Three-Dimensional Computed Tomography: Basic Concepts

Coordinates and Terminology

To understand how 3D images are generated in medical imaging, it is necessary first to identify

and outline four coordinate systems that relate to the CT scanner, the display device, the object, and the scene. These coordinate systems are illustrated in Figure 14-1 and include the scanner coordinate system, abc; the display coordinate system, rst; the object coordinate system, uvw; and the scene coordinate system, xyz. Each of these is defined in Table 14-1.

The most familiar system is the xyz, the scene or Cartesian coordinate system, as it is commonly called. In this system, the x-, y-, and z-axes are positioned at right angles (orthogonal) to one another. The width of an object is described by the x-axis, whereas the height is described by the y-axis. The z-axis, on the other hand, describes the dimension of depth and adds perspective realism to the image.

Use of the coordinate system allows description of an object by measuring distances from the point of intersection, or zero point. Distances can be positive or negative from the zero point, and images can be manipulated to rotate about the three axes. This rotation occurs in what is referred to as 3D space, and computer software helps the observer to view 3D space by displaying the front, back, top, and bottom of the object, providing a perspective from the observer’s vantage point. The technique is known as computer-aided visualization or 3D visualization, and the application of 3D visualization in medicine is called 3D medical imaging.

In medicine, 3D imaging uses a right-handed x, y, and z coordinate system (Russ, 2006; Udupa and Herman, 2000) because images are displayed on a computer screen. The x, y, and z coordinates define a space in which multidimensional data (a set of slices) are represented. This space is called the 3D space or scene space. The coordinate system helps to define the voxels (volume elements) in 3D space and allows use of the voxel information such as CT numbers or signal intensities in MRI to reconstruct 3D images.

Transforming Three-Dimensional Space

Generally, 3D space can be subjected to a series of common 3D transformations (Fig. 14-2). The radiologic technologist can manipulate scene, structure, geometric, and projective transformations and control image processing and image analysis. The technologist may transform 3D space in four ways (Table 14-2).

Modeling

The generation of a 3D object using computer software is called modeling. Modeling uses mathematics to describe physical properties of an object. According to one definition, modeling is “a computer simulation of a physical object in which length, width, and depth are real attributes. A model, with x, y, and z axes can be rotated for viewing from different angles” (Microsoft Press, 2002).

Several modeling techniques are used. In extrusion, one of the most common techniques, computer software is used to transform a 2D profile into a 3D object. In Figure 14-3, for example, a square is changed into a box. Extrusion can also generate a wireframe model from a 2D profile. The wireframe is made up of triangles or polygons often referred to as polygonal mesh. Wireframes were common during the early development of 3D display in medicine, and they are still being used today in other applications.

During the next step of modeling, a surface is added to the object by placing a layer of pixels (image mapping) and patterns (procedural textures) on top of the wireframes. The radiologic technologist can control various attributes of the surface, such as its texture.

Shading and Lighting

Shading and lighting also add realism to the 3D object. There are several shading algorithms, including wireframe shading, flat shading, Gouraud shading, and Phong shading. Each technique has its own set of advantages and disadvantages; however, a full discussion of shading algorithms is outside the scope of this chapter. The interested reader should refer to Russ (2006) for detailed descriptions of these algorithms.

Although shading determines the final appearance of surfaces of the 3D object, lighting helps us to see the shape and texture of the object (Fig. 14-4). Various lighting techniques are available to enhance the appearance of the 3D image; one of the most common is called ray tracing, which is described later in this chapter.

Rendering

Rendering is the final step in the process of generating a 3D object. It involves the creation of the simulated 3D image from data collected from the object space. More specifically, rendering is a computer program that converts the anatomical data collected from the patient into the 3D image seen on the computer screen. With most 3D software, the object must be rendered before the effects of lighting and other attributes can be observed. Rendering therefore adds lighting, texture, and color to the final 3D image.

Two types of 3D rendering algorithms are used in radiology: surface rendering and volume rendering. Surface rendering uses only contour data from the set of slices in 3D space, whereas volume rendering makes use of the entire data set in 3D space. Because it uses more information, volume rendering produces a better image than surface rendering, but it takes longer and requires a more powerful computer. Rendering is described subsequently.

Slice Imaging

Slice imaging is the simplest method of 3D imaging. In 1975 CT operators generated and displayed coronal and sagittal images from the CT axial data set. This technique is known as multiplanar reconstruction (MPR). In the past, other researchers such as Herman and Liu (1977), Marvilla (1978), and Rhodes et al (1980) also used slice imaging to produce coronal, sagittal, and paraxial images from the transaxial scans. Today, MPR is available on all CT and MRI scanners. However, MPR does not produce true 3D images but rather 2D images displayed on a flat computer screen (Dalrymple et al, 2005).

Projective Imaging

Projective imaging is the most popular 3D imaging approach. However, it still does not offer a true 3D mode; it produces a “2.5 D” mode of visualization, an effect somewhere between 2D and 3D. As Udupa and Herman (2000) explain:

The technique of projection is illustrated in Figure 14-5. The contiguous axial sections represent the volume image data. Information from this volume image data is projected at various angles into the 2D view space.

Volume Imaging

Volume imaging must not be confused with volume rendering. Volume rendering belongs to the class of projective imaging, whereas volume imaging produces a true 3D visualization mode. Volume imaging methods include holography, stereoscopic displays, anaglyphic methods, varifocal mirrors, synthalyzers, and rotating multidiode arrays (Jan, 2005). These methods are beyond the scope of this book.

Definition of Three-Dimensional Medical Imaging

Dr. Gabor Herman of the Medical Image Processing Group at the University of Pennsylvania defines 3D medical imaging as “the process that starts with a stack of sectional slices collected by some medical imaging device and results in computer-synthesized displays that facilitate the visualization of underlying spatial relationships” (Herman, 1993). Additionally, Udupa and Herman (2000) emphasize that the term 3D imaging can also refer to the four categories of 3D operations: preprocessing, visualization, manipulation, and analysis.

Four steps are needed to create 3D images (see Fig. 14-6):

These four steps vary slightly depending on which imaging modality is used to acquire the data. Each of the four steps is described in detail, using CT as the method of data acquisition.

Data Acquisition

In CT, data are collected from the patient by x-rays and special electronic detectors. Data can be acquired slice by slice with a conventional CT scanner or in a volume with a spiral/helical CT scanner. During slice-by-slice acquisition, the x-ray tube and detectors rotate to collect data from the first slice of the anatomical area of interest; then the data are sent to the computer for image reconstruction. After the first slice is scanned, the tube and detectors stop, the patient is moved into position for the second slice, and scanning continues. The data from the second slice are transferred to the computer for image reconstruction. This “stop-and-go” technique continues until the last slice has been scanned.

One of the fundamental problems of slice-by-slice CT scanning is that certain portions of the anatomy may be missed because motion caused by the patient’s respiration can interfere with scanning or be inconsistent from scan to scan. This problem can lead to inaccurate generation of 3D and multiplanar images. The final 3D image can have the appearance of steplike contours known as the stairstep artifact.

In volume data acquisition, a volume of tissue rather than a slice is scanned during a single breath-hold. This means that more data are sent to the computer for image reconstruction. Volume scanning is achieved because the x-ray tube rotates continuously as the patient moves through the gantry. One advantage of this technique is that more data are available for 3D processing, improving the quality of the resultant 3D image.

Creation of Three-Dimensional Space or Scene Space

All information collected from the voxels that compose each of the scanned slices goes to the computer for image reconstruction. The voxel information is a CT number calculated from tissue attenuation within the voxel. In MRI the voxel information is the signal intensity from the tissue within the voxel. The result of image reconstruction is the creation of 3D space, where all image data are stored (see Fig. 14-7).

Data in 3D space are systematically organized so that each point in 3D space has a specific address. Each point in 3D space represents the information (CT number or MRI signal intensity) of the voxels within the slice.

Processing for Three-Dimensional Image Display

Processing, which is a major step in the creation of simulated 3D images for display on a 2D computer screen, is accomplished on the workstation. Although it is not within the scope of this chapter to address these operations in detail, it is important that technologists have an understanding of how sectional images are transformed into 3D images as illustrated in Figure 14-7.

In 1990, Mankovich et al (1990) identified two classes of processing to explain 3D image display: voxel-based processing and object-based processing. Voxel-based processing “makes determinations about each voxel and decides to what degree each should contribute to the final 3D display,” whereas object-based processing “uses voxel information to transform the images into a collection of objects with subsequent processing concentrating on the display of the objects.”

Voxel-based processing was used as early as 1975 as a means of generating coronal, sagittal, and oblique images from the stack of contiguous transverse axial set of images—the technique of MPR. Although MPR is not a true 3D display technique, it does provide additional information to enhance our understanding of 3D anatomy (Beigleman-Aubry et al, 2005; Lell et al, 2006). In MPR, the computer scans the 3D space and locates all voxels in a particular plane to produce that particular image (Fig. 14-8).

Object-based processing involves several processing methods to produce a model (called an object model or object representation) from the 3D space and transforms it into a 3D image displayed on a computer screen. According to Russ (2006) and others (Dalrymple et al, 2005; Lell et al, 2006; Udupa and Herman, 2000), the processing of an object model into a simulated 3D image involves steps such as the following:

Surface Rendering

Surface rendering, or shaded surface display (SSD), has evolved through the years with significant improvements in image quality (Fig. 14-9). In surface rendering, the computer creates “an internal representation of surfaces that will be visible in the displayed image. It then ‘lights’ them according to a standard protocol, and displays an image according to its calculation of how the light rays

would be reflected to the viewer’s eye” (Schwartz, 1994).

According to Udupa and Herman (2000), surface rendering involves essentially two steps: surface formation and depiction on a computer screen (rendering) (see box above). Surface formation involves the operation of contouring. Rendering follows surface formation and is intended to add photorealism and create the illusion of depth in an image, making it appear 3D on a 2D computer screen. A simulated light source can be positioned at different locations to enhance features of the displayed 3D image (see Fig. 14-4).

The advantage of surface rendering techniques is that they do not require a lot of computing power because they do not use all the voxel information in 3D space to create the 3D image. Only contour information is used. However, this results in poor image information content.

Heath et al (1995) demonstrated this disadvantage when they used surface rendering to image the liver. They reported the following:

Figure 14-11 illustrates surface rendering numerically. Numbers represent the voxel values for a sample 2D data set. An algorithm is applied to locate a “surface” within the data set at the margin of the region of voxels with intensities ranging from 6 to 9. Standard computer graphics techniques are then used to generate a surface that represents the defined region of voxel values (Heath et al, 1995).

Volume Rendering

Volume rendering is a more sophisticated technique and produces 3D images that have a better image quality and provide more information compared with surface rendering techniques (Neri et al, 2007). Volume rendering overcomes several of the limitations of surface rendering because it uses the entire data set from 3D space. Because of this, volume rendering requires more computing power and is more expensive than surface rendering.

Udupa and Herman (2000) describe the conceptual framework of volume rendering:

The two stages to volume rendering are preprocessing the volume and rendering.

Intensity Projection Renderings

As noted in Figure 14-8, processing of image data from 3D space can also generate intensity projection images. These images, as Kalender (2005) points out, are “an extension of MPR techniques and consists of generating arbitrary thick slices (slabs) from thin slices reducing the noise level and possibly also improving the visualization of structures, for example, vessels present in the several thin slices … . The term sliding thin slabs is known for this technique … .” In addition, Dalrymple et al (2005) note that “multiplanar images can be ‘thickened’ into slabs by tracing a projected ray through the image to the viewer’s eye, then processing the data encountered as the ray passes through the stack of reconstructed sections along the line of sight according to one of several algorithms.” This is clearly illustrated in Figure 14-16.

The algorithms for sliding thin slabs (STS) (or thickening of MPR images) include average intensity projection (AIP), maximum intensity projection (MIP), and minimum intensity projection (MinIP).

Virtual CT Endoscopy

The CT image data from 3D space can be processed in such a way by using sophisticated computer algorithms to generate what has been referred to as virtual endoscopic images. These images are based on both 2D and 3D CT image data sets by using a technique known as perspective volume rendering (pVR) (Kalender, 2005). pVR is used to examine hollow structures such as the colon (CT colonoscopy) and the bronchi (CT bronchoscopy), for example. Furthermore, pVR can create an approach that allows the operator to “fly-through” the hollow structure. Virtual CT endoscopy is described in detail in Chapter 15.

Comparison of Three-Dimensional Rendering Techniques

One early comprehensive comparison of surface and volume rendering techniques was performed in 1991 by Udupa and Herman. They concluded that the surface method had a minor advantage over the volume methods with respect to display ability, clarity of the display, smoothness of ridges and silhouettes, computational time, and storage requirements. It had a significant advantage with its time and storage requirements.

Later in 1995, Heath et al (1995) compared surface rendering, volume rendering, and MIP with spiral/helical CT during arterial portography. They compared the techniques with respect to seven parameters: depiction of 3D relationships, edge delineation, demonstration of overlapping structures, depiction of vessel lumen, percentage of data used, artifacts, and computational cost. Their results are summarized in Table 14-4. It is clearly apparent that volume rendering is superior in all parameters compared; however, it has the highest computational cost.

One of the characteristic features of the MIP technique is that it removes discarded data having low values. The SSD technique removes all data with the exception of the data that are associated with the surface and, as mentioned in Table 14-4, typically uses less than 10% of the data. The effect of this data limitation is illustrated in Figure 14-25.

Although volume-rendered images may look similar to images generated by the SSD technique, the use of 100% of the acquired data set and “assigning a full spectrum of opacity values and separation of the tissue classification and shading processes provide a much more robust and versatile data set than the binary system offered by SSD” (Dalrymple et al, 2005). This is clearly shown in Figure 14-26.

In the past years, 3D volume rendering has been shown to be useful in a wide range of clinical applications (Calhoun et al, 1999), including the thoracic aorta (Christine et al, 1999) and in evaluating carotid artery stenosis (Leclerc et al, 1999).

More recent discussions of the use of 3D rendering techniques for clinical imaging using the data obtained from Multislice CT scanners have been reported by several authors, including Kalender, 2005; Dalrymple et al, 2005; Silva et al, 2006; Lell et al, 2006; and Fishman et al, 2006, and the interested student should refer to these original reports for more information.

Some important considerations to note, however, when these 3D imaging techniques are used are noted by several authors as follows:

1. The volume-rendered 3D technique is much better than the MIP technique for a clear display of the anatomy of interest in the volume data set. The MIP cannot display the 3D anatomical relationships, only because it is 2D.

2. For better clarity of anatomical details, the volume data set must be edited by using thinner slabs compared with the entire volume data set.

3. Several editing tools are available to change the appearance of the images. These include windowing (window width and window length manipulation), color and shading tools, and tools that allow the operator to change the opacity or the transparency of the image display (Fishman et al, 2006) and segmentation (Dalrymple, 2005; Lell et al, 2006).

Stand-Alone Workstations

A number of popular CT equipment manufacturers provide 3D packages for their CT and MRI scanners, and many are offering both 3D hardware and software packages for use in radiology. Although the technical specifications of each workstation vary depending on the manufacturer, typical 3D processing techniques include software to perform the following: