Interactive HighQuality MIP

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Interactive High-Quality MIP

• LU, Mingming
• Presentation II
• For
• Pattern Recognition Course

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Volume Visualization

• Sometimes, isosurfaces are not natural.
• Noises make it hard to extract surfaces of
  objects by specifying a single iso-value.
• Thin vessels cover a wide range of data values.
• Some datasets dont contain a very evident
  surface, e.g., liquid.

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Volume Visualization (cont.)

• Volume Rendering
• Maximum Intensity Projection (MIP)
• Ray Casting
• Splatting
• Shear-Warp
• 3D Texture Mapping

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Surface vs. Volume Rendering

• 3-D model for surfaces
• Convert to triangles
• Draw primitives
• Lose or disguise data
• Good for opaque objects

• Scalar field in 3-D
• Convert to RGBA values
• Rendering volume directly
• See data as given
• Good for complex objects

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Why does MIP work?

• Exploits the fact that within medical data sets,
  the data values of vascular or bone structures
  are higher than the surrounding tissues.
• By depicting the maximum value seen through each
  pixel, these important structures can be captured.

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Why Interactive?

• MIP contains no shading, depth and occlusion
  information. Looks the same from both the front
  and the back.
• To easily interpret the image, animation or
  interactively changing the viewpoint is required.

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Current Difficulties

• Bad performance
• More accurate evaluation of ray maxima
• Process the whole data sets
• Low image quality
• No re-sampling (aliasing)

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Some Improvements

• Optimization of ray traversal and interpolation
• Use of graphics hardware
• Splatting and shear-warp factorization
• Elimination of irrelevant voxels and alternative
  storage schemes

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Improved MIP

• Preprocessing of Volume Data
• Cell Removal
• Noise Compensation
• Cell Storage
• Rendering
• Template Calculation
• Projection
• Evaluation of the Maximum

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Cell Removal

• For trilinear interpolation within cells, the
  cell maximum is always located at on of the
  vertices.
• A cell C does not contribute to MIP from any
  viewing direction, if all rays passing through it
  collect a higher value by passing through other
  cells D either before or after C.

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Cell Removal (cont.)

• Viewing direction independent cell removal is
  ineffective and leads to low cell removal rate.
• Decompose of all viewing directions into 24
  clusters.
• For a certain viewing direction, the set of cells
  of the corresponding cluster is selected.

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Cell Removal (cont.)
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Cell Removal (cont.)

• Advantages
• For each viewing direction cluster, we have a
  large cell removal rate, e.g. 70.
• Speed up the following MIP processing
• Disadvantages
• Large memory requirement. Almost as 7 times large
  as the original data set.
• Improvement is not that significant.

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Cell Removal (cont.)
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Noise Compensation

• Remove cells which violate the exact criteria by
  a factor which does not exceed a user specified
  threshold (removal tolerance).
• After the processing with a 1 tolerance, 30 of
  all cells are left.

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Cell Storage

• Reference coordinates of a cell. (x, y, z)
  (min(xi), min(yi), min(zi))
• Cells are sorted according to descending Cmax
  values within a 1D array. Within a group of cells
  with the same Cmax, sub-sorting is done according
  to descending Cmin. 4 bytes for each cell (2048 x
  2048 x 1024).

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Cell Storage (cont.)
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Cell Storage (cont.)

• Advantage
• Fast computation of MIP
• Progressive refinement is achieved automatically,
  as cells which are most relevant to MIP are
  projected first.
• Computation for cheap preview is simple.

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Template Calculation

• Used to determine all pixels of the image which
  are covered by a cells projection.
• Images of cells differ by an individual sub-pixel
  displacement with respect to the pixels of the
  image can lead to different sets of pixels
  covered by the cells image.
• 4 x 4 grid within a pixel.

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Template Calculation (cont.)
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Template Calculation (cont.)

• For each pixel in a template
• The offset from the cells origin
• Interpolation weights (u, v, w) for ray entry and
  exit coordinators at the pixel.
• The number of interpolation steps required along
  the ray/cell intersection.
• A (du, dv, dw) vector defining a step along the
  ray.

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Evaluation of the Max

• The most expensive part by using trilinear
  interpolation.
• Values of pixels covered by the current cell
  which are lower than the cell maximum potentially
  have to be replaced by a higher value.
• Good guess for the ray maximum can avoid more
  evaluations.

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Evaluation of the Max (cont.)

• The max is located on the entry or exit point of
  the ray. Max(entry, exit)
• The max in within the cell. Min(Cmax, max(entry,
  exit) deviation)

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Evaluation of the Max (cont.)

• A fast approximation of the deviation is
  deviation Max(0, Max((vi vj)/2) c) with vi,
  vj being data values at the vertices located at
  the ends of the four space diagonals of the cell
  and c being the trilinearly interpolated value at
  the cells center (cheap, as special case).

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Evaluation of the Max (cont.)

• Not a strict upper bound in all cases, but its
  violated only once in about 20000 25000 cases.
• On average, 30 lower than Cmax. 60 trilinear
  evaluations have been saved.

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Conclusion

• 50 times faster than brute-force MIP and at least
  20 times faster than comparable optimized
  techniques.
• Further possible improvements
• A more selective preprocessing technique.
• A more rigid upper bound approximation.

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Reference

• Lukas Mroz, Helwig Hauser and Eduard Groller.
  Interactive High-Quality Maximum Intensity
  Projection.
• Lukas Mroz, Andreas Konig and Eduard Groller.
  Real-Time Maximum Intensity Projection.