Comparison of bicubic and Bezier polynomials for surface parameterization in volumetric images

Curvature-based surface features are well suited for use in multimodal medical image registration. The accuracy of such feature-based registration techniques is dependent upon the reliability of the feature computation. The computation of curvature features requires second derivative information that is best obtained from a parametric surface representation. We present a method of explicitly parameterizing surfaces from volumetric data. Surfaces are extracted, without a global thresholding, using active contour models. A Mong basis for each surface patch is estimated and used to transform the patch into local, or parametric, coordinates. Surface patches are fit to first a bicubic polynomial and second to a Bezier polynomial. The bicubic polynomial is fit in local coordinates using least squares solved by singular value decomposition. Bezier polynomial is fit using de Casteljau algorithm. We tested our method by reconstructing surfaces from the surface model and analytically computing Gaussian and mean curvatures. The model was tested on analytical and medical data and the results of both methods are compared.