Surface Interpolation with Radial Basis Functions for Medical Imaging

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Surface Interpolation with Radial Basis Functions
for Medical Imaging

• Jonathan C. Carr et al
• IEEE Trans. on Medical Imaging, Vol. 16, No. 1,
  Feb. 1997
• Byeong-Seon Jeong in CGVR Lab.

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Goal

• Design of cranial implants for the repair of
  defects

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System Overview
Obtain CT data
Extract depth-maps
Interpolate depth-maps
Mill
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RBF Approximation 1
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RBF Approximation 2
Conditions
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RBF Approximation 3
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RBF Approximation 4
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RBF Approximation 5

• In this paper, 2D thin-plate spline

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Fitted Surface 1

• CT data

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Fitted Surface 2

• Depth-map fitted surface

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Thin-plate spline 1

• C1 continuity
• Minimize the energy functional

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Thin-plate spline 2

• Original thin-plate spline

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Thin-plate spline 3

• Thin-plate spline vs Linear

max error 0.60 mm
max error 0.56 mm
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Thin-plate spline 4

• Natural choice for cranial implant design

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Thin-plate spline 5

• Smoothness

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Evaluation
Fig. 8
Fig. 11