Mathematics of Shapes and Applications
Другое / Образование
Основная информация:
Название: Mathematics of Shapes and Applications
Жанр: Нет
Автор: Sergey Kushnarev, Anqi Qiu
Год выпуска: 2019
Формат: PDF
Размер: 26.7 MB
ISBN: 689531725319
Язык: Английский
СКАЧАТЬ Mathematics of Shapes and Applications БЕСПЛАТНО EPUB - DOC - DJVU - RTF - PDFОписание: 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. 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.