Introduction to Volume Rendering

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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?

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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

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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

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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)

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Volume Data
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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)

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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

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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

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Volume Data
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Volume Rendering

• techniques for volume rendering
• ray casting
• J. T. Kajiya, B. P. V. Herzen, "Ray Tracing
  Volume Densities," Computer Graphics, 1984, Vol.
  18, No. 3, pp. 165-174
• 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. 451-458

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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

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Ray Casting
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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

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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

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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

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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

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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

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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.

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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

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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

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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

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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 -1000 HU (black)
• Fat -50
• Water 0 HU
• muscle 40
• Bone 1000 3000 HU (white)
• rescale to 0, 4095 to use unsigned ints

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Computed Tomography (CT)

• The Hounsfield scale of CT numbers

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Computed Tomography (CT)

• the human eye cant 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

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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

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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)

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Other Volume Data Sources

• measurements
• seismic data
• atmospheric data
• scientific modeling
• plasma physics
• atmospheric modeling
• geophysical earth models
• plenty of others

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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
• http//medical.nema.org/dicom/

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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

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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
• XYZ aspect ratio of each voxel is 112
• 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

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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

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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

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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

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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

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Example CT scan

• isolate bone in a view, set
• Level 2000
• Window 1900
• isolate soft tissue, set
• Level 1100
• Window 260

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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

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Example CT scan

• Scalar Color Mapping
• the scalar data is mapped to colors
• blue scalar gt 30 (air) ? Hue 0.67
• green scalar gt 1059 ? Hue 0.33
• red scalar gt 1433 (bone) ? Hue 0
• saturation and value are constant and the Hue is
  linearly interpolated between control points

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Example CT scan

• Scalar Opacity Mapping
• scalar values are given an opacity
• scalar 0 ? opacity 0
• scalar gt 1406 ? opacity 0.2

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Example CT scan

• we are seeing the red (less transparent) bone
  through greenish (more transparent) soft tissue

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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

opacity1
opacity0
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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

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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

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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 (H0.05, S0.76, V0.92)
• click close to the left node to add another brown
  node and move it to a scalar value S725
• move the middle white node to S810

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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

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Example CT scan
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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!

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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 weve seen earlier.