7.1Vis_04

Data VisualizationData Visualization

Lecture 73D Scalar Visualization

Part 2 : Volume Rendering-Introduction

7.2Vis_04

Volume RenderingVolume Rendering

This is a quite different mapping technique for visualization of 3D scalar data (compared with isosurfacing)

Aims to relate volume to a partially opaque gel material - colour and opacity at a point depending on the scalar value

By controlling the opacity, we can:– EITHER show surfaces through setting

opacity to 0 or 1– OR see both exterior and interior regions by

grading the opacity from 0 to 1

[Note: opacity = 1 - transparency]

7.3Vis_04

Example - Forest FireExample - Forest Fire

From Numerical Model of Forest Fire, NCAR, USA

7.4Vis_04

Medical ImagingMedical Imaging

Major application area is medical imaging

Different scanning techniques include:– CT (Computed Tomography)– MRI (Magnetic Resonance Imaging)

Three-dimensional images constructed from multiple 2D slices Scanners give average

value for a region - ratherthan value at a point

Interslice gap

Slice

Slice

7.5Vis_04

Examples of Brain ScansExamples of Brain Scans

ComputerizedTomography

MagneticResonanceImaging

SPECT

7.6Vis_04

Example - Medical ImagingExample - Medical Imaging

Renderedby VolPacksoftware

CT scan data256x256x226

7.7Vis_04

Data Classification –Assigning Opacity to CT

data

Data Classification –Assigning Opacity to CT

data

CT will identify fat, soft tissue and bone– Each will have known absorption

levels, say ffat, fsoft_tissue, fbone

CT value

Opacity

fsoft_tissue

0

1This transfer function will highlight soft tissue

7.8Vis_04

Data Classificatiion –Assigning Opacity to CT

Data

Data Classificatiion –Assigning Opacity to CT

Data

To show all types of tissue, we assign opacities to each type and linearly interpolate between them

CT value

Opacity

fsoft_tissue

0

1

ffat fbone

7.9Vis_04

Data Classification - Constructing the Gel - CT

Data

Data Classification - Constructing the Gel - CT

Data

CT number

opacity

0.0

1.0This is knownas opacitytransfer function

In practice, the boundaries between materialsare of key importance - hence a two-stage algorithmused:(i) Calculate as above(ii) Scale by gradient of function to highlight boundaries

* = |grad f | grad f = [df/dx,df/dy,df/dz]

(f)

? So what is opacity in homogeneous areas ?

7.10Vis_04

Data Classification - Constructing the Gel - CT

Data

Data Classification - Constructing the Gel - CT

Data

Colour classification is done similarly

white

red

yellow

Air Fat SoftTissue

Bone

CT number

Known as colour transfer function

7.11Vis_04

Data Classification - Constructing the Gel -

Temperature Data

Data Classification - Constructing the Gel -

Temperature Data

Volume rendering is also useful for other data - eg CFD temperature

Opacity transfer function: possibly increase with temperature

Colour transfer function:

blue(0,0,1)

red(1,0,0)

temperature

7.12Vis_04

Data Classification in IRIS Explorer

Data Classification in IRIS Explorer

The ColourMap tool in IRIS Explorer can be used to assign colour and transparency to data

7.13Vis_04

ExampleExample

Storm clouddata renderedby IRIS Explorer –Isosurface & volumerendering

7.14Vis_04

Ray Casting to Render the Volume

Ray Casting to Render the Volume

1 Assign colour and opacity to data values

– Classification process assigns gel colour to the original data

2 Apply light to volume– Lighting model will give the light reflected

to the viewer at any point in volume - if we know the normal

– Imagine an isosurface shell through each data point - surface normal is provided by gradient vector (see lecture 6)

– Thus we get colour reflected at each data point

7.15Vis_04

Casting the Rays and Taking Samples

Casting the Rays and Taking Samples

eyepoint

data volume

imageplane

ray

entrypoint

exit point

sample pointsone unit apart(colour andopacity byinterpolation)

3. For each pixel in image

a) cast ray from eye through pixel into volume, taking samples at regular unit intervals

b) measure colour reflected at each sample in direction of ray

c) composite colour from all samples along ray, taking into account the opacity of gel it passes through - en route to the eye

7.16Vis_04

Compositing the Samples along a Ray - One SampleCompositing the Samples along a Ray - One Sample

opaque background,emitting I0

eyepoint

I0I*

Intensity - I1

Opacity -

I* = I0 (1 - ) + I1

Imagine block of gel, one unit wide around sample point

7.17Vis_04

Compositing the Samples along a Ray - Two SamplesCompositing the Samples

along a Ray - Two Samples

opaque backgroundeye

point

I0I*

Intensity - I1

Opacity -

I* = I0 (1 - ) + I1

Intensity - I2

Opacity - 2

I**

I** = I* (1 - 2) + I2 2

= I0 (1 - 1)(1 - 2) + I11(1 - 2) + I22

7.18Vis_04

Compositing the Samples along a Ray

Compositing the Samples along a Ray

The process continues for all samples, yielding a final intensity, or colour, for the ray - and this is assigned to the pixel– try it for a third sample, then you

should be able to deduce a general formulaI = n

i=0 Iii nj=i+1(1 - j)

Note that if one compositing step is done for each ray in turn, then the next step, and so on, the image will be created in a sweep from back to front, showing all the data (even behind opaque parts)

7.19Vis_04

Front to Back CompositingFront to Back Compositing

Compositing can also work front-to-back:

Intensity In

Opacity n

eyepoint

I*I* = n In

Intensity In

Opacity n

eyepoint

I**I** = I* + (1 - *)n-1In-1

Intensity In-1

Opacity n-1

* = n - cumulative opacity

** = * + (1-*)n-1

7.20Vis_04

Front-to-Back Compositing - Early Termination

Front-to-Back Compositing - Early Termination

The advantage of front-to-back compositing is that we can stop the process if the accumulated opacity reaches 1.0 - no point in going further

Again, you should be able to deduce the general formula if you look at three samples – can you show that front-to-back and

back-to-front compositing give the same answer?

7.21Vis_04

Maximum Intensity Projection

Maximum Intensity Projection

When performance rather than accuracy is the goal, we can avoid compositing altogether and approximate I by maximum intensity along ray

MIP : Maximum Intensity Projection

Often used in angiography...

7.22Vis_04

Maximum Intensity Projection

Maximum Intensity Projection

Performance is major issue

– lack of shading in image drives need for real-time rotation

– fast identification of maximum becomes important

imageplane

volume

- analytical maximumin each cell along ray- maximum of samplesalong ray- skip cells below maximum

7.23Vis_04

Next LectureNext Lecture

Parkinson Room 108 Monday 10-11

Hope to have a second lecture on Monday 11.00 – 12.00 … room to be announced!