The identification of important structures from volume data is a challenging problem in information visualization due to the complexity and amount of detail found in volume data sets. In particular, medical imaging devices generate scans which contain a significant amount of important anatomical structures, some of which are hidden, occluded or otherwise difficult to highlight. Conventional density and gradient-based classification methods fail to uncover such structures, thereby creating the necessity for more elaborate visualization methods and the involvement of multiple visual criteria in order to generate quality representations of the volume data. We propose a volume visualization approach which extends the conventional rendering pipeline by incorporating visibility-based quality criteria into the color and opacity mapping process. Our method consists in using two stacked transfer functions which handle visual mappings: one based on the density domain of the data set, and the other on a custom metric which quantifies the visibility of volumetric structures. We show that this arrangement allows the generation of improved representations of meaningful hidden structures from medical CT data, while constituting a reliable means of identifying volumetric details not representable using traditional approaches.