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Proceedings Paper

Spline-based approach for averaging three-dimensional curves and surfaces
Author(s): Court B. Cutting; Fred L. Bookstein; Betsy Haddad; David Dean; David Kim
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Paper Abstract

Our topic is the construction of a detailed parametric average of three-dimensional surface form from a sample of specimens labelled in accordance with the features of that average. The labelling, which takes the conceptual and topological form of a smooth wire mesh, is a hybrid of biological information and linearized geometric schemes applying to a variety of geometric elements: points, curves, and surface patches. We do not 'smooth' the individual specimens of a sample; instead, we carefully restrict the scope of differentiations of empirical geometric elements so as to apply only after specimens have been averaged. Likewise, while we carry out all averaging in a single Cartesian coordinate system, we carefully 'unwarp' the largest- scale aspects of biological variability within this system before proceeding with the averaging of features at smaller scales. The resulting algorithms underlie useful visualizations of 'typical' or 'normative' anatomy and its variability for consideration in formal computations of statistical atypicality and optimization of interventions and should be crucial to future approaches to image analysis via the automatic deformation of geometrically extended templates.

Paper Details

Date Published: 23 June 1993
PDF: 16 pages
Proc. SPIE 2035, Mathematical Methods in Medical Imaging II, (23 June 1993); doi: 10.1117/12.146610
Show Author Affiliations
Court B. Cutting, New York Univ. (United States)
Fred L. Bookstein, Univ. of Michigan (United States)
Betsy Haddad, New York Univ. (United States)
David Dean, New York Univ. (United States)
David Kim, New York Univ. (United States)


Published in SPIE Proceedings Vol. 2035:
Mathematical Methods in Medical Imaging II
Joseph N. Wilson; David C. Wilson, Editor(s)

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