. Author manuscript; available in PMC: 2009 Jun 1.

Published in final edited form as: Med Image Anal. 2009 Feb 5;13(3):432–444. doi: 10.1016/j.media.2009.01.004

Table 1.

Directional Functions

Function

Signal

ODF

dlVP

B sin²^k(θ_i)

B cos²^k(θ_i)

Watson

C⁻¹ exp(−k cos² θ_i)

C^{- 1} exp (- \frac{k}{2} {sin}^{2} θ_{i})

vMF

A exp(k sin θ_i)

A exp(k cos θ_i)

where C = ₁F₁(0.5; 1.5; k), $A = \frac{k}{4 π sinh (k)}$ and B are normalization constants.