Volume Rendering

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Volume Rendering
Volume Modeling Volume Rendering
20 Apr. 2000
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Volume Modeling Rendering

• Some data is more naturally modeled as a volume,
  not a surface
• You could always convert the volume to a surface,
  but thats not always best
• Volume rendering render the volume directly

Ray-traced isosurface f(x,y,z)c
Same data, rendered as a volume
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Why Bother with Volume Rendering?

• Isnt surface modeling rendering easier?
• Show all your data
• more informative
• less misleading (the isosurface of noisy data is
  unpredictable)
• Constructive Solid Geometry (CSG) is natural
• Simpler and more efficient than converting a very
  complex data volume (like the inside of someones
  head) to polygons and then rendering them

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Contrasts

• Surface Rendering
• Surface rendering is the "usual" type of
  rendering.
• Data is converted to geometrical primitives (e.g.
  triangles), which are then drawn.
• Everything you see is a 2D surface, embedded in a
  3D space.
• The conversion to geometrical primitives may lose
  or disguise some data.
• Good for opaque objects, objects with smooth
  surface.

• Volume Rendering
• Data consists of one or more (supposedly
  continuous) fields in 3D.
• A Transfer Function maps the data into a volume
  of RGBA values.
• This volume is rendered directly, like a blob of
  colored jello.
• Data is seen more directly less likely to be
  hidden.
• Works well for complex surfaces.

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Applications

• medical
• Computed Tomography (CT)
• Magnetic Resonance Imaging (MRI)
• Ultrasound
• engineering science
• Computational Fluid Dynamics (CFD) aerodynamic
  simulations
• meteorology weather prediction
• astrophysics simulate galaxies
• Computer Graphics
• Participating media
• Texels

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Brief History of Volume Visualization

• 1970s modeling rendering with 3-D grids and
  octrees
• 1984 ray casting volume models
• 1986 3-D scan conversion of lines, polygons into
  3-D grid
• 1987 marching cubes algorithm (convert volume
  model to surface model)
• 1988 direct volume rendering with painters
  algorithm
• 1989 splatting
• 1990s volume rendering hardware

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Volume Rendering Pipeline

• Data volumes come in all types tissue density
  (CT), relaxation time of certain molecules (MRI),
  windspeed, pressure, temperature, value of
  implicit function.
• Data volumes are used as input to a transfer
  function, which produces a sample volume of
  colors and opacities as output.
• Typical might be a 256x256x64 CT scan
• That volume is rendered to produce a final image.

transfer function
sample volume
rendering
final image
data volumes
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Transfer Functions

• The transfer function takes (multiple) scalar
  data values as input, and outputs RGBA
• It gets applied to every voxel in the volume
  model
• It can be very simple (a color lookup table) or
  very complicated (implementing CSG, voxel
  texturing, etc.)

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Rendering

• Usually one just integrates color through the
  volume (ray casting)
• Recursive ray tracing is also possible
• But it gets confusing pretty quickly (shadows,
  filtered light, reflections, etc)
• For lighting we need surfaces!
• We can use the magnitude of the local gradient to
  check for surfaces (for example, bone is denser
  than fat on CT scans)
• And we can use the (negative of the) gradient
  direction as a lighting normal!
• Some, all, or none of the voxels will have
  surface lighting.

• And we need material properties!
• Either assume all the data is one material type,
• Or use a separate set of segmentation data to
  identify voxel materials.

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Some Details

• Regular x-y-z data grids are easiest and fastest
  to handle, but algorithms exist for handling
  irregular grids like finite element models, where
  the voxels (volume elements) are not all
  parallelepipeds.
• Resample it
• or just deal with it
• Finite element data, ultrasound data
• Geometrical primitives can be handled by
  "rasterizing" them into data grids.

This model was rasterized and rendered with
VolVis
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Accumulating Opacity

• By convention, opacity (alpha) ranges from 0.0 to
  1.0, 1.0 being completely opaque.
• Multiple layers of material are composited
  according to their opacity.
• An ideal, continuous material takes the limit of
  this process as it goes to an infinite number of
  infinitely thin layers (exponentials).
• The local gradient of opacity can be used to
  detect surfaces, and as the normal for the
  lighting equation.

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Ray Casting Volumes

• Just integrate color and opacity along the ray
• Simplest scheme just takes equal steps along ray,
  sampling opacity and color
• Grids make it easiest to find the next cell
• Its simple to include volumes as primitives in a
  ray tracer
• clouds, fog, smoke, fire done this way

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Trilinear Interpolation

• How do you compute RGBA values which are not at
  sample points?
• Nearest neighbor (point sampling) yields blocky
  images
• Trilinear interpolation is better, but slower
• Just like texture mapping
• You can even mipmap in 3D

Nearest Neighbor
Trilinear Interpolation
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Splatting

• Wonderfully simple
• Working back-to-front (or front-to-back), draw a
  splat for each chunk of data
• Easy to implement, but not as accurate as ray
  casting
• works reasonably for non-gridded data

closeup of a splat
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Other Techniques

• Shear-Warp (Lacroute and Levoy)
• requires a grid
• sort of like Bresenham for volumes
• very fast with no hardware acceleration, but
  implementation is tricky
• Polygons 3D texture
• Build a 3D texture, including opacity
• Draw a stack of polygons from back to front, with
  that texture
• Very efficient on machines with hardware
  acceleration that supports opacity

3D RGBA Texture
Viewpoint
Draw polygons back to front
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CSG is Easy

• The transfer function can be used to mask a
  volume or merge volumes
• You are still confined to the grid, of course

not
and
or
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Another CSG example
(VolVis again)
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Acceleration Techniques

• Limit yourself to what you can do in cache...
• and do multiple blocks if necessary
• Octrees
• Quit integration early- that last bit is slowest
• Error measures
• Parallelism

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Pictures
colliding galaxies