Efficient visibility-driven medical image visualisation via adaptive binned visibility histogram.

'Visibility' is a fundamental optical property that represents the observable, by users, proportion of the voxels in a volume during interactive volume rendering. The manipulation of this 'visibility' improves the volume rendering processes; for instance by ensuring the visibility of regions of interest (ROIs) or by guiding the identification of an optimal rendering view-point. The construction of visibility histograms (VHs), which represent the distribution of all the visibility of all voxels in the rendered volume, enables users to explore the volume with real-time feedback about occlusion patterns among spatially related structures during volume rendering manipulations. Volume rendered medical images have been a primary beneficiary of VH given the need to ensure that specific ROIs are visible relative to the surrounding structures, e.g. the visualisation of tumours that may otherwise be occluded by neighbouring structures. VH construction and its subsequent manipulations, however, are computationally expensive due to the histogram binning of the visibilities. This limits the real-time application of VH to medical images that have large intensity ranges and volume dimensions and require a large number of histogram bins. In this study, we introduce an efficient adaptive binned visibility histogram (AB-VH) in which a smaller number of histogram bins are used to represent the visibility distribution of the full VH. We adaptively bin medical images by using a cluster analysis algorithm that groups the voxels according to their intensity similarities into a smaller subset of bins while preserving the distribution of the intensity range of the original images. We increase efficiency by exploiting the parallel computation and multiple render targets (MRT) extension of the modern graphical processing units (GPUs) and this enables efficient computation of the histogram. We show the application of our method to single-modality computed tomography (CT), magnetic resonance (MR) imaging and multi-modality positron emission tomography-CT (PET-CT). In our experiments, the AB-VH markedly improved the computational efficiency for the VH construction and thus improved the subsequent VH-driven volume manipulations. This efficiency was achieved without major degradation in the VH visually and numerical differences between the AB-VH and its full-bin counterpart. We applied several variants of the K-means clustering algorithm with varying Ks (the number of clusters) and found that higher values of K resulted in better performance at a lower computational gain. The AB-VH also had an improved performance when compared to the conventional method of down-sampling of the histogram bins (equal binning) for volume rendering visualisation.