4.5 Classification

Classification aims to group voxels of a same substance, based on some similarity characteristic. Levoy's classification method uses the density of voxels, to categorize them belonging to a same substance.

In this step, each voxel is assigned an opacity, which is the light attenuation. Opacity describes how transparent a particular voxel is. The opacity of a voxel is assigned according to its density. Therefore, voxels of similar density end up with similar opacity values. Since a specific surface is defined by a density value, classification makes it possible to select a surface of interest, which will be displayed in the rendering process. Opacity values are between zero and one : voxels that are given full opacity of one are completely opaque and cannot been through; voxels of opacity zero are transparent and have no influence in the rendering of the final picture.

Correctly selecting the density, $\rho_v$, corresponding to the surface of interest located inside the volume is difficult. For example, selecting a density, $\rho_v$, that well defines the skin surface of a CT-scanned human head is a matter of trial-and-error. Once the density $\rho_v$ of a surface is found, the classification process assigns an opacity close to one for all voxels whose density is close to $\rho_v$. It is important to give such voxels a density just below but close of one to avoid aliasing artifacts.

Levoy's classification equations produce this effect by assigning opacities close to one (inversely proportional to the magnitude of the local gradient vector $\vert\nabla \rho(\vec x)\vert$) to voxels inside a transition region of voxel thickness $r$. The opacity $\alpha(\vec x)$ at a given sample point $\vec x$, is calculated according to :

$$\alpha(\vec x) = \alpha_v \left\{ \begin{array}{ll} 1 & \mbox... ...ho(\vec x)\vert $} \\ 0 & \mbox{otherwise} \end{array}\right.$$

This classification method can be slightly modified to permit the superimposition of multiple semi-transparent surfaces by defining a table of opacity values. An implementation of this rendering is described in section 4.4.