The book discusses novel visualization techniques driven by the needs in medicine and life sciences as well as new application areas and challenges for visualization within these fields. It presents ideas and concepts for visual analysis of data from scientific studies of living organs or to the delivery of healthcare. Target scientific domains include the entire field of biology at all scales - from genes and proteins to organs and populations - as well as interdisciplinary research based on technological advances such as bioinformatics, biomedicine, biochemistry, or biophysics. Moreover, they comprise the field of medicine and the application of science and technology to healthcare problems. This book does not only present basic research pushing the state of the art in the field of visualization, but it also documents the impact in the fields of medicine and life sciences.

The book discusses novel visualization techniques driven by the needs in medicine and life sciences as well as new application areas and challenges for visualization within these fields. It presents ideas and concepts for visual analysis of data from scientific studies of living organs or to the delivery of healthcare. Target scientific domains include the entire field of biology at all scales - from genes and proteins to organs and populations - as well as interdisciplinary research based on technological advances such as bioinformatics, biomedicine, biochemistry, or biophysics. Moreover, they comprise the field of medicine and the application of science and technology to healthcare problems. This book does not only present basic research pushing the state of the art in the field of visualization, but it also documents the impact in the fields of medicine and life sciences.

The book discusses novel visualization techniques driven by the needs in medicine and life sciences as well as new application areas and challenges for visualization within these fields. It presents ideas and concepts for visual analysis of data from scientific studies of living organs or to the delivery of healthcare. Target scientific domains include the entire field of biology at all scales - from genes and proteins to organs and populations - as well as interdisciplinary research based on technological advances such as bioinformatics, biomedicine, biochemistry, or biophysics. Moreover, they comprise the field of medicine and the application of science and technology to healthcare problems. This book does not only present basic research pushing the state of the art in the field of visualization, but it also documents the impact in the fields of medicine and life sciences.

This research book on Mathematical Visualization contains state of the art presentations on visualization problems in mathematics, on fundamental mathematical research in computer graphics, and on software frameworks for the application of visualization to real-world problems.All contributions were written by leading experts in the field and peer-refereed by an international editorial team. The book grew out of the third international workshop "Visualization and Mathematics", which was held from May 22-25, 2002 in Berlin.The themes of the book cover important recent developments on- Geometry and Combinatorics of Meshes - Discrete Vector Fields and Topology- Geometric Modelling- Image Based Visualization- Software Environments and Applications- Education and CommunicationThe variety of topics makes the book a suitable resource for researchers, lecturers, and practitioners; http://www-sfb288.math.tu-berlin.de/vismath/

The MathFilm DVD presents a juried collection of innovative short math videos. The films are winners of the international competition of the MathFilm Festival 2008. Following the May premiere in Berlin, the festival films are shown in public viewings throughout Germany. The festival is part of the "Year of Mathematics" initiative of the Federal Ministry of Education and Research. The films target a broad audience of students, teachers, and everyone with an interest in mathematics. The topics range from geometry to graphics, from computing to visualization, from historic to modern achievements, from abstract mathematical worlds to real-world applications. The DVD provides entertaining and informative insights into modern mathematics and is an exciting resource for lively school and university courses.

Die MathFilm DVD präsentiert eine Sammlung preisgekrönter mathematischer Kurzfilme. Bei den Filmen handelt es sich um die Gewinner des internationalen Wettbewerbs zum MathFilm Festival 2008. Seit der Premiere des Festivals im Mai 2008 in Berlin werden die Filme öffentlich in vielen Städten in Deutschland vorgeführt. Das MathFilm Festival 2008 ist Teil des „Jahres der Mathematik", einer Initiative des Bundesministeriums für Bildung und Forschung. Die Filme richten sich an einen breiten Zuschauerkreis: Schüler, Studenten, Lehrer und alle jene mit einem Interesse an den bunten Seiten der Mathematik. Die Themen reichen von Geometrie bis Computergraphik, vom wissenschaftlichen Rechnen bis Visualisierung, von historischen zu modernen Errungenschaften, von abstrakten mathematischen Ideen bis zu Anwendungen in der realen Welt. Die DVD vermittelt unterhaltsame und informative Einblicke in die moderne Mathematik und bietet anschauliche und fesselnde Filme für lebendige Schul- und Universitätskurse.

Visualization research aims to provide insight into large, complicated data sets and the phenomena behind them. While there are di?erent methods of reaching this goal, topological methods stand out for their solid mathem- ical foundation, which guides the algorithmic analysis and its presentation. Topology-based methods in visualization have been around since the beg- ning of visualization as a scienti?c discipline, but they initially played only a minor role. In recent years,interest in topology-basedvisualization has grown andsigni?cantinnovationhasledto newconceptsandsuccessfulapplications. The latest trends adapt basic topological concepts to precisely express user interests in topological properties of the data. This book is the outcome of the second workshop on Topological Methods in Visualization, which was held March 4–6, 2007 in Kloster Nimbschen near Leipzig,Germany.Theworkshopbroughttogethermorethan40international researchers to present and discuss the state of the art and new trends in the ?eld of topology-based visualization. Two inspiring invited talks by George Haller, MIT, and Nelson Max, LLNL, were accompanied by 14 presentations by participants and two panel discussions on current and future trends in visualization research. This book contains thirteen research papers that have been peer-reviewed in a two-stage review process. In the ?rst phase, submitted papers where peer-reviewed by the international program committee. After the workshop accepted papers went through a revision and a second review process taking into account comments from the ?rst round and discussions at the workshop. Abouthalfthepapersconcerntopology-basedanalysisandvisualizationof ?uid?owsimulations;twopapersconcernmoregeneraltopologicalalgorithms, while theremaining papers discuss topology-based visualization methods in application areas like biology, medical imaging and electromagnetism.

Visualization research aims to provide insight into large, complicated data sets and the phenomena behind them. While there are di?erent methods of reaching this goal, topological methods stand out for their solid mathem- ical foundation, which guides the algorithmic analysis and its presentation. Topology-based methods in visualization have been around since the beg- ning of visualization as a scienti?c discipline, but they initially played only a minor role. In recent years,interest in topology-basedvisualization has grown andsigni?cantinnovationhasledto newconceptsandsuccessfulapplications. The latest trends adapt basic topological concepts to precisely express user interests in topological properties of the data. This book is the outcome of the second workshop on Topological Methods in Visualization, which was held March 4–6, 2007 in Kloster Nimbschen near Leipzig,Germany.Theworkshopbroughttogethermorethan40international researchers to present and discuss the state of the art and new trends in the ?eld of topology-based visualization. Two inspiring invited talks by George Haller, MIT, and Nelson Max, LLNL, were accompanied by 14 presentations by participants and two panel discussions on current and future trends in visualization research. This book contains thirteen research papers that have been peer-reviewed in a two-stage review process. In the ?rst phase, submitted papers where peer-reviewed by the international program committee. After the workshop accepted papers went through a revision and a second review process taking into account comments from the ?rst round and discussions at the workshop. Abouthalfthepapersconcerntopology-basedanalysisandvisualizationof ?uid?owsimulations;twopapersconcernmoregeneraltopologicalalgorithms, while theremaining papers discuss topology-based visualization methods in application areas like biology, medical imaging and electromagnetism.

Mathematical Visualization aims at an abstract framework for fundamen­ tal objects appearing in visualization and at the application of the manifold visualization techniques to problems in geometry, topology and numerical mathematics. The articles in this volume report on new research results in this field, on the development of software and educational material and on mathematical applications. The book grew out of the third international workshop "Visualization and Mathematics", which was held from May 22-25, 2002 in Berlin (Germany). The workshop was funded by the DFG-Sonderforschungsbereich 288 "Dif­ ferential Geometry and Quantum Physics" at Technische Universitat Berlin and supported by the Zuse Institute Berlin (ZIB) and the DFG research cen­ ter "Mathematics for Key Technologies" (FZT 86) in Berlin. Five keynote lectures, eight invited presentations and several contributed talks created a stimulating atmosphere with many scientific discussions. The themes of this book cover important recent developments in the fol­ lowing fields: - Geometry and Combinatorics of Meshes - Discrete Vector Fields and Topology - Geometric Modelling - Image Based Visualization - Software Environments and Applications - Education and Communication We hope that the research articles of this book will stimulate the readers' own work and will further strenghten the development of the field of Mathe­ matical Visualization. VI Preface We appreciate the thorough work of the authors and reviewers on each of the individual articles, and we thank you all.

For some time, medicine has been an important driver for the development of data processing and visualization techniques. Improved technology offers the capacity to generate larger and more complex data sets related to imaging and simulation. This, in turn, creates the need for more effective visualization tools for medical practitioners to interpret and utilize data in meaningful ways. The first edition of Visualization in Medicine and Life Sciences (VMLS) emerged from a workshop convened to explore the significant data visualization challenges created by emerging technologies in the life sciences. The workshop and the book addressed questions of whether medical data visualization approaches can be devised or improved to meet these challenges, with the promise of ultimately being adopted by medical experts. Visualization in Medicine and Life Sciences II follows the second international VMLS workshop, held in Bremerhaven, Germany, in July 2009. Internationally renowned experts from the visualization and driving application areas came together for this second workshop. The book presents peer-reviewed research and survey papers which document and discuss the progress made, explore new approaches to data visualization, and assess new challenges and research directions.

For some time, medicine has been an important driver for the development of data processing and visualization techniques. Improved technology offers the capacity to generate larger and more complex data sets related to imaging and simulation. This, in turn, creates the need for more effective visualization tools for medical practitioners to interpret and utilize data in meaningful ways. The first edition of Visualization in Medicine and Life Sciences (VMLS) emerged from a workshop convened to explore the significant data visualization challenges created by emerging technologies in the life sciences. The workshop and the book addressed questions of whether medical data visualization approaches can be devised or improved to meet these challenges, with the promise of ultimately being adopted by medical experts. Visualization in Medicine and Life Sciences II follows the second international VMLS workshop, held in Bremerhaven, Germany, in July 2009. Internationally renowned experts from the visualization and driving application areas came together for this second workshop. The book presents peer-reviewed research and survey papers which document and discuss the progress made, explore new approaches to data visualization, and assess new challenges and research directions.

Mathematical Visualization aims at an abstract framework for fundamen­ tal objects appearing in visualization and at the application of the manifold visualization techniques to problems in geometry, topology and numerical mathematics. The articles in this volume report on new research results in this field, on the development of software and educational material and on mathematical applications. The book grew out of the third international workshop "Visualization and Mathematics", which was held from May 22-25, 2002 in Berlin (Germany). The workshop was funded by the DFG-Sonderforschungsbereich 288 "Dif­ ferential Geometry and Quantum Physics" at Technische Universitat Berlin and supported by the Zuse Institute Berlin (ZIB) and the DFG research cen­ ter "Mathematics for Key Technologies" (FZT 86) in Berlin. Five keynote lectures, eight invited presentations and several contributed talks created a stimulating atmosphere with many scientific discussions. The themes of this book cover important recent developments in the fol­ lowing fields: - Geometry and Combinatorics of Meshes - Discrete Vector Fields and Topology - Geometric Modelling - Image Based Visualization - Software Environments and Applications - Education and Communication We hope that the research articles of this book will stimulate the readers'' own work and will further strenghten the development of the field of Mathe­ matical Visualization. VI Preface We appreciate the thorough work of the authors and reviewers on each of the individual articles, and we thank you all.

Visualization research aims to provide insight into large, complicated data sets and the phenomena behind them. While there are di?erent methods of reaching this goal, topological methods stand out for their solid mathem- ical foundation, which guides the algorithmic analysis and its presentation. Topology-based methods in visualization have been around since the beg- ning of visualization as a scienti?c discipline, but they initially played only a minor role. In recent years,interest in topology-basedvisualization has grown andsigni?cantinnovationhasledto newconceptsandsuccessfulapplications. The latest trends adapt basic topological concepts to precisely express user interests in topological properties of the data. This book is the outcome of the second workshop on Topological Methods in Visualization, which was held March 4–6, 2007 in Kloster Nimbschen near Leipzig,Germany.Theworkshopbroughttogethermorethan40international researchers to present and discuss the state of the art and new trends in the ?eld of topology-based visualization. Two inspiring invited talks by George Haller, MIT, and Nelson Max, LLNL, were accompanied by 14 presentations by participants and two panel discussions on current and future trends in visualization research. This book contains thirteen research papers that have been peer-reviewed in a two-stage review process. In the ?rst phase, submitted papers where peer-reviewed by the international program committee. After the workshop accepted papers went through a revision and a second review process taking into account comments from the ?rst round and discussions at the workshop. Abouthalfthepapersconcerntopology-basedanalysisandvisualizationof ?uid?owsimulations;twopapersconcernmoregeneraltopologicalalgorithms, while theremaining papers discuss topology-based visualization methods in application areas like biology, medical imaging and electromagnetism.

The book discusses novel visualization techniques driven by the needs in medicine and life sciences as well as new application areas and challenges for visualization within these fields. It presents ideas and concepts for visual analysis of data from scientific studies of living organs or to the delivery of healthcare. Target scientific domains include the entire field of biology at all scales - from genes and proteins to organs and populations - as well as interdisciplinary research based on technological advances such as bioinformatics, biomedicine, biochemistry, or biophysics. Moreover, they comprise the field of medicine and the application of science and technology to healthcare problems. This book does not only present basic research pushing the state of the art in the field of visualization, but it also documents the impact in the fields of medicine and life sciences.

The book discusses novel visualization techniques driven by the needs in medicine and life sciences as well as new application areas and challenges for visualization within these fields. It presents ideas and concepts for visual analysis of data from scientific studies of living organs or to the delivery of healthcare. Target scientific domains include the entire field of biology at all scales - from genes and proteins to organs and populations - as well as interdisciplinary research based on technological advances such as bioinformatics, biomedicine, biochemistry, or biophysics. Moreover, they comprise the field of medicine and the application of science and technology to healthcare problems. This book does not only present basic research pushing the state of the art in the field of visualization, but it also documents the impact in the fields of medicine and life sciences.

The book discusses novel visualization techniques driven by the needs in medicine and life sciences as well as new application areas and challenges for visualization within these fields. It presents ideas and concepts for visual analysis of data from scientific studies of living organs or to the delivery of healthcare. Target scientific domains include the entire field of biology at all scales - from genes and proteins to organs and populations - as well as interdisciplinary research based on technological advances such as bioinformatics, biomedicine, biochemistry, or biophysics. Moreover, they comprise the field of medicine and the application of science and technology to healthcare problems. This book does not only present basic research pushing the state of the art in the field of visualization, but it also documents the impact in the fields of medicine and life sciences.

This research book on Mathematical Visualization contains state of the art presentations on visualization problems in mathematics, on fundamental mathematical research in computer graphics, and on software frameworks for the application of visualization to real-world problems.All contributions were written by leading experts in the field and peer-refereed by an international editorial team. The book grew out of the third international workshop "Visualization and Mathematics", which was held from May 22-25, 2002 in Berlin.The themes of the book cover important recent developments on- Geometry and Combinatorics of Meshes - Discrete Vector Fields and Topology- Geometric Modelling- Image Based Visualization- Software Environments and Applications- Education and CommunicationThe variety of topics makes the book a suitable resource for researchers, lecturers, and practitioners; http://www-sfb288.math.tu-berlin.de/vismath/

The MathFilm DVD presents a juried collection of innovative short math videos. The films are winners of the international competition of the MathFilm Festival 2008. Following the May premiere in Berlin, the festival films are shown in public viewings throughout Germany. The festival is part of the "Year of Mathematics" initiative of the Federal Ministry of Education and Research. The films target a broad audience of students, teachers, and everyone with an interest in mathematics. The topics range from geometry to graphics, from computing to visualization, from historic to modern achievements, from abstract mathematical worlds to real-world applications. The DVD provides entertaining and informative insights into modern mathematics and is an exciting resource for lively school and university courses.

Die MathFilm DVD präsentiert eine Sammlung preisgekrönter mathematischer Kurzfilme. Bei den Filmen handelt es sich um die Gewinner des internationalen Wettbewerbs zum MathFilm Festival 2008. Seit der Premiere des Festivals im Mai 2008 in Berlin werden die Filme öffentlich in vielen Städten in Deutschland vorgeführt. Das MathFilm Festival 2008 ist Teil des „Jahres der Mathematik", einer Initiative des Bundesministeriums für Bildung und Forschung. Die Filme richten sich an einen breiten Zuschauerkreis: Schüler, Studenten, Lehrer und alle jene mit einem Interesse an den bunten Seiten der Mathematik. Die Themen reichen von Geometrie bis Computergraphik, vom wissenschaftlichen Rechnen bis Visualisierung, von historischen zu modernen Errungenschaften, von abstrakten mathematischen Ideen bis zu Anwendungen in der realen Welt. Die DVD vermittelt unterhaltsame und informative Einblicke in die moderne Mathematik und bietet anschauliche und fesselnde Filme für lebendige Schul- und Universitätskurse.

Visualization research aims to provide insight into large, complicated data sets and the phenomena behind them. While there are di?erent methods of reaching this goal, topological methods stand out for their solid mathem- ical foundation, which guides the algorithmic analysis and its presentation. Topology-based methods in visualization have been around since the beg- ning of visualization as a scienti?c discipline, but they initially played only a minor role. In recent years,interest in topology-basedvisualization has grown andsigni?cantinnovationhasledto newconceptsandsuccessfulapplications. The latest trends adapt basic topological concepts to precisely express user interests in topological properties of the data. This book is the outcome of the second workshop on Topological Methods in Visualization, which was held March 4–6, 2007 in Kloster Nimbschen near Leipzig,Germany.Theworkshopbroughttogethermorethan40international researchers to present and discuss the state of the art and new trends in the ?eld of topology-based visualization. Two inspiring invited talks by George Haller, MIT, and Nelson Max, LLNL, were accompanied by 14 presentations by participants and two panel discussions on current and future trends in visualization research. This book contains thirteen research papers that have been peer-reviewed in a two-stage review process. In the ?rst phase, submitted papers where peer-reviewed by the international program committee. After the workshop accepted papers went through a revision and a second review process taking into account comments from the ?rst round and discussions at the workshop. Abouthalfthepapersconcerntopology-basedanalysisandvisualizationof ?uid?owsimulations;twopapersconcernmoregeneraltopologicalalgorithms, while theremaining papers discuss topology-based visualization methods in application areas like biology, medical imaging and electromagnetism.

Visualization research aims to provide insight into large, complicated data sets and the phenomena behind them. While there are di?erent methods of reaching this goal, topological methods stand out for their solid mathem- ical foundation, which guides the algorithmic analysis and its presentation. Topology-based methods in visualization have been around since the beg- ning of visualization as a scienti?c discipline, but they initially played only a minor role. In recent years,interest in topology-basedvisualization has grown andsigni?cantinnovationhasledto newconceptsandsuccessfulapplications. The latest trends adapt basic topological concepts to precisely express user interests in topological properties of the data. This book is the outcome of the second workshop on Topological Methods in Visualization, which was held March 4–6, 2007 in Kloster Nimbschen near Leipzig,Germany.Theworkshopbroughttogethermorethan40international researchers to present and discuss the state of the art and new trends in the ?eld of topology-based visualization. Two inspiring invited talks by George Haller, MIT, and Nelson Max, LLNL, were accompanied by 14 presentations by participants and two panel discussions on current and future trends in visualization research. This book contains thirteen research papers that have been peer-reviewed in a two-stage review process. In the ?rst phase, submitted papers where peer-reviewed by the international program committee. After the workshop accepted papers went through a revision and a second review process taking into account comments from the ?rst round and discussions at the workshop. Abouthalfthepapersconcerntopology-basedanalysisandvisualizationof ?uid?owsimulations;twopapersconcernmoregeneraltopologicalalgorithms, while theremaining papers discuss topology-based visualization methods in application areas like biology, medical imaging and electromagnetism.

Mathematical Visualization aims at an abstract framework for fundamen­ tal objects appearing in visualization and at the application of the manifold visualization techniques to problems in geometry, topology and numerical mathematics. The articles in this volume report on new research results in this field, on the development of software and educational material and on mathematical applications. The book grew out of the third international workshop "Visualization and Mathematics", which was held from May 22-25, 2002 in Berlin (Germany). The workshop was funded by the DFG-Sonderforschungsbereich 288 "Dif­ ferential Geometry and Quantum Physics" at Technische Universitat Berlin and supported by the Zuse Institute Berlin (ZIB) and the DFG research cen­ ter "Mathematics for Key Technologies" (FZT 86) in Berlin. Five keynote lectures, eight invited presentations and several contributed talks created a stimulating atmosphere with many scientific discussions. The themes of this book cover important recent developments in the fol­ lowing fields: - Geometry and Combinatorics of Meshes - Discrete Vector Fields and Topology - Geometric Modelling - Image Based Visualization - Software Environments and Applications - Education and Communication We hope that the research articles of this book will stimulate the readers' own work and will further strenghten the development of the field of Mathe­ matical Visualization. VI Preface We appreciate the thorough work of the authors and reviewers on each of the individual articles, and we thank you all.

For some time, medicine has been an important driver for the development of data processing and visualization techniques. Improved technology offers the capacity to generate larger and more complex data sets related to imaging and simulation. This, in turn, creates the need for more effective visualization tools for medical practitioners to interpret and utilize data in meaningful ways. The first edition of Visualization in Medicine and Life Sciences (VMLS) emerged from a workshop convened to explore the significant data visualization challenges created by emerging technologies in the life sciences. The workshop and the book addressed questions of whether medical data visualization approaches can be devised or improved to meet these challenges, with the promise of ultimately being adopted by medical experts. Visualization in Medicine and Life Sciences II follows the second international VMLS workshop, held in Bremerhaven, Germany, in July 2009. Internationally renowned experts from the visualization and driving application areas came together for this second workshop. The book presents peer-reviewed research and survey papers which document and discuss the progress made, explore new approaches to data visualization, and assess new challenges and research directions.

For some time, medicine has been an important driver for the development of data processing and visualization techniques. Improved technology offers the capacity to generate larger and more complex data sets related to imaging and simulation. This, in turn, creates the need for more effective visualization tools for medical practitioners to interpret and utilize data in meaningful ways. The first edition of Visualization in Medicine and Life Sciences (VMLS) emerged from a workshop convened to explore the significant data visualization challenges created by emerging technologies in the life sciences. The workshop and the book addressed questions of whether medical data visualization approaches can be devised or improved to meet these challenges, with the promise of ultimately being adopted by medical experts. Visualization in Medicine and Life Sciences II follows the second international VMLS workshop, held in Bremerhaven, Germany, in July 2009. Internationally renowned experts from the visualization and driving application areas came together for this second workshop. The book presents peer-reviewed research and survey papers which document and discuss the progress made, explore new approaches to data visualization, and assess new challenges and research directions.

Mathematical Visualization aims at an abstract framework for fundamen­ tal objects appearing in visualization and at the application of the manifold visualization techniques to problems in geometry, topology and numerical mathematics. The articles in this volume report on new research results in this field, on the development of software and educational material and on mathematical applications. The book grew out of the third international workshop "Visualization and Mathematics", which was held from May 22-25, 2002 in Berlin (Germany). The workshop was funded by the DFG-Sonderforschungsbereich 288 "Dif­ ferential Geometry and Quantum Physics" at Technische Universitat Berlin and supported by the Zuse Institute Berlin (ZIB) and the DFG research cen­ ter "Mathematics for Key Technologies" (FZT 86) in Berlin. Five keynote lectures, eight invited presentations and several contributed talks created a stimulating atmosphere with many scientific discussions. The themes of this book cover important recent developments in the fol­ lowing fields: - Geometry and Combinatorics of Meshes - Discrete Vector Fields and Topology - Geometric Modelling - Image Based Visualization - Software Environments and Applications - Education and Communication We hope that the research articles of this book will stimulate the readers'' own work and will further strenghten the development of the field of Mathe­ matical Visualization. VI Preface We appreciate the thorough work of the authors and reviewers on each of the individual articles, and we thank you all.

Visualization research aims to provide insight into large, complicated data sets and the phenomena behind them. While there are di?erent methods of reaching this goal, topological methods stand out for their solid mathem- ical foundation, which guides the algorithmic analysis and its presentation. Topology-based methods in visualization have been around since the beg- ning of visualization as a scienti?c discipline, but they initially played only a minor role. In recent years,interest in topology-basedvisualization has grown andsigni?cantinnovationhasledto newconceptsandsuccessfulapplications. The latest trends adapt basic topological concepts to precisely express user interests in topological properties of the data. This book is the outcome of the second workshop on Topological Methods in Visualization, which was held March 4–6, 2007 in Kloster Nimbschen near Leipzig,Germany.Theworkshopbroughttogethermorethan40international researchers to present and discuss the state of the art and new trends in the ?eld of topology-based visualization. Two inspiring invited talks by George Haller, MIT, and Nelson Max, LLNL, were accompanied by 14 presentations by participants and two panel discussions on current and future trends in visualization research. This book contains thirteen research papers that have been peer-reviewed in a two-stage review process. In the ?rst phase, submitted papers where peer-reviewed by the international program committee. After the workshop accepted papers went through a revision and a second review process taking into account comments from the ?rst round and discussions at the workshop. Abouthalfthepapersconcerntopology-basedanalysisandvisualizationof ?uid?owsimulations;twopapersconcernmoregeneraltopologicalalgorithms, while theremaining papers discuss topology-based visualization methods in application areas like biology, medical imaging and electromagnetism.