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A central concept: the scene

As a visualization application, 3D Slicer provides graphical representations of patient-specific data within a graphical interface. Such patient-specific data are provided by a number of medical imaging modalities, across different spatial and temporal scales. The 3D Slicer focuses on the modalities with volumetric possibilities, such as CT, MRI and PET, due to their clinical relevance, but it is also possible to integrate 1D and 2D signals, in addition to 3D, as well as the variations of these images over time (both in real time and over time).

Since 3D Slicer is largely based on the Visualization Toolkit (VTK), it is recommended that you read the manual [Visualization Toolkit: An Object-Oriented Approach to 3D Graphics], 4th edition, also known as the VTK Textbook. This is the official reference guide for the VTK.

The coordinate systems

In visualization and graphics, the scene consists of a virtual world in which objects (sometimes called actors), lights and cameras provide representations to be presented to the user.

Model coordinates

Figure 1: model coordinate systems

Each of the different models that will be part of the scene has its own coordinate system. These model coordinate systems are object-dependent and have their own coordinate axis: the origin of these axes and also their orientation may differ as they depend on how the data of that object is captured. Model coordinate systems can be 3D or 2D.

As can be seen in Figure 1 there are 4 different types of objects: OBJECT #1: a sphere, with the origin of the coordinates placed in the very center of the sphere. OBJECT #2: a cube, with the origin or coordinates placed in one of the corners OBJECT #3: a cube too, with the origin of the coordinates placed in a different corner and also a different axis orientation OBJECT #4: a 2D object, with an X and Y coordinate

Now all these 4 elements/objects must have their coordinate systems unified in order to be displayed coherently together, which leads us to the next step.

Object types

An approximate classification of the different object types found at the scene is as follows:

• Actors: the elements to be shown. In our particular case (medical image), these actors come from different data sources such as a CT scan, MRI, ultrasound, X-ray, etc....
• Lights: light sources that interact with the actors and allow them to be seen
• Cameras: virtual devices that define what will be displayed on the screen

Keep in mind that there may be as many objects as necessary, but at least there must be one of each type to build a scene.

World coordinates

Figure 2: actors positioned with the same coordinate system

The world establishes a reference system on the basis of which actors, lights and cameras are positioned.

In Figure 2 are the same 4 objects of the previous step, defined in the same coordinate system (axes represented in black), the world. Note that now the origin of the coordinate system, the point (0.0,0) and the orientation of the axis do not coincide with any of the coordinate systems that the objects had, since this coordinate system of the world is common to all of them. In this example, object #4, displayed in purple, was a 2D object that is now placed in a 3D coordinate system.

Figure 3: world coordinate systems

The scene configuration is completed with the addition of a light source and a camera, all of them referenced in the world's coordinate system, as you can see in Figure 3

Affine transformations relate cameras, objects and object components to the world's reference system. They consist of translation sequences, rotations and scale changes, which can be represented using homogeneous coordinates using 4x4 matrices. Perspective and orthographic projections from 3D space onto the image plane of the vision cameras can also be represented with 4x4 (or 4x3) matrices. In fact, they are all cases of projective transformations, which can be represented by these 4x4 matrices. In fact, all elements of the virtual world are represented with respect to the world's reference system by 4x4 matrix transformation sequences, possibly arranged in a hierarchy (for example: represent internal object components). For more information on coordinate transformations, see [pdf here].

RAS system

In our specific case we will not be working with abstract elements such as spheres, cubes or squares; we will be working with volumetric data collected with different scanners and medical devices.

Figure 4: RAS basis

The coordinate systems used, when applied to human bodies, are the so-called "SARs". This term is an acronym for the three-coordinate axis name, with unit vectors pointing in the following directions:

• Right-Left: corresponds to the sagittal plane, perpendicular to the ground and separating the right R from the left L (shown in blue at Figure 4)
• Anterior-Posterior: corresponds to the coronal plane, perpendicular to the ground and separating the front A from the back P (shown in red at Figure 4)
• Superior-inferior: corresponds to the axial plane, parallel to the ground and separates the head S from the feet I (shown in green in Figure 4)

This system is common, scanner-independent and patient-centered, enabling consistent integration and visualization of multiple images and data types in 2D and 3D viewfinders. The global 3D Slicer baseline corresponds to the patient-specific RAS and any data must be transformed into this system.

IJK system

The volumetric data of the image is acquired and provided in the rasterized scan reference system " IJK, also called column, row and section (i and j are the coordinates of the column and row, and k is the section number). For integration into 3D Slicer as objects or actors in the scene, it is necessary to provide the IJKtoRAS transformation matrix for each data set. See Figure 5.

Figure 5: IJK coordinates

Sytem XYZ

This is the coordinate system of the scanner. In MRI and CT devices, the coordinate system is fixed with respect to the surface on which the patient is placed, the table. See Figure 6.

Figure 6: Scanner coordinates

View coordinates

Figure 7: view coordinates system

The view coordinate system represents what is visible to the camera. It consists of a pair of x and y values, ranging from (-1.1) to a depth coordinate z; see Figure 7. The x, y values specify the location in the image plane, while the z coordinate represents the distance or range from the camera.

Display coordinates

The display coordinate system uses the same frame as the view coordinate system, but instead of using one by one negative as a range, the coordinates are x-locations, and real pixels in the image plane. Factors such as window size on the screen determine how the range of view coordinates (-1,1) is mapped in pixel locations. This is also where the view view comes into effect, so that different views can be integrated in the same window (see Chapter 3 and Fig. 3-14 of the VTK textbook).

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