A collection of state-of-the-art presentations on visualization problems in mathematics, fundamental mathematical research in computer graphics, and software frameworks for the application of visualization to real-world problems. Contributions have been written by leading experts and peer-refereed by an international editorial team. The book grew out of the third international workshop ‘Visualization and Mathematics’, May 22-25, 2002 in Berlin. The variety of topics covered makes the book ideal for researcher, lecturers, and practitioners.

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.

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.

The assembled papers span the frontiers of VMLS, examining these topics:

* Feature Extraction

* Classification

* Volumes and Shapes

* Tensor Visualization

* Visualizing Genes, Proteins, and Molecules"

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 the remaining papers discuss topology-based visualization methods in application areas like biology, medical imaging and electromagnetism.

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.

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.

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 the remaining papers discuss topology-based visualization methods in application areas like biology, medical imaging and electromagnetism.

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.