Errata

(Pre-print only !!!) Last sentence, paragraph 3.2, Pre- and Post-Classification:
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.


Section 3.5, formula 8:
T(s_f)-T(s_b)

should be

T(s_b)-T(s_f)


End of Section 3.3:
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