An analytical ray casting of volume data

When volume data is visualized by the ray casting method, the color value of each pixel in the image is obtained by composing the color contributions of the sample points that lie on the ray cast from the pixel point. In most ray tracing methods, including M. Levoy's (1988; 1990) classical method, the color composition is formulated as a summation of the color contributions of the discrete sample points. However the more precise color composition is formulated as differential equations over the color contributions of the continuous sample points. The discrete formulation is used, because analytical solutions to the continuous formulation are hard to find. However we have discovered a semi-analytical solution to the continuous formulation of a typical ray tracing of volume data. We have applied both Levoy's method and ours to the same set of data, and compared the visual quality of both results. The comparison shows that our method produces a more fine grained visualization of volume data.