Integral Volume

The integral image was introduced to the image processing community by Viola and Jones[3] similar to summed area tables in texture mapping[1], it gives a fast way to calculate block features in an image.
We, along with others[4], have taken this into the temporal domain, in a video stream one can imagine the images stacked one behind the other in temporal order. To create a space time integral any point (x,y,z) now contains the sum of all points to its upper left plus those before it as shown in figure 1. Now to calculate a block summation four subtractions and three additions are required, regardless of the block size.

figure 1 - The value of the integral volume point (x,y,z) is the sum of all the points in the current and previous frames to the upper left of itself