Ray casting, described in Section 3.2, work from the image space to the object space (volume dataset), thus it is called a backward projection method. Another way of achieving volume rendering is to try to reconstruct the image from the object space to the image space, by computing for every element in the dataset its contribution to the image. Several such techniques have been developed [45,46,12]. The technique described here was developed by Lee Westover at the University of North Carolina at Chapel Hill [12].
In splatting, the final image is generated by computing for each voxel in the volume dataset its contribution to the final image. The algorithm works by virtually ``throwing'' the voxels onto the image plane. In this process every voxel in the object space leaves a footprint in the image space that will represent the object. The computation is processed by virtually ``peeling'' the object space in slices, and by accumulating the result in the image plane.
Formally the process consists of reconstructing the signal that represents the original object, sampling it and computing the image from the resampled signal. This reconstruction is done in steps, one voxel at a time. For each voxel, the algorithm calculates its contribution to the final image, its footprint, and then it accumulates that footprint in the image plane buffer. The computation can take place in back-to-front or front-to-back order. The footprint is in fact the reconstruction kernel and its computation is key to the accuracy of the algorithm.
In his paper, Westover [11] proves that the
footprint does not depend on the spatial position of voxel 
itself, thus he is able
to use a lookup table to approximate the footprint. During
computation the algorithm just need to multiply the footprint with
the color of the voxel, instead of having to perform a more
expensive operation.