Geometry of Digital Spaces (Applied and Numerical Harmonic Analysis) - Hardcover

Herman, Gabor T.

Hardcover

ISBN 10: 0817638970 ISBN 13: 9780817638979

Publisher: Birkhäuser, 1998

Synopsis

"La narraci6n literaria es la evocaci6n de las nostalgias. " ("Literary narration is the evocation of nostalgia. ") G. G. Marquez, interview in Puerta del Sol, VII, 4, 1996. A Personal Prehistory In 1972 I started cooperating with members of the Biodynamics Research Unit at the Mayo Clinic in Rochester, Minnesota, which was under the direction of Earl H. Wood. At that time, their ambitious (and eventually realized) dream was to build the Dynamic Spatial Reconstructor (DSR), a device capable of collecting data regarding the attenuation of X-rays through the human body fast enough for stop-action imaging the full extent of the beating heart inside the thorax. Such a device can be applied to study the dynamic processes of cardiopulmonary physiology, in a manner similar to the application of an ordinary cr (computerized tomography) scanner to observing stationary anatomy. The standard method of displaying the information produced by a cr scanner consists of showing two-dimensional images, corresponding to maps of the X-ray attenuation coefficient in slices through the body. (Since different tissue types attenuate X-rays differently, such maps provide a good visualization of what is in the body in those slices; bone - which attenuates X-rays a lot - appears white, air appears black, tumors typically appear less dark than the surrounding healthy tissue, etc. ) However, it seemed to me that this display mode would not be appropriate for the DSR.

About this title

Review

"There are only a few books that address the processing of digital spaces...in a mathematically rigorous manner: this book is one of them... A valuable contribution to formally study and present modern digital data processing methods."

–Mathematical Reviews

Synopsis

Concerned with the mathematical theory of surfaces, objects and their boundaries in discrete spaces, this text provides a self-contained and mathematically precise introduction to the field. It is application-oriented and presents problems of visualization and analysis of multidimensional data sets. The primary areas of mathematics used are graph theory and topology.

Edition details

• Publisher: Birkhäuser
• Publication date: 1998
• Language: English
• ISBN 10: 0817638970
• ISBN 13: 9780817638979
• Binding: Hardcover
• Number of pages: 226