23 June 1993 Future directions in surface fitting
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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.'
© (1993) COPYRIGHT Society of Photo-Optical Instrumentation Engineers (SPIE). Downloading of the abstract is permitted for personal use only.
Fred L. Bookstein, Fred L. Bookstein, } "Future directions in surface fitting", Proc. SPIE 2035, Mathematical Methods in Medical Imaging II, (23 June 1993); doi: 10.1117/12.146609; https://doi.org/10.1117/12.146609

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