Nonetheless , post-classification is useful under certain circumstances; in particular, because it may be used as a basic segmentation technique.

should be

Nonetheless , pre-classification is useful under certain
circumstances; in particular, because it may be used as a basic
segmentation technique.

T(s_f)-T(s_b)

should be

T(s_b)-T(s_f)

However, non-linear features of transfer functions may considerably increase the sampling rate required for a correct evaluation of the volume rendering integral as the Nyquist frequency of the fields $\ctilde\bigl(s(\mathbf{x})\bigr)$ and $\tau\bigl(s(\mathbf{x})\bigr)$ for the sampling along the viewing ray is approximately the product of the Nyquist frequencies of the scalar field $s(\mathbf{x})$ and the maximum of the Nyquist frequencies of the two transfer functions $\ctilde(s)$ and $\tau(s)$ (or of the product $\cwotilde(s)\tau(s)$).

should be

However, non-linear features of transfer functions may considerably
increase the sampling rate required for a correct evaluation of the
volume rendering integral as an approximation
for an appropriate sampling frequency of the fields
$\ctilde\bigl(s(\mathbf{x})\bigr)$ and $\tau\bigl(s(\mathbf{x})\bigr)$
for the sampling along the viewing ray is
(apart from small constants) given by the product of the
Nyquist frequencies of the scalar field $s(\mathbf{x})$ and the
maximum of the Nyquist frequencies of the two transfer functions
$\ctilde(s)$ and $\tau(s)$ (or of the product
$\cwotilde(s)\tau(s)$).

(For details see forthcoming PhD thesis of Martin Kraus.)

Klaus Engel, 23. Apr 2001