Volume Visualization by Ray Tracing

• Introduction
• Binary Volume Rendering by Ray Tracing
• Probabilistic Volume Rendering by Ray Tracing

Introduction

Ray tracing is now common in the field of computer graphics, and the technique has also gained popularity in volumetric visualization. This is due to its ability to enhance spatial perception of the scene using such effects as transparency, mirroring and shadow casting. Correct understanding of the nature of the processed data further necessitates usage of various visualization techniques. In the framework of its basic scheme, ray tracing enables the implementation of various surface as well as volume rendering techniques (color compositing, reprojection, MIP), which makes it an ideal tool for data exploration.

Advantages of the ray tracing approach:

• Enhancement of spatial perception by transparency, mirrors and shadows (Figure 1).
• Implementation of different visualization techniques (surface and volume rendering, MIP, reprojection) is possible (Figure 2).

Disadvantages of the ray tracing approach:

• Large computational demands (10⁶ - 10⁸ voxels to be processed)

Due to the fact that the scene is defined within a 3D discrete raster the ray should be represented as a discrete ray, i.e., as an ordered sequence of voxels pierced by the given ray with the following properties:

• To enable supersampling and recursivity, the ray should be able to start at any point outside of the scene, or inside, and with arbitrary direction,
• To get correct images, no object voxels along the ray should be missed. Therefore, the ray should, at least in the vicinity of an object, fulfill the demands of 6-connectivity.

• Process the uninteresting (background) regions of data as fast as possible, either by sampling the ray with lower resolution or by skipping them completely

Figure 1: Enhancement of spatial relationships of different views by mirrors and shadows. The object (cca 3 cm long, scanned by a NMR scanner) is a cast of a human hearth ventricle cavity.

(a)	(b)	(c)
(d)	(e)	(f)
Figure 2: Example of different volume rendering techniques: surface rendering (a,d), (b,e) volume volume rendering by ray tracing and (c, f) reprojection.

Binary Volume Rendering by Ray Tracing

• Characteristics:
  • Only surfaces contribute to rendered images
  • No explicit surface model - surfaces defined by means of interpolation function (NN, trilinear, tricubic).
• Foreground (interesting) and background (uninteresting) voxels:
  • Binary object masks
  • Identified by segmentation
• Ray traversal phases (Figure 3):
  • Initialization: scene entry and exit points
  • Background traversal: skipping empty region usually surrounding the object
  • Hit-miss test: test, if ray surface intersection exists within the voxel
  • Surface detection: computation of ray-surface intersection

Figure 3: Background traversal, hit-miss test and surface detection

Probabilistic Volume Rendering by Ray Tracing

• Characteristics:
  • Accumulation of sample contributions to the image along the ray
• Techniques:
  • Unshaded: contribution dependent only on sample value (reprojection, maximum intensity projection-MIP) (Figure 2c,f).
  • Shaded: surfaces enhanced by shading, surface normal and strength estimation (Figure 2b,e).
• Foreground and background voxels:
  • A culling function can be defined, identifying voxels with no contribution to the image (dependent on the chosen technique)
• Ray traversal phases (Figure 4):
  • Initialization
  • Background traversal
  • Accumulation of samples

Figure 4: Background traversal and accumulation

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