric; Diffeomorphic Registration of Discrete Geometric Distributions; Riemannian Geometry for Shape Analysis and Computational Anatomy; Stochastic Metamorphosis with Template Uncertainties; Existence and Continuity of Minimizers for the Estimation of Growth Mapped Evolutions for Current Data Term and Counterexamples for Varifold Data Term; Heat Kernel Smoothing in Irregular Image Domains