Volume Visualization Visualization II MSIM 842, CS 795/895

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Volume VisualizationVisualization IIMSIM 842,
CS 795/895

• Instructor
• Jessica Crouch

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Volume Viz Problem

• Data points fill a 3D volume
• You can only display one 2D image at a time
• Naïve rendering of a volume will just let you see
  the surface
• How can you visualize the volume data in a way
  that lets you understand the internal structure
  of the data?

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Structured vs. Scattered Data

• The best approach will depend on the
  characteristics of the data
• Data points arranged in rows, columns, and layers
  (3D image) can be referred to as voxels
  (volumetric-pixels)
• Data points that follow a non-gridded pattern are
  called scattered

Wikipedia image
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Volume Viz Data Dimensionality

• Each data point has
• 3D coordinates (x,y,z), specifying a position in
  the volume
• and one of the following
• Scalar a single number, 0D data
• Vector a list of numbers, 1D data
• Tensor a matrix or ND array of numbers, for Ngt1

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Data examples

• Scalar Data
• CT Scan ? x-ray opacity for each voxel
• PET Scan ? positron radiation for each voxel
• Atmospheric simulation (or measurement) ?
  pollutant concentration
• Ocean temperature distribution
• Vector Data
• Velocity vectors at each voxel
• Fluid flow (river water, arterial blood, etc.)
• Displacement vectors at each voxel
• Provides mapping between different deformed
  configurations of the same object
• Tensor data
• Higher dimensional data is more complicated
• Stress and strain matrices
• Gradients of 3D functions

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Simplest Case

• Lets consider continuous, scalar, voxel data
• Geometrically regular arrangement (3D grid)
• Just 1 data value per voxel
• Think of CT data (3D x-ray)
• What would you be interested in seeing?
• How would you construct a visualization?

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Scalar Voxel Viz.

• Simplest possible visualization is to just look
  at the slices
• Use color mapping (or grayscale mapping) to see
  slice values
• Slices can be useful
• We can do more interesting things

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Scalar Voxel Viz.

• Bone voxels will be bright (have large values),
  other voxels will be dark
• How could you visualize the surface of the bones?
• Several alternatives exist, including
• 1. Render an isosurface Use Marching Cubes
  Algorithm
• 2. Ray Casting Integrate scalar variable along
  the view direction
• 3. Splatting

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Isosurfaces from 3D

• How to construct a polygonal surface from a 3D
  dataset?
• Find points on the isosurface of a scalar
  variable
• 3D analog of 2D contour maps
• You pick a meaningful threshold value
• Voxels with data values below the threshold sit
  on one side of the isosurface, voxel with data
  values above the threshold sit on the other
• Simplifying assumption is that threshold value
  0
• To force this, just subtract the desired
  threshold value from all data points
• Tessellate points on the isosurface to create a
  polygonal representation of the surface
• The Marching Cubes algorithm does this
• This is one of the famous, older (gt20 yrs) viz.
  algorithms
• Render the tessellated isosurface using normal 3D
  graphics methods

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Isosurfaces Opacity
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The Visible Man Image Data
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Visible Man Isosurfaces
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Marching Cubes Considered

• How effective is the visualization perceptually?
• What can you see?
• What cant you see?
• How is this in terms of efficiency?
• Phase I
• Phase II
• Rendering
• Compare other approaches

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Ray Casting Volume Data
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Review Ordinary Ray Casting

• How does it work?

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Ray Casting with a Voxel
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Ray Casting for Approximation of Light Integral
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Examples
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Ray Casting Considered

• How effective?
• How are the images different from those produced
  by Marching Cubes?
• How efficient?
• Another alternative

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Volume Splatting

• Ray casting is an image space method
• Ray are generated per pixel, and travel out into
  the volume
• Volume splatting is an object space method
• Data points in the volume are mapped (splatted)
  onto the image plane

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Splatting A Feed Forward Process
Feed forward Splatting
Splat!
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Splatting (feed-forward)
?
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Fill the holes
We need to fill the pixel values between the
volume projection samples
?
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3D Kernel for Splatting
Need to know the 3D extent of each voxel, and
Then project the extent to the image plane
This is called footprint
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Visibility

• How does occlusion work?
• Splatting uses back to front compositing
• Samples in front are added on top of and
  partially obscure previously splatted (further
  back) samples

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Gaussian kernel

• A popular kernel is the Gaussian function (think
  bell curve)
• Sigma controls the width
• Gaussians have circular splat footprints

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Ray Casting vs. Splatting

• What are the differences in the images produced?
• Think about aliasing
• Efficiency considerations?
• In what order are the voxel data points accessed?
• For ray casting?
• For splatting?

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Summary of Techniques

• Marching cubes
• Construct polygonal isosurfaces
• Render with regular graphics pipeline
• Ray casting
• Image space algorithm
• Shoot rays from image into volume, integrate
  color opacity along each ray
• Volume splatting
• Object space algorithm
• Project each voxel onto the image plane
• These are good ways of looking directly at the
  recorded data. What could you do to focus
  attention on significant features in the data?

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Feature Extraction

• What is a significant feature?
• Answer is application dependent
• Often, regions with a high gradient are
  significant
• What is the gradient of a voxel volume?
• Look at the gradient of a 2D image

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10 50 250 100 10
10 50 250 100 10
250 250 250 250 250
100 100 250 100 100
10 10 250 10 10
25 120 25 -120 -50
25 120 25 -120 -50
125 0 0 0 -125
50 75 0 -75 -50
5 120 0 -120 -5
-.5 0 .5
-.5 0 .5
-.5 0 .5
Derivative in X direction
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10 50 250 100 10
10 50 250 100 10
250 250 250 250 250
100 100 250 100 100
10 10 250 10 10
-5 -25 -125 -50 -5
-120 -100 0 -75 -120
-45 -25 0 0 -45
120 120 0 120 120
50 50 125 50 50
.5 .5 .5
0 0 0
-.5 -.5 -.5
Derivative in Y direction
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Gradient Direction Vectors
dI/dx
dI/dy
25 120 25 -120 -50
25 120 25 -120 -50
125 0 0 0 -125
50 75 0 -75 -50
5 120 0 -120 -5
-5 -25 -125 -50 -5
-120 -100 0 -75 -120
-45 -25 0 0 -45
120 120 0 120 120
50 50 125 50 50
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Volume gradient

• Is a 3x1 vector
• dI/dx dI/dy dI/dz
• Vector points uphill in direction of increasing
  data value
• Vector length (magnitude) indicates how quickly
  data values in the neighborhood are changing

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Gradient Magnitude

• Given scalar data, the gradient magnitude can be
  computed
• Result is another scalar data set
• Each voxel value gets the length of the gradient
  vector computed for the original data
• Large gradient magnitude values in a region
  indicate sharp changes in the original data

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Gradient Magnitude Viz.

• Sharp changes are often significant
• May indicate an edge or surface
• Large gradient in CT data indicate a voxel is on
  bone surface
• May indicate where something important is
  happening
• Large temperature gradient in atmosphere can
  indicate a weather front
• Can apply the three visualization methods already
  discussed to the gradient magnitude data

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Other feature extraction methods

• Can apply other types of pre-processing to the
  input data to find areas of interest
• Search for blobs of a certain size
• Search for areas with a certain texture or
  pattern
• Filter out high frequency noise from input data
• Create new data set by assigning voxel values
  based on how well original data matches the
  search criteria
• Have to know what youre looking for, what
  defines significant for a particular
  application

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Still to come

• Consideration of volume viz. for higher
  dimensional data
• Vectors
• Tensors
• Time-varying sequences
• Data with probabilistic uncertainty

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Streamlines
Follow the flow of a vector field, tracing the
path a particle would take
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Tensor Glyphs

• Ellipsoids, Cuboids, Superquadratics (see
  right), other 3D polyhedra and implicit surface
  shapes
• For 3x3 matrices, illustrates 3 axes (or
  eigenvectors)