High Quality Rendering of Attributed Volume Data

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High Quality Rendering of Attributed Volume Data

• Ulf Tiede Thomas Schiemann Karl Heinz H ohne

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Introduction

• Three-dimensional visualization (CT, MR)
• Isosurface, volume-rendering
• Partial-volume-effect
• The limited spatial resolution of the scanning
  devices
• Segmentation
• Threshold
• The average intensity value of adjacent objects
• If different objects share the same intensity
  range
• Segmentation has to be done manually.
• Additional volume containing discrete attribute
  values for each voxel

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Problem

• Ray-casting
• Discrete scan-conversion algorithms
• Staircase looking surfaces
• The real boundary of an object cannot be
  reconstructed exactly
• A better approximation is required

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Method

• Reconstruction of object boundaries in subvoxel
  resolution based on the object classification
  resulting from the segmentation step.
• Idea
• Ray-casting using floating-point
• Reclassification of the sample position
• Interpolation of the surface location between
  successive sample points
• Surface normal at the subvoxel surface
• Detection and handling manually segmented objects

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Computation of the Attribute Value

• The attribute value at a particular subvoxel
  sample position
• Initialize a counter to zero
• Calculate the gray value at the sample position
  using tri-linear or higher order interpolation
  (e.g. B-splines )
• Check if the gray value is within the intensity
  range(in the 222 neighborhood)
• The counter is 0, i.e. No fitting object
• The counter is 1, take the attribute value of
  this object.
• The counter is 2 or greater.
• Nearest-neighbor
• Interpolation

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Interpolation of the Surface Location

• Linear interpolate
• Tri-linear interpolation of the intensities
  produces curved boundaries
• Bisection algorithm
• Approximates B2

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Segmentation

• Exactly one boundary exists
• If the intensity ranges form a gap there are two
  surfaces.
• In cases where the intensities of the objects
  overlap
• Pi is inside Oi, pi-1 is outside Oi
• Pi-1 is inside Oi-1 , pi is outside Oi
• Using interpolated attributed value

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Detecting Thin and Small Objects

• Classical over sampling
• Nyquist frequency is not known
• A tradeoff between computation time and the
  accuracy of small structures has to be made.

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Interpolating Attribute Values

• To check if a sample position is inside of a
  specific object
• Create a binary subvolume (222)
• For each voxel
• Set to 1, if the attribute value in the
  corresponding attribute volume is the same we are
  testing
• Tri-linear interpolated value
• 256 configurations

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Extension for Multi-modality Volume Data

• Change the basic algorithm
• Determine all distinct attribute values in the
  neighborhood
• Compute an interpolated intensity value for each
  of these attribute values
• Increase the counter if the interpolated value
  fits into the intensity range of the respective
  object

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Calculating Surface Color

• To get a more realistic color we can shift the
  interpolation center along the surface normal
  underneath the surface

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Results
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Results

• Computational costs
• Floating-point calculation
• Tri-linear (or higher order) interpolation of the
  gray-values at each sample position
• Examination of the 8 neighbors
• Calculation of the surface location between
  sample points.
• For opaque surface this is only done once per
  pixel.