Surface interpolation with radial basis functions for medical imaging

  • Carr J
  • Richard Fright W
  • Beatson R
  • 116


    Mendeley users who have this article in their library.
  • 256


    Citations of this article.


Radial basis functions are presented as a practical solution to the problem of interpolating incomplete surfaces derived from three-dimensional (3-D) medical graphics. The specific application considered is the design of cranial implants for the repair of defects, usually holes, in the skull. Radial basis functions impose few restrictions on the geometry of the interpolation centers and are suited to problems where the interpolation centers do not form a regular grid. However, their high computational requirements have previously limited their use to problems where the number of interpolation centers is small (< 300). Recently developed fast evaluation techniques have overcome these limitations and made radial basis interpolation a practical approach for larger data sets. In this paper radial basis functions are fitted to depth-maps of the skull's surface, obtained from X-ray computed tomography (CT) data using ray-tracing techniques. They are used to smoothly interpolate the surface of the skull across defect regions. The resulting mathematical description of the skull's surface can be evaluated at any desired resolution to be rendered on a graphics workstation or to generate instructions for operating a computer numerically controlled (CNC) mill.

Author-supplied keywords

  • CT imaging
  • Medical graphics
  • Radial basis function approximation
  • Surface interpolation
  • Titanium cranioplasty

Get free article suggestions today

Mendeley saves you time finding and organizing research

Sign up here
Already have an account ?Sign in

Find this document


  • Jonathan C. Carr

  • W. Richard Fright

  • Richard K. Beatson

Cite this document

Choose a citation style from the tabs below

Save time finding and organizing research with Mendeley

Sign up for free