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Three-dimensional (3D) rendering of biomedical volumes has become essential for faster comprehension of anatomy, better communication with patients, surgical planning, and training. However, depending on the algorithm, level of detail, volume size, and transfer function, rendering can be quite slow. A multi-target optimization method – voxelization – can be applied to biomedical volume rendering enhancement for empty space skipping, optimized maximum intensity calculation, and advanced Woodcock tracking. Empirical results indicate that the voxelization technique can increase the performance of Direct Volume Rendering (DVR) by up to ten times, Monte Carlo Path Tracing (MCPT) by five times, and Maximum Intensity Projection (MIP) by two times of the original velocity. In this study, we investigate the influence of a 3D fractal dimension of the rendered volumes to the rendering speed and the optimal super voxel size, used in voxelization process, to guarantee the best performance of DVR, MCPT, and MIP, using voxelization. 3D fractal dimensions are calculated for five common transfer functions applied to the Cone-Beam Computed Tomography (CBCT) scans of exotic animals and human extremities (postmortem). Preliminary findings suggest that volumes rendered with similar transfer functions have comparable 3D fractal dimension and, moreover, there is a statistically significant relationship between the DVR and MCPT speed and the 3D fractal dimension. Furthermore, the structures with higher 3D fractal dimension require the smaller super voxel sizes for empty space skipping, meanwhile, optimized maximum intensity calculation and advanced Woodcock tracking are 3D fractal dimension independent. The research encourages the further exploration of the structural complexity to 3D rendering optimization for biomedical volumes.
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