The MLI representation is designed to make the process of reconstructing a
target image with transparencies and colors chosen by the user simple
and efficient. The color of each pixel (x, y) is constructed from
the sequence 
by blending the appropriate intensity of each
structure's color in proportions dictated by its transparency.
Simultaneously, an image-map is constructed that records the frontmost
visible structure at each pixel. This allows picking to be
accomplished with a simple lookup in the map. The procedure for
constructing the image and the image-map from an MLI R is given in
Figure 2.
Figure 2: Reconstructing the image and image map from MLI R. We assume that ``+'' and ``*'' operate component-wise on RGB colors.
The procedure implements blended transparency according to the standard model:
where 
is the opacity of the 
structure
from the back, of n total structures, 
is its RGB
color, and (R(i), G(i), B(i)) is the color of the i back-most
structures. Assuming a black background, R(0) = G(0) = B(0) = 0.
Unrolling one of the recurrences, we see that the color can be
calculated from front to back if a transmission coefficient, equal to
after k structures have been
processed, is maintained:
This front-to-back strategy also allows the calculation of the sum to be truncated when the transmission coefficient becomes small, which happens when the frontmost structures obscure structures behind them. This optimization is similar to early ray termination, which has been used in ray-casting algorithms for volume rendering [15].