Lecture 5b

Volume Visualization

Outline Introduction

Common Volume Visualization Steps

Approaches to Volume Visualization

Marching Cubes Algorithm

Ray-casting Algorithm

GPU based Volume Rendering

Volume Visualization - Examples

MRI Face Mask (1994) CVH Visualization


Volumetric data are very common.

3D Volume Data (Voxels) 2D Image Plane (Pixels)

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

Other Special Volume Data

Visible Human Project

CT Human Head:Visible Human Project,US National Library of Medicine, Maryland, USA

Video Show

Volume Visualization Terms

Space/Grid/Lattice

Grid Traversal

Voxels

Cells

Geometric Primitives

Extent Planes

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

Different number can change color

Common Vol. Vis. Steps Data Acquistion

Slice Processing

Volume Reconstruction

Volume Enhancement

Data Classification or Thresholding

Mapping to Primitives

Shading & Transforming Primitives

Displaying Primitives

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.

Common Approaches to


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.

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

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

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

Results (MC vs ASC)

MC ASC, N = 1

Results (MC vs ASC)

MC ASC, N = 2

Results (MC vs ASC)

MC ASC, N = 4

Results (MC vs ASC)

MC ASC, N = 8

Marching Cubes

Marching Cubes

Ratio

Marching Cubes

Marching Cubes

Problem - Ambiguous cases can result in holes

Marching Cubes

Inconsistent Choice

Marching Cubes

Results in holes

Direct Volume Rendering

Ray-casting Algorithm

3D texture mapping for volume rendering

hardware dependent (in Part II)

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

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.

Less sampling

More sample

Can be less expensive

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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Lecture 5b

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Transcript of Lecture 5b