Handbook of Variational Methods for Nonlinear Geometric Data
暫譯: 非線性幾何數據變分方法手冊
Grohs, Philipp, Holler, Martin, Weinmann, Andreas
- 出版商: Springer
- 出版日期: 2020-04-04
- 售價: $8,640
- 貴賓價: 9.5 折 $8,208
- 語言: 英文
- 頁數: 701
- 裝訂: Hardcover - also called cloth, retail trade, or trade
- ISBN: 3030313506
- ISBN-13: 9783030313500
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相關主題
商品描述
This book covers different, current research directions in the context of variational methods for non-linear geometric data. Each chapter is authored by leading experts in the respective discipline and provides an introduction, an overview and a description of the current state of the art.
Non-linear geometric data arises in various applications in science and engineering. Examples of nonlinear data spaces are diverse and include, for instance, nonlinear spaces of matrices, spaces of curves, shapes as well as manifolds of probability measures. Applications can be found in biology, medicine, product engineering, geography and computer vision for instance.
Variational methods on the other hand have evolved to being amongst the most powerful tools for applied mathematics. They involve techniques from various branches of mathematics such as statistics, modeling, optimization, numerical mathematics and analysis. The vast majority of research on variational methods, however, is focused on data in linear spaces. Variational methods for non-linear data is currently an emerging research topic.
As a result, and since such methods involve various branches of mathematics, there is a plethora of different, recent approaches dealing with different aspects of variational methods for nonlinear geometric data. Research results are rather scattered and appear in journals of different mathematical communities.
The main purpose of the book is to account for that by providing, for the first time, a comprehensive collection of different research directions and existing approaches in this context. It is organized in a way that leading researchers from the different fields provide an introductory overview of recent research directions in their respective discipline. As such, the book is a unique reference work for both newcomers in the field of variational methods for non-linear geometric data, as well as for established experts that aim at to exploit new research directions or collaborations.
Chapter 9 of this book is available open access under a CC BY 4.0 license at link.springer.com.
商品描述(中文翻譯)
本書涵蓋了變分方法在非線性幾何數據方面的不同當前研究方向。每一章均由各自領域的領先專家撰寫,提供了介紹、概述以及當前技術的描述。
非線性幾何數據在科學和工程的各種應用中出現。非線性數據空間的例子多種多樣,包括非線性矩陣空間、曲線空間、形狀以及概率測度的流形等。應用範圍可見於生物學、醫學、產品工程、地理學和計算機視覺等領域。
另一方面,變分方法已發展為應用數學中最強大的工具之一。這些方法涉及來自數學各個分支的技術,如統計學、建模、優化、數值數學和分析。然而,絕大多數關於變分方法的研究集中在線性空間中的數據上。針對非線性數據的變分方法目前是一個新興的研究主題。
因此,由於這些方法涉及數學的各個分支,針對非線性幾何數據的變分方法有許多不同的、近期的研究方法,處理不同的方面。研究結果相對分散,出現在不同數學社群的期刊中。
本書的主要目的是首次提供一個全面的不同研究方向和現有方法的集合。它的組織方式使得來自不同領域的領先研究者能夠提供其各自學科中近期研究方向的介紹性概述。因此,本書對於變分方法在非線性幾何數據領域的新手以及希望利用新研究方向或合作的資深專家來說,都是一本獨特的參考著作。
本書的第九章在 link.springer.com 上以 CC BY 4.0 授權開放訪問。
作者簡介
Martin Holler was born on May 21, 1986 in Austria. He received his MSc (2010) and his PhD (2013) with a "promotio sub auspiciis praesidentis rei publicae" in Mathematics from the University of Graz. After research stays at the University of Cambridge, UK, and the Ecole Polytechnique, Paris, he currently holds a University Assistant position at the Institute of Mathematics and Scientific Computing of the University of Graz. His research interests include inverse problems and mathematical image processing, in particular the development and analysis of mathematical models in this context as well as applications in biomedical imaging, image compression and beyond.
Andreas Weinmann was born on July 18, 1979 in Augsburg, Germany. He studied mathematics with minor in computer science at TU Munich, and received his Diploma degree in mathematics and computer science from TU Munich in 2006 (with highest distinction). He was assistant at the Institute of Geometry, TU Graz. He obtained his Ph.D. degree from TU Graz in 2010 (with highest distinction). Then he worked as a researcher at Helmholtz Center Munich and TU Munich. Since 2015 he holds a position as Professor of Mathematics and Image Processing at Hochschule Darmstadt. He received his habilitation in 2018 from University Osnabruck. Andreas's research interests include applied analysis, in particular variational methods, nonlinear geometric data spaces, inverse problems as well as computer vision, signal and image processing and imaging applications, in particular Magnetic Particle Imaging.
作者簡介(中文翻譯)
菲利普·格羅斯教授(Prof. Dr. Philipp Grohs)於1981年7月7日出生於奧地利,自2016年以來一直擔任維也納大學的教授。2019年,他還成為奧地利科學院約翰·拉登計算與應用數學研究所(RICAM)的研究小組負責人。格羅斯在維也納科技大學(TU Wien)完成學業、獲得博士學位並擔任博士後研究員後,轉至沙烏地阿拉伯的阿卜杜拉國王科技大學(King Abdullah University of Science and Technology),隨後又轉至瑞士的蘇黎世聯邦理工學院(ETH Zürich),在那裡擔任助理教授,任期為2011年至2016年。格羅斯於2014年獲得ETH Zurich Latsis Prize。2020年,他獲選為亞歷山大·馮·洪堡教授獎(Alexander-von-Humboldt-Professorship),這是德國最高的研究獎項。他是奧地利數學學會的董事會成員,IEEE信息理論學會的成員,以及多本專業期刊的編輯委員會成員。
馬丁·霍勒(Martin Holler)於1986年5月21日出生於奧地利。他於2010年獲得格拉茨大學的碩士學位(MSc),並於2013年以「promotio sub auspiciis praesidentis rei publicae」的榮譽獲得數學博士學位(PhD)。在英國劍橋大學和法國巴黎高等師範學校進行研究後,他目前在格拉茨大學數學與科學計算研究所擔任大學助理職位。他的研究興趣包括反問題和數學影像處理,特別是在此背景下數學模型的開發與分析,以及在生物醫學影像、影像壓縮等方面的應用。
安德烈亞斯·維因曼(Andreas Weinmann)於1979年7月18日出生於德國奧格斯堡。他在慕尼黑工業大學(TU Munich)學習數學,並輔修計算機科學,於2006年獲得數學與計算機科學的文憑(Diploma)學位(以最高榮譽畢業)。他曾在格拉茨大學幾何學研究所擔任助理。2010年,他在格拉茨大學獲得博士學位(以最高榮譽畢業)。隨後,他在慕尼黑亥姆霍茲中心和慕尼黑工業大學擔任研究員。自2015年以來,他在達姆施塔特應用科技大學(Hochschule Darmstadt)擔任數學與影像處理教授。2018年,他在奧斯納布魯克大學獲得了晉升資格(habilitation)。安德烈亞斯的研究興趣包括應用分析,特別是變分方法、非線性幾何數據空間、反問題,以及計算機視覺、信號與影像處理及影像應用,特別是磁性粒子成像(Magnetic Particle Imaging)。