Introduction

Volume data are three-dimensional (3D) entities that may have information inside them, may not consist of surfaces and edges, or may be too voluminous to be represented geometrically. Volume visualization is a method of extracting meaningful information from volumetric data using interactive graphics and imaging. It is concerned with volume data representation, modeling, manipulation, and rendering [30,32,33]. Volume data are obtained by sampling, simulation, or modeling techniques. For example, a sequence of 2D slices obtained from magnetic resonance imaging (MRI) or computed tomography (CT) is 3D reconstructed into a volume model and visualized for diagnostic purposes or for planning of treatment or surgery. In many computational fields, as in fluid dynamics, the results of simulation typically running on a supercomputer are often visualized as volume data for analysis and verification. In addition, many traditional geometric computer graphics applications, such as CAD and simulation, as well as applications mixing geometric objects with medical data (see Fig. 1), have exploited the advantages of volume techniques called volume graphics for modeling, manipulation, and visualization [31].

Over the years many techniques have been developed to visualize 3D data. Since methods for displaying geometric primitives were already well established, most of the early methods involved approximating a surface contained within the data using geometric primitives. When volumetric data are visualized using a surface rendering technique, a dimension of information is essentially lost. In response to this, volume rendering techniques were developed in an attempt to capture the entire 3D data in a single 2D image. Volume rendering conveys more information than surface rendering images, but at the cost of increased algorithm complexity, and consequently increased rendering times. To improve interactivity in volume rendering, many optimization methods as well as several special-purpose volume rendering machines have been developed.

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