Book chapters

1. Virtual cranio-maxillofacial surgery planning with stereo graphics and haptics
   Author: Ingela Nyström, Pontus Olsson, Johan Nysjö, Fredrik Nysjö, Filip Malmberg, Stefan Seipel, Jan-Michaél Hirsch(1), Ingrid B. Carlbom
   (1) Dept. of Surgical Sciences, Oral and Maxillofacial Surgery, Uppsala University, Uppsala, Sweden
   Book: Computer-Assisted Musculoskeletal Surgery -Thinking and Executing in 3D, pages 29-42
   Editors: Lucas E. Ritacco, Federico E. Milano, Edmund Chao
   Publisher: Springer Verlag
   Abstract: Cranio-maxillofacial surgery to restore normal skeletal anatomy in patients with serious facial conditions is both complex and time consuming. There is, however, ample evidence that careful pre-operative planning leads to a better outcome with a higher degree of function and reduced morbidity and at the same time reduced time in the operating room. We are building a cranio-maxillofacial surgery planning system that, based on patient specific three-dimensional CT data, allows the surgeon to plan the surgical procedure without the help of a technician. Using a combination of stereo visualization with six degrees-of-freedom, high-fidelity haptic feedback, the system allows the surgeon to test alternative surgical solutions, move bone fragments, and design patient-specific implants and plates. Our goal is a system where the surgeon, after minimal training, can plan a complex procedure in less than an hour. Preliminary tests indicate that this goal is achievable.

2. Image segmentation, processing and analysis in microscopy and life science
   Author: Carolina Wählby
   Book: Mathematical Models in Biology: Bringing Mathematics to Life, 16 pages
   Editors: Valeria Zazzu, Maria Brigida Ferraro, Mario R. Guarracino
   Publisher: Springer International Publishing
   Abstract: Microscopes have been used for more than 400 years to understand biological and biomedical processes by visual observation. Science is the art of observing, but science also requires measuring, or quantifying, what is observed. Research based on microscopy image data therefore calls for methods for quantitative, unbiased, and reproducible extraction of meaningful measurements describing what is observed. Digital image processing and analysis is based on mathematical models of the information contained in image data, and allows for automated extraction of quantitative measurements. Automated methods are reproducible and, if applied consistently and accurately across experiments with positive as well as negative controls, also unbiased. Digital image processing is further motivated by the development of scanning microscopes and digital cameras that can capture image data in multiple spatial-, time-, and spectral-dimensions, making visual assessment cumbersome or even impossible due to the complexity and size of the collected data. The process of analyzing a digital image is usually divided into several steps, where the objects of interest are first identified, or ``segmented'', followed by extraction of measurements and statistical analysis. This chapter starts from the basics of describing images as matrices of pixel intensities. Emphasis is thereafter put on image segmentation, which is often the most crucial and complicated step. A number of common mathematical models used in digital image processing of microscopy images from biomedical experiments are presented, followed by a brief description of large-scale image-based biomedical screening.

3. Matematiska rum. (The Swedish title means both ``Mathematical Spaces'' and ``Mathematical Rooms''.)
   Author: Christer O. Kiselman
   Book: Sundelöfs Societet, pages 25-42
   Editors: Mats Almgren, Ulla Birgegård, Kristina Glimelius
   Publisher: Royal Society of Sciences in Uppsala
   Abstract: This essay starts by commenting on mathematical terms in several languages, especially those that concern mathematical spaces. It discusses successful mathematical models based on real numbers and then proceeds to discrete models, which have quite different properties. Knotted carpets and mosaics are actually predecessors of digital geometry. With the development of computers, discrete models have become even more important. Finally, some warnings of a more personal character are issued.