lecture 5b
DESCRIPTION
MRI medical imagingTRANSCRIPT
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Volume Visualization
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Outline Introduction
Common Volume Visualization Steps
Approaches to Volume Visualization
Marching Cubes Algorithm
Ray-casting Algorithm
GPU based Volume Rendering
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Volume Visualization - Examples
MRI Face Mask (1994) CVH Visualization
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Volume Visualization
Volumetric data are very common.
3D Volume Data (Voxels) 2D Image Plane (Pixels)
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Sources of Medical Volume Data Medical Data
CT (Computed Tomography)
MRI (Magnetic Resonance Imaging)
PET (Positron Emission Tomography)
Angiography Data
3D US Data
CT Angiography:Dept. of NeuroradiologyUniversity of Erlangen,Germany
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Other Special Volume Data
Visible Human Project
CT Human Head:Visible Human Project,US National Library of Medicine, Maryland, USA
Video Show
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Volume Visualization Terms
Space/Grid/Lattice
Grid Traversal
Voxels
Cells
Geometric Primitives
Extent Planes
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Grid Types
Uniform grid (voxels)
Reconstruction with
trilinear interpolation
Unstructured grid
Decomposed into
tetrahedra
Reconstruction with
linear interpolation
REAL-TIME VOLUME GRAPHICS
Daniel Weiskopf
Institute of Visualization and Interactive Systems, University of Stuttgrat, Germany
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Different number can change color
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Common Vol. Vis. Steps Data Acquistion
Slice Processing
Volume Reconstruction
Volume Enhancement
Data Classification or Thresholding
Mapping to Primitives
Shading & Transforming Primitives
Displaying Primitives
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Voxelization
three dimensional scan conversion
the process of converting a geometric
representation of a synthetic model into a set
of voxels that best represents that synthetic
model within the discrete voxel space.
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Common Approaches to
Volume Visualization
Surface Rendering
an indirect technique used for visualizating
volume primitives by first converting them
into an intermediate surface representation and
then employing conventional computer
graphics techniques to render them to the
screen, e.g. Marching Cube Algorithm.
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Common approaches ...
Direct Volume Rendering
These techniques deal directly with volume
primitives without any intermediate conversion
of the volume data to surface representation,
e.g. ray tracing of volume data, 3D texture
mapping rendering
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Surface Rendering Techniques
Marching Cubes Algorithm
creates triangles
floating point representation
use case table to create triangles
use general graphics hardware for rendering
can generate large number of triangles for
medical data, e.g. 0.5 million triangles for a
human skull.
After break
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Marching CubesAlgorithm Summary
Create a cube
Classify each vertex
Build an index
Get edge list
Interpolate triangle vertices
Calculate and interpolate normals
References:
1. http://en.wikipedia.org/wiki/Marching_cubes
2. William E. Lorensen, Harvey E. Cline: Marching Cubes: A high resolution 3D surface
construction algorithm. In: Computer Graphics, Vol. 21, Nr. 4, July 1987
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Results (MC vs ASC)
MC ASC, N = 1
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Results (MC vs ASC)
MC ASC, N = 2
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Results (MC vs ASC)
MC ASC, N = 4
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Results (MC vs ASC)
MC ASC, N = 8
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Marching Cubes
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Marching Cubes
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Marching Cubes
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Marching Cubes
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Marching Cubes
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Marching Cubes
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Marching Cubes
Ratio
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Marching Cubes
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Marching Cubes
Problem - Ambiguous cases can result in holes
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Marching Cubes
Inconsistent Choice
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Marching Cubes
Results in holes
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Direct Volume Rendering
Ray-casting Algorithm
3D texture mapping for volume rendering
hardware dependent (in Part II)
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Data Classification
Surface rendering
User picks threshold value
Direct volume rendering
User specifies color table map data values to
meaningful colors
User specifies opacity table map interesting
data to opaque, map other data to transparent
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Ray-Casting Methods
Cast Rays from image plane through
volume to find pixel color
No intermediate surfaces
renders volume directly
References:
1. http://en.wikipedia.org/wiki/Volume_ray_casting
2. Marc Levoy, Efficient Ray Tracing of Volume Data, ACM
Transactions on Graphics, 9(3):245-261, July 1990.
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Less sampling
More sample
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Can be less expensive
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Compositing
Compositing describes the way that the
individual contributions from the sample
points are accumulated
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Compositing
Back to front compositing
the contribution at sample position k is computed
by the previous contribution weighted by the
transparency at the current sample, plus the color
at the current sample
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Compositing
Front to back compositing
Compose samples from the front of the volume
dataset along the ray to the back end of the dataset
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Compositing
Compositing variationsFirst Hit
sample the casted rays until we find two sample points below and above acertain intensity threshold
Pseudo X-ray Traverse and accumulate sample values along the rays throughout the
whole volume
Threshold sensitive compositing Similar to pseudo X-ray, but considering only sample values above a
certain intensity threshold
Maximum intensity projection (MIP) Search for the sample point with the highest intensity value
Closest vessel projection (CVP) Take the first sample with a local maximum that surpasses a specified
threshold
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Compositing
Left: pseudo X-ray. Right: threshold-sensitive
compositing
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Compositing
Left: maximum intensity projection. Right:
closest vessel projection
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Compositing
Thin slab volume rendering
Consider only a small number of slices from
the full volume dataset
Allow a better representation of the spatial
coherence between individual slices
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Compositing
Slab volume rendering of about 10 cm of CT
thorax data
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Compositing
Left: single slice representation. Right: thin
slab maximum intensity projection
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