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Biennial International Conference on Information Processing in Medical Imaging

IPMI 1997: Information Processing in Medical Imaging pp 15–28Cite as

Quadratic variation of deformations

Part of the Lecture Notes in Computer Science book series (LNCS,volume 1230)

Abstract

Hitherto no constitutive formalism of deformations provides a parameterization for the visually obvious features of their transformation grids. This paper notes a property of the thin-plate spline that one may exploit to this end. The bending energy that is minimized by the spline, usually expressed in matrix form, is also the double integral of the output of a nonlinear differential operator, the quadratic variation (sum of squared second partial derivatives of displacement), over the whole picture plane. Displaying this integrand as a scalar field over the medical image or template may prove a helpful guide to the interesting regions of a deformation, and the peaks of this field localize and orient a promising set of features for simplistically parameterized deformations that approximate the original.

Keywords

  • Corpus Callosum
  • Displacement Field
  • Quadratic Variation
  • Shape Space
  • Picture Plane

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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  • DOI: 10.1007/3-540-63046-5_2
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  1. University of Michigan, 48109, Ann Arbor, Michigan, USA

    Fred L. Bookstein

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  1. Fred L. Bookstein
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    © 1997 Springer-Verlag Berlin Heidelberg

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    Bookstein, F.L. (1997). Quadratic variation of deformations. In: Duncan, J., Gindi, G. (eds) Information Processing in Medical Imaging. IPMI 1997. Lecture Notes in Computer Science, vol 1230. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-63046-5_2

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    • DOI: https://doi.org/10.1007/3-540-63046-5_2

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