1. Introduction to Volume Rendering
Jon Johansson
Academic Information and Communication Technologies
November 30, 2005

2. Volume Data Volumes of data can be measured or generated
measured: CT, MRI, Ultrasound
modeled: atmospheric models, air flow over wing
The big question:
If your data is represented as a solid volume of points, how do you see the internal structure?

3. Volume Data
we have looked at some techniques to extract geometric objects within a volume of data
these techniques fall under the heading “Volume Visualization”
many data sets for volume rendering are composed of a Cartesian grid with data values at each node

4. Volume Data AVS/Express sample data set hydrogen.fld
three-dimensional, uniform volume with byte data (integers Î [0, 255])
grid dimensions:
64x64x64 ® 262,122 points
633 voxels (volume elements)
transparent isosurfaces can show how the field behaves quite nicely

5. Volume Data
the data values are separated by constant spacing on a Cartesian grid
the connections are regular, forming hexahedrons (cubes in this case actually)
the smallest connected volumes are called Voxels (volume elements)

6. Volume Data

7. Volume Data
a voxel typically has data values associated with the corner points
to find a data value at an arbitrary location in the voxel we need to interpolate
commonly use tri-linear interpolation
some data sets will have a single data value for the volume (referred to as cell data)

8. Volume Data
we are now going to look at rendering volumetric data directly instead of constructing geometric primitives
treat the volume as being composed of semitransparent material
transmits and absorbs light
light is scattered by the particles

9. Volume Data
we can see into the volume depending on how transparent the material is:
transparency → fraction of light that passes through a surface or an object; a = 1 Þ all light passes
opacity → fraction of light that is absorbed at a surface or an object; opacity = 1 Þ no light passes
opacity = 1 – transparency
transparency commonly refers to visible light
it can actually refer to any type of radiation: e.g.. flesh is transparent to X-rays, while bone is not, allowing the use of medical X-ray machines

10. Volume Data

11. Volume Rendering techniques for volume rendering ray casting splatting
J. T. Kajiya, B. P. V. Herzen, "Ray Tracing Volume Densities," Computer Graphics, 1984, Vol. 18, No. 3, pp
splatting
Westover, L., “Splatting: A Parallel, Feed-Forward Volume Rendering Algorithm”. PhD Dissertation, July 1991
hardware texture memory
Brian Cabral , Nancy Cam , Jim Foran, “Accelerated volume rendering and tomographic reconstruction using texture mapping hardware”, Proceedings of the 1994 symposium on Volume visualization, p.91-98, October 17-18, 1994, Tysons Corner, Virginia, United States
shear-warp factorization
Philippe Lacroute and Marc Levoy, “Fast Volume Rendering Using a Shear-Warp Factorization of the Viewing Transformation”, Proc. SIGGRAPH '94, Orlando, Florida, July, 1994, pp

12. Ray Casting
a widely used ray casting technique is based on the model of Blinn and Kajiya
in order to find the color of a pixel in the image:
send a ray R through the volume
the material has a density D(x,y,z) = D(t) varying in space
parameterize movement along the ray by t e [t1, t2]
at each point there is an illumination I(x,y,z) = I(t) from any light sources
determining the illumination function is difficult since it depends on how light is attenuated by the material in the volume
in many calculations I(x,y,z) = I(t) = constant

13. Ray Casting

14. Ray Casting
the attenuation of radiation due to the density along the ray can be calculated as
the intensity of light arriving at the eye along the ray due to all points between t1 and t2 is then

15. Ray Casting
to take away from this, in this ray casting calculation we want to find the intensity of light for a pixel in our image
calculate the attenuation of light along the ray: integrate along the ray through the volume
calculate the intensity of light reaching the image location – integrate along the ray again
to include lighting effects we need to calculate the amount of light from the sources reaching each point along the ray – more integration
multiple scattering effects – lots more integrations

16. Ray Casting
in order to do the integrations along the rays we need to find values of the scalar field at arbitrary positions in a voxel
use Trilinear Interpolation
4 1-D interps in x
2 1-D interps in y
1 1-D interps in z

17. Volume Rendering – Hardware
volume rendering seems like it might benefit from hardware acceleration
VolumePro by TeraRecon
PCI card for PCs
real-time 3D volume rendering of volumes up to 512x512x512
there are other solutions as well of course

18. Volume Rendering – Software
many visualization packages have volume rendering capability
AVS/Express – Advanced Visual Systems
VTK (Visualization Toolkit) – Kitware
VolView – based on VTK from Kitware
commercial system which focuses on volume rendering
has support for the VolumePro card

19. Volume Rendering
the entire body of 3D data must be processed each time an image is drawn or displayed
imaginary "rays" are cast through the data, picking up color and opacity as they traverse it
the rays are then projected onto a computer screen or display surface
to make the image move or to manipulate it interactively, the data is re-processed in rapid succession, fast enough for interactive frame rates – this needs fast hardware.

20. Volume Rendering
in order to render a 3D volume into a 2D image we need to:
cast the rays through the volume
assign color and opacity values to the sample points
calculate gradients and assign lighting to the image
sum up all the color and opacity values to create the image

21. Computed Tomography (CT)
Computed Tomography (CT) or Computed Axial Tomography (CAT)
uses a combination of X-rays and computer technology to produce cross-sectional images of the body
an x-ray tube rotates in a circle around the patient, making many pictures as it rotates
final slice images are generated utilizing the basic principle that the internal structure of the body can be reconstructed from multiple X-ray projections
physicians can then examine “slices” through different organs and show detailed images of any part of the body

22. Computed Tomography (CT)
General Electric Volume CT scanner
X-ray head moves in a circle in the gantry while the bed moves the patient through the hole
data is taken in a helix around the body
slices through the body are then constructed

23. Computed Tomography (CT)
image sizes are at most 1024x1024 pixels or less – actual physical resolution depends on a sample size
scanners can now provide 0.5 mm slice widths for small samples (more usually use 1-10 mm)
can distinguish a tissue density difference of 1 percent
CT densities (grey levels) in the range [-1024, 3071] Hounsfield Units (HU)
Air: HU (black)
Fat: -50
Water: 0 HU
muscle: +40
Bone: – 3000 HU (white)
rescale to [0, 4095] to use unsigned ints

24. Computed Tomography (CT)
A very nice description of CT:
The Hounsfield scale of CT numbers

25. Computed Tomography (CT)
the human eye can’t actually distinguish between 4000 different shades of grey
“Window Width” (contrast) covers the HU of all the tissues of interest
“Window Level” (brightness) represents the central HU of all the numbers within the window width
a visually useful grey scale is achieved by setting the WW and WL to suitable values
tissues with CT numbers outside the range are displayed as either black or white

26. Computed Tomography (CT)
in a CT chest exam:
to highlight the soft tissue, set:
WW = 350
WL = +40
to highlight the lung fields (mostly air)
WW = 1500
WL = -600
Source:

27. Other Volume Data Sources
lots of bio-medical measurement sources
Magnetic Resonance Imaging (MRI)
Positron Emission Tomography (PET)
Single Photon Emission Computed Tomography (SPECT, ECT)
Ultrasound Imaging
2-D and 3-D Microscopy Imaging (Light, Electron, Confocal, Atomic Force)
Notes on MRI at:

28. Other Volume Data Sources
measurements
seismic data
atmospheric data
scientific modeling
plasma physics
atmospheric modeling
geophysical earth models
plenty of others

29. Medical Data - DICOM
Digital Imaging and Communications in Medicine (DICOM)
main objective of this standard is to create a vendor independent platform for the communication of medical images and related data

30. Medical Data - DICOM
a set of rules that allow medical images to be exchanged between instruments, computers, and hospitals
a DICOM file contains:
a header
stores information about the patient's name, the type of scan, image dimensions, etc.
all of the image data
which can contain information in three dimensions

31. Example – CT scan VolView from Kitware
based on the Visualization Toolkit
look at sample data from the University of North Carolina
Description: CT study of a cadaver head
Dimensions: 113 slices of 256 x 256 pixels,
voxel grid is rectangular, and
X:Y:Z aspect ratio of each voxel is 1:1:2
Files: 113 binary files, one file per slice
File format: 16-bit integers (Mac byte ordering), file contains no header
Data source: acquired on a General Electric CT Scanner and provided courtesy of North Carolina Memorial Hospital

32. Example – CT scan
there is information about the data set available from the Information panel:
View→Information
summarizes the information that had to be provided to import to VolView

33. Example – CT scan
if only the volume display appears, select the 1 over 3 option in the Window menu
get 3 slices through the data in addition to the volume
the slices give detail about local structure

34. Example – CT scan
select Y-Z image from the upper left corner for the Volume window
the Y-Z slice then occupies the large window
sliders along the bottom of each window allow a view of a slice at any depth

35. Example – CT scan get the Image Display page from: View→Image Display
the Probe Information panel reports the pointer position and the value of the scalar at that point

36. Example – CT scan isolate bone in a view, set:
Level = 2000
Window = 1900
isolate soft tissue, set:
Level = 1100
Window = 260

37. Example – CT scan
choose Volume under the Window menu to get rid of the slice windows
choose Appearance under the View menu
the Appearance page controls how the rendering will look
lots of power here to give us what we want

38. Example – CT scan Scalar Color Mapping
the scalar data is mapped to colors
blue: scalar > 30 (air) → Hue = 0.67
green: scalar > → Hue = 0.33
red: scalar > 1433 (bone) → Hue = 0
saturation and value are constant and the Hue is linearly interpolated between control points

39. Example – CT scan Scalar Opacity Mapping
scalar values are given an opacity
scalar = 0 → opacity = 0
scalar > 1406 → opacity = 0.2

40. Example – CT scan
we are seeing the red (less transparent) bone through greenish (more transparent) soft tissue

41. Example – CT scan Gradient Opacity Mapping
at each point in the volume a gradient is calculated
the gradient magnitude is mapped to the opacity ramp
opacity=1
opacity=0

42. Example – CT scan
places of rapid change in the scalar field are opaque
areas of constant field are transparent
we see the boundaries
air → tissue
tissue → bone
a way to get “surfaces”

43. Example – CT scan now adjust color settings
select the folder icon in the Scalar Color Mapping area
select the White option to set the color to solid white
all the scalar data is now mapped to white

44. Example – CT scan
add a node to the center of the editing area by left clicking there
click on the left node to select it and make the color brown (~H=0.05, S=0.76, V=0.92)
click close to the left node to add another brown node and move it to a scalar value S=725
move the middle white node to S=810

45. Example – CT scan
Modify the Scalar Opacity Mappings to look like this (points numbered from left to right):
1 → S = 0, O = 0
2 → S = 561, O = 0
3 → S = 620, O = 0.357
4 → S = 930, O = 0.357
5 → S = 1194, O = 0.5

46. Example – CT scan

47. Example – CT scan
the Appearance panel in VolView 2.0 is the most complex interface
it defines the core parameters that affect the volume rendered image
this is where the control is for effectively visualizing data!

48. Conclusion
Volume rendering is a powerful tool for visualization and can assist in understanding volumetric data sets
useful to add to the toolkit to compliment the geometric techniques that we’ve seen earlier.