A large number of applications in medical imaging require geometric models of the surface of various anatomical structures. Although recent direct volume rendering techniques provide high visual quality  and speed, using cost-effective special purpose hardware , surfaces are very effective for showing the spatial relationship between different structures. (Radio-therapy planning visualization provides an excellent bio-medical example of this .) Surface extraction is necessary when surfaces (meshes) are used for further analysis and processing, independently of visualization. Such processes include finite element analysis (Chapter 19) and registration (see Chapter 8). Several methods have recently been developed to help guide surgery using computer-generated displays of anatomical structures registered with live imagery of the patient. Such methods often use surface models for registration and rendering [4-6].
This chapter is cross-disciplinary. One of its goals is to illustrate the flexibility in choosing a surface representation. Surface representations are reviewed in Section 6.2 and illustrated with various examples. Another goal is to describe recent techniques that have been developed for surface extraction from medical images in Sections 6.3, 6.4, and 6.5 and to provide references for further reading.
We also study some methods for optimizing surface models in Section 6.6, such as smoothing (fairing) and simplification. We introduce a few algorithms that operate on a surface and accompany them with real-world examples in Section 6.7.
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