Constrained distance transforms for spatial atlas registration

BMC Bioinformatics

Table 1 Radial basis functions and their form

Radial basis function	Form
Thin plate spline	ϕ(r)=r ² logr
Multiquadric	\( \phi (r) = (r^{2} + c^{2})^{\frac {1}{2}}\)
Inverse multiquadric	\(\phi (r) = (r^{2} + c^{2})^{-\frac {1}{2}}\)
Wendland’s functions	\(\phi (r) = \left \{ \begin {array}{r@{\quad :\quad }l} p(r) & 0 \leq r \leq 1 \\ 0 & r > 1 \end {array} \right. \)

Outline form of radial basis functions based on the thin plate spline, multiquadric, inverse multiquadric and Wendland’s functions. In Wendland’s functions p(r) is a univariate polynomial.

ISSN: 1471-2105