Volume Modelling

This chapter will present an overview of the emerging research area of volume modelling. To date, there has been considerable research on the development of techniques for visualising volume data, but very little on modelling volume data. This is somewhat surprising since the potential benefits of volume models are tremendous. This situation is somewhat explained by the fact that volume data is relatively new and researchers have spent their efforts in figuring out ways to " look " at the data and have not been able to afford the resources needed to develop methods for modelling volume data. In addition to providing a means for visualising volume data, some of the benefits of a volume model are the generation of hierarchical and multi-resolution models which are extremely useful for the efficient analysis, visualisation, transmission, and archiving of volume data. In addition, the volume model can serve as the mathematical foundation for subsequent engineering simulations and analysis required for design and fabrication. While interest is steadily growing, the area of volume modelling is still in its infant stages and currently there are few techniques and little expertise available. In the next section, we give some precise definitions and describe the scope of our vision of volume modelling and generally make an appeal for its development. It is important to realise that practically all visualisation tools require some type of volume model for their application. Sometimes the model is so obvious that we may fail to notice it. (For example, the linear interpolation into voxels used by the standard marching cubes algorithm.) Many of the relatively simple modelling techniques used for the more popular visualisation tools of today do not apply or scale up to the data sets currently of interest. These data sets require much more sophisticated modelling techniques. Another barrier to analysing volume data sets is the fact that they are often large, and because of this, they are normally associated with complex and complicated phenomena. Multi-resolution models can be helpful in this regard. Wavelet models (and the concepts related to wavelet models) have traditionally been targeted at compression, but they can also form the basis for analysis tools that allow for removal of clutter and detail and assist in efficient browsing and zooming. In the third section of this chapter, we will discuss some research issues in representing volume models. We think that it would benefit our readers if …