Derivative reconstruction

It is not dream - it is not, I fear, even madness - for too much has already happened to give me these merciful doubts. H. P. Lovecraft, ``The Hound''

Only a few volume visualization algorithms need just the function itself. More often, derivative information up to a certain degree is also needed.

The gradient, which is the first derivative of the function, can be interpreted as a normal to a surface of equal values (an iso-surface) passing through the point of interest. Consequently, the gradient can be used to shade surfaces, since most lighting models (for instance Gouraud shading [17] or Phong shading [48]) make use of it or it can be used for classification in ray casting techniques [26]. Möller et al. even concede gradient reconstruction having a greater impact on image quality than function reconstruction itself [41].

Second derivative information (curvature properties) has been widely used for surface analysis and design [1,11,54] and to enhance the visualization especially of multiple semi-transparent surfaces in three dimensions [20,21,22].