4 October 2000 Navigating solid medical images by pencils of sectioning planes
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Beyond their involvement in ordinary surface rendering, the boundaries of organs in medical images have differential properties that make them quite useful for quantitative understanding. In particular, their geometry affords a framework for navigating the original solid, representing its R3 contents quite flexibility as multiple pseudovolumes R2 x T, where T is ar eal-valued parameter standing for screen time. A navigation is a smoothly parameterized series of image sections characterized by normal direction, centerpoint, scale and orientation. Such filmstrips represent a radical generalization of conventional medical image dynamics. The lances encountered in these navigations can be represented by constructs from classic differential geometry. Sequences of plane sections can be formalized as continuous pencils of planes, sets of cardinality (infinity) 1 that are sometimes explicitly characterized by a real-value parameter and sometimes defined implicitly as the intersection (curve of common elements) of a pair of bundles of (infinity) 2 planes. An example of the first type of navigation is the pencil of planes through the tangent line at one point of a curve; of the second type, the cone of planes through a point tangent to a surface. The further enhancements of centering, orienting, and rescaling in the medical context are intended to leave landmark points or boundary intersections invariant on the screen. Edgewarp, a publicly available software package, allows free play with pencils of planes like these as they section one single enormous medical data resource, the Visible Human data sets from the National Library of Medicine. This paper argues the relative merits of such visualizations over conventional surface-rendered flybys for understanding and communication of associated anatomical knowledge.
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Fred L. Bookstein, Brian D. Athey, William D. K. Green, Arthur W. Wetzel, "Navigating solid medical images by pencils of sectioning planes", Proc. SPIE 4121, Mathematical Modeling, Estimation, and Imaging, (4 October 2000); doi: 10.1117/12.402432; https://doi.org/10.1117/12.402432

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