Future directions in surface fitting

Fred L. Bookstein

doi:10.1117/12.146609

23 June 1993 Future directions in surface fitting

Fred L. Bookstein

Proceedings Volume 2035, Mathematical Methods in Medical Imaging II; (1993) https://doi.org/10.1117/12.146609
Event: SPIE's 1993 International Symposium on Optics, Imaging, and Instrumentation, 1993, San Diego, CA, United States

Abstract

Approaches to surface fitting can be classified according to the nature of the raw data (visible surfaces or extracted surfaces, variously crossclassified by aspects of the case or of the conditions of observation), context of measurement (are queries qualitative or quantitative? are we in the operating room or producing an Atlas of normal variation?), geometrical model (topology, position, derivatives, statistics), biometrical model (landmarks, curves, or neither), and criterion of fit (a-priori parameters, geometric or other 'distances,' or a more general 'equilibrium'). After reviewing the current approaches under these rubrics I conclude that the topic of surface fitting badly needs a shared mathematical formalism, and I modestly suggest a composite that might work: a combination of the thin-plate spline with two separate diffusion algebras, Pizer's for features of single grey-scale images and Grenander's for deformations as 'patterns.'

Citation Download Citation

Fred L. Bookstein "Future directions in surface fitting", Proc. SPIE 2035, Mathematical Methods in Medical Imaging II, (23 June 1993); https://doi.org/10.1117/12.146609

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KEYWORDS

Diffusion

Biometrics

Algorithm development

Data modeling

Medical imaging

Mathematical modeling

Statistical modeling

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