Chapter 2 Volume Rendering

Our display screens are composed of a two-dimensional array of pixels each representing a unit area. A volume is a three-dimensional array of cubic elements, each representing a unit of space. Individual elements of a three-dimensional space are called volume elements or voxels. A number associated with each point in a volume is called the value at that point. The collection of all these values is called a scalar field on the volume. The set of all points in the volumewith a given scalar value is called a level surface. Volume rendering is the process of displaying scalar fields [1]. It is a method for visualizing a three dimensional data set. The interior information about a data set is projected to a display screen using the volume rendering methods. Along the ray path from each screen pixel, interior data values are examined and encoded for display. How the data are encoded for display depends on the application. Seismic data, for example, is often examined to find the maximum and minimum values along each ray. The values can then be color coded to give information about the width of the interval and the minimum value. In medical applications, the data values are opacity factors in the range from 0 to 1 for the tissue and bone layers. Bone layers are completely opaque, while tissue is somewhat transparent [2, 3]. Voxels represent various physical characteristics, such as density, temperature, velocity, and pressure. Other measurements, such as area, and volume, can be extracted from the volume datasets [4, 5]. Applications of volume visualization are medical imaging (e.g., computed tomography, magnetic resonance imaging, ultrasonography), biology (e.g., confocal microscopy), geophysics (e.g., seismic measurements from oil and gas exploration), industry (e.g., finite element models), molecular systems (e.g., electron density maps), meteorology (e.g., stormy (prediction), computational fluid dynamics (e.g., water flow), computational chemistry (e.g., new materials), digital signal and image processing (e.g., CSG ) [6, 7]. Numerical simulations and sampling devices such as magnetic resonance imaging (MRI), computed tomography (CT), positron emission tomography (PET), ultrasonic imaging, confocal microscopy, supercomputer simulations, geometric models, laser scanners, depth images estimated by stereo disparity, satellite imaging, and sonar are sources of large 3D datasets.

3D scientific data can be generated in a variety of disciplines by using sampling methods [8]. Volumetric data obtained from biomedical scanners typically come in the form of 2D slices of a regular, Cartesian grid, sometimes varying in one or more major directions. The typical output of supercomputer and Finite Element Method (FEM) simulations is irregular grids. The raw output of an ultrasound scan is a sequence of arbitrarily oriented, fan-shaped slices, which constitute partially structured point samples [9]. A sequence of 2D slices obtained from these scanners is reconstructed into a 3D volume model. Imaging machines have a resolution of millimeters scale so that many details important for scientific purposes can be recorded [4].

It is often necessary to view the dataset from continuously changing positions to better understand the data being visualized [4]. The real-time interaction is the most essential requirement and preferred even if it is rendered in a somewhat less realistic way [10, 11]. A real-time rendering system is important for the following reasons [4]:

·   to visualize rapidly changing datasets,

·   for real-time exploration of 3D datasets, (e.g. virtual reality)

·   >for interactive manipulation of visualization parameters, (e.g. classification)

·   for interactive volume graphics.

Rendering and processing does not depend on the object’s complexity or type, it depends only on volume resolution. The dataset resolutions are generally anywhere from 128³ to 1024³ and may be non-symmetric (i.e. 1024 x 1024 x 512).