Improved perspective visibility ordering for object-order volume rendering

Finding a correct a priori back-to-front (BTF) visibility ordering for the perspective projection of the voxels of a rectangular volume poses interesting problems. The BTF ordering presented by Frieder et al. [6] and the permuted BTF presented by Westover [14] are correct for parallel projection but not for perspective projection [12]. Swan presented a constructive proof for the correctness of the perspective BTF (PBTF) ordering [12]. This was a significant improvement on the existing orderings. However, his proof assumes that voxel projections are not larger than a pixel, i.e. voxel projections do not overlap in screen space. Very often the voxel projections do overlap, e.g. with splatting algorithms. In these cases, the PBTF ordering results in highly visible and characteristic rendering artefacts.